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dezakezu, non aurkitu nahi duzuna"><span>Txokoa</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Berezi:AzkenAldaketak" title="Wikiko azken aldaketen zerrenda. [r]" accesskey="r"><span>Aldaketa berriak</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Berezi:Ausazkoa" title="Ausazko orrialde bat kargatu [x]" accesskey="x"><span>Ausazko orria</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Laguntza:Sarrera" title="Aurkitzeko lekua."><span>Laguntza</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Azala" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="Entziklopedia askea" src="/static/images/mobile/copyright/wikipedia-tagline-eu.svg" width="120" height="13" style="width: 7.5em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Berezi:Bilatu" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Wikipedia(e)n bilatu [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Bilatu</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Wikipedia wikian bilatu" aria-label="Wikipedia wikian bilatu" autocapitalize="sentences" title="Wikipedia(e)n bilatu [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Berezi:Bilatu"> </div> <button class="cdx-button cdx-search-input__end-button">Bilatu</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Tresna pertsonalak"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Itxura"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Itxura" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Itxura</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_eu.wikipedia.org&uselang=eu" class=""><span>Dohaintza egin</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Berezi:KontuaSortu&returnto=Abiadura" title="Kontu bat sortu eta horrekin saioa hastea eskatu nahi genizuke; 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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Hasi saioa</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Izena eman gabeko erabiltzaileentzako orrialdeak <a href="/wiki/Laguntza:Sarrera" aria-label="Artikuluak aldatzeari buruz gehiago ikasi"><span>gehiago ikasi</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Berezi:NireEkarpenak" title="IP helbide honetatik egindako aldaketen zerrenda [y]" accesskey="y"><span>Ekarpenak</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Berezi:NireEztabaida" title="Zure IParen eztabaida [n]" accesskey="n"><span>Eztabaida</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Gunea"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Edukiak" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Edukiak</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ezkutatu</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">⇑ Gora</div> </a> </li> <li id="toc-Abiadura_kontzeptuaren_historia" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Abiadura_kontzeptuaren_historia"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Abiadura kontzeptuaren historia</span> </div> </a> <button aria-controls="toc-Abiadura_kontzeptuaren_historia-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Abiadura kontzeptuaren historia azpiatal</span> </button> <ul id="toc-Abiadura_kontzeptuaren_historia-sublist" class="vector-toc-list"> <li id="toc-Aristoteles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aristoteles"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Aristoteles</span> </div> </a> <ul id="toc-Aristoteles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Erdi_Aroko_aurrerapausoak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Erdi_Aroko_aurrerapausoak"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Erdi Aroko aurrerapausoak</span> </div> </a> <ul id="toc-Erdi_Aroko_aurrerapausoak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Galileo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Galileo"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Galileo</span> </div> </a> <ul id="toc-Galileo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Newton_eta_Leibnitz" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Newton_eta_Leibnitz"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Newton eta Leibnitz</span> </div> </a> <ul id="toc-Newton_eta_Leibnitz-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Partikula_puntualaren_higidura" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Partikula_puntualaren_higidura"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Partikula puntualaren higidura</span> </div> </a> <ul id="toc-Partikula_puntualaren_higidura-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Batez_besteko_abiadurak" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Batez_besteko_abiadurak"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Batez besteko abiadurak</span> </div> </a> <ul id="toc-Batez_besteko_abiadurak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aldiuneko_abiadurak" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Aldiuneko_abiadurak"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Aldiuneko abiadurak</span> </div> </a> <ul id="toc-Aldiuneko_abiadurak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Posizioaren_adierazpena_abiadura_eta_denboraren_funtzioan" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Posizioaren_adierazpena_abiadura_eta_denboraren_funtzioan"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Posizioaren adierazpena abiadura eta denboraren funtzioan</span> </div> </a> <ul id="toc-Posizioaren_adierazpena_abiadura_eta_denboraren_funtzioan-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Abiadura_kontzeptu_erlatiboa_da" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Abiadura_kontzeptu_erlatiboa_da"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Abiadura kontzeptu erlatiboa da</span> </div> </a> <button aria-controls="toc-Abiadura_kontzeptu_erlatiboa_da-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Abiadura kontzeptu erlatiboa da azpiatal</span> </button> <ul id="toc-Abiadura_kontzeptu_erlatiboa_da-sublist" class="vector-toc-list"> <li id="toc-Elkarrekiko_translazio-higidura_zuzen_eta_uniformea_duten_bi_erreferentzia-sistemaren_kasua" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elkarrekiko_translazio-higidura_zuzen_eta_uniformea_duten_bi_erreferentzia-sistemaren_kasua"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Elkarrekiko translazio-higidura zuzen eta uniformea duten bi erreferentzia-sistemaren kasua</span> </div> </a> <ul id="toc-Elkarrekiko_translazio-higidura_zuzen_eta_uniformea_duten_bi_erreferentzia-sistemaren_kasua-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Abiaduren_batuketa_mekanika_klasikoan" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Abiaduren_batuketa_mekanika_klasikoan"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Abiaduren batuketa mekanika klasikoan</span> </div> </a> <ul id="toc-Abiaduren_batuketa_mekanika_klasikoan-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Elkarrekiko_biraketa-higidura_duten_bi_erreferentzia-sistemaren_kasua" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elkarrekiko_biraketa-higidura_duten_bi_erreferentzia-sistemaren_kasua"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Elkarrekiko biraketa-higidura duten bi erreferentzia-sistemaren kasua</span> </div> </a> <ul id="toc-Elkarrekiko_biraketa-higidura_duten_bi_erreferentzia-sistemaren_kasua-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Abiadura_neurtzeko_unitateak" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Abiadura_neurtzeko_unitateak"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Abiadura neurtzeko unitateak</span> </div> </a> <button aria-controls="toc-Abiadura_neurtzeko_unitateak-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Abiadura neurtzeko unitateak azpiatal</span> </button> <ul id="toc-Abiadura_neurtzeko_unitateak-sublist" class="vector-toc-list"> <li id="toc-Nazioarteko_SI_unitate-sistema" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nazioarteko_SI_unitate-sistema"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Nazioarteko SI unitate-sistema</span> </div> </a> <ul id="toc-Nazioarteko_SI_unitate-sistema-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-CGS_sistema_(sistema_zegesimala)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#CGS_sistema_(sistema_zegesimala)"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>CGS sistema (sistema zegesimala)</span> </div> </a> <ul id="toc-CGS_sistema_(sistema_zegesimala)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Unitate-sistema_anglosaxoia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Unitate-sistema_anglosaxoia"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>Unitate-sistema anglosaxoia</span> </div> </a> <ul id="toc-Unitate-sistema_anglosaxoia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Itsas_nabigazioko_unitatea" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Itsas_nabigazioko_unitatea"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.4</span> <span>Itsas nabigazioko unitatea</span> </div> </a> <ul id="toc-Itsas_nabigazioko_unitatea-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aeronautikako_unitate_berezia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aeronautikako_unitate_berezia"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.5</span> <span>Aeronautikako unitate berezia</span> </div> </a> <ul id="toc-Aeronautikako_unitate_berezia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Argiaren_abiadura" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Argiaren_abiadura"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.6</span> <span>Argiaren abiadura</span> </div> </a> <ul id="toc-Argiaren_abiadura-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Abiadura_mekanika_erlatibistan" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Abiadura_mekanika_erlatibistan"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Abiadura mekanika erlatibistan</span> </div> </a> <ul id="toc-Abiadura_mekanika_erlatibistan-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Abiadura-modulua" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Abiadura-modulua"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Abiadura-modulua</span> </div> </a> <ul id="toc-Abiadura-modulua-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Abiaduraren_bidez_definituriko_bi_magnitude_fisiko" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Abiaduraren_bidez_definituriko_bi_magnitude_fisiko"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Abiaduraren bidez definituriko bi magnitude fisiko</span> </div> </a> <ul id="toc-Abiaduraren_bidez_definituriko_bi_magnitude_fisiko-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ariketak" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Ariketak"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span><figcaption></figcaption><p> Ariketak</p></span> </div> </a> <ul id="toc-Ariketak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Erreferentziak" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Erreferentziak"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Erreferentziak</span> </div> </a> <ul id="toc-Erreferentziak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ikus,_gainera" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Ikus,_gainera"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>Ikus, gainera</span> </div> </a> <ul id="toc-Ikus,_gainera-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kanpo_estekak" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Kanpo_estekak"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>Kanpo estekak</span> </div> </a> <ul id="toc-Kanpo_estekak-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Edukiak" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Eduki taularen ikusgarritasuna aldatu" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Eduki taularen ikusgarritasuna aldatu</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Abiadura</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Joan beste hizkuntza batean idatzitako artikulu batera. 130 hizkuntzatan eskuragarri." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-130" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">130 hizkuntza</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Snelheid" title="Snelheid – afrikaansa" lang="af" hreflang="af" data-title="Snelheid" data-language-autonym="Afrikaans" data-language-local-name="afrikaansa" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Geschwindigkeit" title="Geschwindigkeit – Suitzako alemana" lang="gsw" hreflang="gsw" data-title="Geschwindigkeit" data-language-autonym="Alemannisch" data-language-local-name="Suitzako alemana" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8D%8D%E1%8C%A5%E1%8A%90%E1%89%B5" title="ፍጥነት – amharera" lang="am" hreflang="am" data-title="ፍጥነት" data-language-autonym="አማርኛ" data-language-local-name="amharera" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Velocidat" title="Velocidat – aragoiera" lang="an" hreflang="an" data-title="Velocidat" data-language-autonym="Aragonés" data-language-local-name="aragoiera" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%B5%E0%A5%87%E0%A4%97" title="वेग – angikera" lang="anp" hreflang="anp" data-title="वेग" data-language-autonym="अंगिका" data-language-local-name="angikera" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B3%D8%B1%D8%B9%D8%A9_%D9%85%D8%AA%D8%AC%D9%87%D8%A9" title="سرعة متجهة – arabiera" lang="ar" hreflang="ar" data-title="سرعة متجهة" data-language-autonym="العربية" data-language-local-name="arabiera" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A7%87%E0%A6%97" title="বেগ – assamera" lang="as" hreflang="as" data-title="বেগ" data-language-autonym="অসমীয়া" data-language-local-name="assamera" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Velocid%C3%A1" title="Velocidá – asturiera" lang="ast" hreflang="ast" data-title="Velocidá" data-language-autonym="Asturianu" data-language-local-name="asturiera" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DB%8C%D8%A4%D9%86%D8%A6%DB%8C%D9%84%DB%8C_%D8%B3%D9%88%D8%B1%D8%B9%D8%AA" title="یؤنئیلی سورعت – South Azerbaijani" lang="azb" hreflang="azb" data-title="یؤنئیلی سورعت" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A2%D0%B8%D2%99%D0%BB%D0%B5%D0%BA" title="Тиҙлек – baxkirera" lang="ba" hreflang="ba" data-title="Тиҙлек" data-language-autonym="Башҡортса" data-language-local-name="baxkirera" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Gschwindigkeit" title="Gschwindigkeit – Bavarian" lang="bar" hreflang="bar" data-title="Gschwindigkeit" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Belosidad" title="Belosidad – Central Bikol" lang="bcl" hreflang="bcl" data-title="Belosidad" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D0%BA%D0%BE%D1%80%D0%B0%D1%81%D1%86%D1%8C" title="Скорасць – bielorrusiera" lang="be" hreflang="be" data-title="Скорасць" data-language-autonym="Беларуская" data-language-local-name="bielorrusiera" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A5%D1%83%D1%82%D0%BA%D0%B0%D1%81%D1%8C%D1%86%D1%8C" title="Хуткасьць – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Хуткасьць" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D0%BA%D0%BE%D1%80%D0%BE%D1%81%D1%82" title="Скорост – bulgariera" lang="bg" hreflang="bg" data-title="Скорост" data-language-autonym="Български" data-language-local-name="bulgariera" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%B5%E0%A5%87%E0%A4%97" title="वेग – Bhojpuri" lang="bh" hreflang="bh" data-title="वेग" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A6%A4%E0%A6%BF%E0%A6%AC%E0%A7%87%E0%A6%97" title="গতিবেগ – bengalera" lang="bn" hreflang="bn" data-title="গতিবেগ" data-language-autonym="বাংলা" data-language-local-name="bengalera" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Brzina" title="Brzina – bosniera" lang="bs" hreflang="bs" data-title="Brzina" data-language-autonym="Bosanski" data-language-local-name="bosniera" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%A5%D1%83%D1%80%D0%B4%D0%B0%D0%BD" title="Хурдан – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Хурдан" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Velocitat" title="Velocitat – katalana" lang="ca" hreflang="ca" data-title="Velocitat" data-language-autonym="Català" data-language-local-name="katalana" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/S%C3%B3k-d%C3%B4" title="Sók-dô – Mindong" lang="cdo" hreflang="cdo" data-title="Sók-dô" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%A1%D0%B8%D1%85%D0%B0%D0%BB%D0%BB%D0%B0" title="Сихалла – txetxenera" lang="ce" hreflang="ce" data-title="Сихалла" data-language-autonym="Нохчийн" data-language-local-name="txetxenera" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Tulin_(pisika)" title="Tulin (pisika) – cebuanoera" lang="ceb" hreflang="ceb" data-title="Tulin (pisika)" data-language-autonym="Cebuano" data-language-local-name="cebuanoera" class="interlanguage-link-target"><span>Cebuano</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AE%DB%8E%D8%B1%D8%A7%DB%8C%DB%8C_(%D9%81%DB%8C%D8%B2%DB%8C%DA%A9)" title="خێرایی (فیزیک) – erdialdeko kurduera" lang="ckb" hreflang="ckb" data-title="خێرایی (فیزیک)" data-language-autonym="کوردی" data-language-local-name="erdialdeko kurduera" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Rychlost" title="Rychlost – txekiera" lang="cs" hreflang="cs" data-title="Rychlost" data-language-autonym="Čeština" data-language-local-name="txekiera" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A5%C4%83%D0%B2%C4%83%D1%80%D1%82%D0%BB%C4%83%D1%85" title="Хăвăртлăх – txuvaxera" lang="cv" hreflang="cv" data-title="Хăвăртлăх" data-language-autonym="Чӑвашла" data-language-local-name="txuvaxera" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Cyflymder" title="Cyflymder – galesa" lang="cy" hreflang="cy" data-title="Cyflymder" data-language-autonym="Cymraeg" data-language-local-name="galesa" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hastighed" title="Hastighed – daniera" lang="da" hreflang="da" data-title="Hastighed" data-language-autonym="Dansk" data-language-local-name="daniera" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Geschwindigkeit" title="Geschwindigkeit – alemana" lang="de" hreflang="de" data-title="Geschwindigkeit" data-language-autonym="Deutsch" data-language-local-name="alemana" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CE%B1%CF%87%CF%8D%CF%84%CE%B7%CF%84%CE%B1" title="Ταχύτητα – greziera" lang="el" hreflang="el" data-title="Ταχύτητα" data-language-autonym="Ελληνικά" data-language-local-name="greziera" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Velocity" title="Velocity – ingelesa" lang="en" hreflang="en" data-title="Velocity" data-language-autonym="English" data-language-local-name="ingelesa" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Vektora_rapido" title="Vektora rapido – esperantoa" lang="eo" hreflang="eo" data-title="Vektora rapido" data-language-autonym="Esperanto" data-language-local-name="esperantoa" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Velocidad" title="Velocidad – gaztelania" lang="es" hreflang="es" data-title="Velocidad" data-language-autonym="Español" data-language-local-name="gaztelania" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kiirus" title="Kiirus – estoniera" lang="et" hreflang="et" data-title="Kiirus" data-language-autonym="Eesti" data-language-local-name="estoniera" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Velocid%C3%A1" title="Velocidá – Extremaduran" lang="ext" hreflang="ext" data-title="Velocidá" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B3%D8%B1%D8%B9%D8%AA_%D8%A8%D8%B1%D8%AF%D8%A7%D8%B1%DB%8C" title="سرعت برداری – persiera" lang="fa" hreflang="fa" data-title="سرعت برداری" data-language-autonym="فارسی" data-language-local-name="persiera" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Nopeus" title="Nopeus – finlandiera" lang="fi" hreflang="fi" data-title="Nopeus" data-language-autonym="Suomi" data-language-local-name="finlandiera" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Kib%C3%B5husvektor" title="Kibõhusvektor – Võro" lang="vro" hreflang="vro" data-title="Kibõhusvektor" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Vecteur_vitesse" title="Vecteur vitesse – frantsesa" lang="fr" hreflang="fr" data-title="Vecteur vitesse" data-language-autonym="Français" data-language-local-name="frantsesa" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Faard" title="Faard – iparraldeko frisiera" lang="frr" hreflang="frr" data-title="Faard" data-language-autonym="Nordfriisk" data-language-local-name="iparraldeko frisiera" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Faasje" title="Faasje – mendebaldeko frisiera" lang="fy" hreflang="fy" data-title="Faasje" data-language-autonym="Frysk" data-language-local-name="mendebaldeko frisiera" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Treoluas" title="Treoluas – irlandera" lang="ga" hreflang="ga" data-title="Treoluas" data-language-autonym="Gaeilge" data-language-local-name="irlandera" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Velocidade" title="Velocidade – galiziera" lang="gl" hreflang="gl" data-title="Velocidade" data-language-autonym="Galego" data-language-local-name="galiziera" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Bieauid-jeerit" title="Bieauid-jeerit – manxera" lang="gv" hreflang="gv" data-title="Bieauid-jeerit" data-language-autonym="Gaelg" data-language-local-name="manxera" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%94%D7%99%D7%A8%D7%95%D7%AA" title="מהירות – hebreera" lang="he" hreflang="he" data-title="מהירות" data-language-autonym="עברית" data-language-local-name="hebreera" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A5%87%E0%A4%97" title="वेग – hindia" lang="hi" hreflang="hi" data-title="वेग" data-language-autonym="हिन्दी" data-language-local-name="hindia" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Raftaar" title="Raftaar – Fiji Hindi" lang="hif" hreflang="hif" data-title="Raftaar" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Brzina" title="Brzina – kroaziera" lang="hr" hreflang="hr" data-title="Brzina" data-language-autonym="Hrvatski" data-language-local-name="kroaziera" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Velosite" title="Velosite – Haitiko kreolera" lang="ht" hreflang="ht" data-title="Velosite" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitiko kreolera" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Sebess%C3%A9g" title="Sebesség – hungariera" lang="hu" hreflang="hu" data-title="Sebesség" data-language-autonym="Magyar" data-language-local-name="hungariera" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D6%80%D5%A1%D5%A3%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Արագություն – armeniera" lang="hy" hreflang="hy" data-title="Արագություն" data-language-autonym="Հայերեն" data-language-local-name="armeniera" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Velocitate" title="Velocitate – interlingua" lang="ia" hreflang="ia" data-title="Velocitate" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kecepatan" title="Kecepatan – indonesiera" lang="id" hreflang="id" data-title="Kecepatan" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiera" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ie mw-list-item"><a href="https://ie.wikipedia.org/wiki/Velocit%C3%A1" title="Velocitá – interlingue" lang="ie" hreflang="ie" data-title="Velocitá" data-language-autonym="Interlingue" data-language-local-name="interlingue" class="interlanguage-link-target"><span>Interlingue</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Hra%C3%B0i" title="Hraði – islandiera" lang="is" hreflang="is" data-title="Hraði" data-language-autonym="Íslenska" data-language-local-name="islandiera" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Velocit%C3%A0" title="Velocità – italiera" lang="it" hreflang="it" data-title="Velocità" data-language-autonym="Italiano" data-language-local-name="italiera" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%80%9F%E5%BA%A6" title="速度 – japoniera" lang="ja" hreflang="ja" data-title="速度" data-language-autonym="日本語" data-language-local-name="japoniera" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Kacepetan" title="Kacepetan – javera" lang="jv" hreflang="jv" data-title="Kacepetan" data-language-autonym="Jawa" data-language-local-name="javera" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%98%E1%83%A9%E1%83%A5%E1%83%90%E1%83%A0%E1%83%94" title="სიჩქარე – georgiera" lang="ka" hreflang="ka" data-title="სიჩქარე" data-language-autonym="ქართული" data-language-local-name="georgiera" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Arured_amaway" title="Arured amaway – kabiliera" lang="kab" hreflang="kab" data-title="Arured amaway" data-language-autonym="Taqbaylit" data-language-local-name="kabiliera" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%96%D1%8B%D0%BB%D0%B4%D0%B0%D0%BC%D0%B4%D1%8B%D2%9B" title="Жылдамдық – kazakhera" lang="kk" hreflang="kk" data-title="Жылдамдық" data-language-autonym="Қазақша" data-language-local-name="kazakhera" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%9B%E1%9F%92%E1%9E%94%E1%9E%BF%E1%9E%93" title="ល្បឿន – khemerera" lang="km" hreflang="km" data-title="ល្បឿន" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khemerera" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B5%E0%B3%87%E0%B2%97" title="ವೇಗ – kannada" lang="kn" hreflang="kn" data-title="ವೇಗ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%86%8D%EB%8F%84" title="속도 – koreera" lang="ko" hreflang="ko" data-title="속도" data-language-autonym="한국어" data-language-local-name="koreera" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/%D9%88%DB%8C%D9%96%DA%AF" title="ویٖگ – kaxmirera" lang="ks" hreflang="ks" data-title="ویٖگ" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="kaxmirera" class="interlanguage-link-target"><span>कॉशुर / کٲشُر</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Uskitter" title="Uskitter – kornubiera" lang="kw" hreflang="kw" data-title="Uskitter" data-language-autonym="Kernowek" data-language-local-name="kornubiera" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Velocitas" title="Velocitas – latina" lang="la" hreflang="la" data-title="Velocitas" data-language-autonym="Latina" data-language-local-name="latina" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Rapidia_vetoral" title="Rapidia vetoral – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Rapidia vetoral" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Snelheid" title="Snelheid – limburgera" lang="li" hreflang="li" data-title="Snelheid" data-language-autonym="Limburgs" data-language-local-name="limburgera" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Velocitaa" title="Velocitaa – Lombard" lang="lmo" hreflang="lmo" data-title="Velocitaa" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Vektorinis_greitis" title="Vektorinis greitis – lituaniera" lang="lt" hreflang="lt" data-title="Vektorinis greitis" data-language-autonym="Lietuvių" data-language-local-name="lituaniera" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C4%80trums" title="Ātrums – letoniera" lang="lv" hreflang="lv" data-title="Ātrums" data-language-autonym="Latviešu" data-language-local-name="letoniera" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Hafainganam-pandeha" title="Hafainganam-pandeha – malgaxea" lang="mg" hreflang="mg" data-title="Hafainganam-pandeha" data-language-autonym="Malagasy" data-language-local-name="malgaxea" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Laju" title="Laju – minangkabauera" lang="min" hreflang="min" data-title="Laju" data-language-autonym="Minangkabau" data-language-local-name="minangkabauera" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D1%80%D0%B7%D0%B8%D0%BD%D0%B0" title="Брзина – mazedoniera" lang="mk" hreflang="mk" data-title="Брзина" data-language-autonym="Македонски" data-language-local-name="mazedoniera" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%B5%E0%B5%87%E0%B4%97%E0%B4%82" title="പ്രവേഗം – malabarera" lang="ml" hreflang="ml" data-title="പ്രവേഗം" data-language-autonym="മലയാളം" data-language-local-name="malabarera" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D1%83%D1%80%D0%B4" title="Хурд – mongoliera" lang="mn" hreflang="mn" data-title="Хурд" data-language-autonym="Монгол" data-language-local-name="mongoliera" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A5%87%E0%A4%97" title="वेग – marathera" lang="mr" hreflang="mr" data-title="वेग" data-language-autonym="मराठी" data-language-local-name="marathera" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Halaju" title="Halaju – malaysiera" lang="ms" hreflang="ms" data-title="Halaju" data-language-autonym="Bahasa Melayu" data-language-local-name="malaysiera" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%9C%E1%80%BB%E1%80%84%E1%80%BA" title="အလျင် – birmaniera" lang="my" hreflang="my" data-title="အလျင်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmaniera" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%B2%D0%BA%D1%81" title="Молевкс – erziera" lang="myv" hreflang="myv" data-title="Молевкс" data-language-autonym="Эрзянь" data-language-local-name="erziera" class="interlanguage-link-target"><span>Эрзянь</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Snelligkeid" title="Snelligkeid – behe-alemana" lang="nds" hreflang="nds" data-title="Snelligkeid" data-language-autonym="Plattdüütsch" data-language-local-name="behe-alemana" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%97%E0%A4%A4%E0%A4%BF" title="गति – nepalera" lang="ne" hreflang="ne" data-title="गति" data-language-autonym="नेपाली" data-language-local-name="nepalera" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Snelheid" title="Snelheid – nederlandera" lang="nl" hreflang="nl" data-title="Snelheid" data-language-autonym="Nederlands" data-language-local-name="nederlandera" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Hastigheit" title="Hastigheit – nynorsk (norvegiera)" lang="nn" hreflang="nn" data-title="Hastigheit" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorsk (norvegiera)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Hastighet" title="Hastighet – bokmål (norvegiera)" lang="nb" hreflang="nb" data-title="Hastighet" data-language-autonym="Norsk bokmål" data-language-local-name="bokmål (norvegiera)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Velocitat" title="Velocitat – okzitaniera" lang="oc" hreflang="oc" data-title="Velocitat" data-language-autonym="Occitan" data-language-local-name="okzitaniera" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Ariitii" title="Ariitii – oromoera" lang="om" hreflang="om" data-title="Ariitii" data-language-autonym="Oromoo" data-language-local-name="oromoera" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B5%E0%A9%87%E0%A8%97" title="ਵੇਗ – punjabera" lang="pa" hreflang="pa" data-title="ਵੇਗ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabera" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pr%C4%99dko%C5%9B%C4%87" title="Prędkość – poloniera" lang="pl" hreflang="pl" data-title="Prędkość" data-language-autonym="Polski" data-language-local-name="poloniera" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Andi" title="Andi – Piedmontese" lang="pms" hreflang="pms" data-title="Andi" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%88%D9%84%D8%A7%D8%B3%D9%B9%DB%8C" title="ولاسٹی – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ولاسٹی" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Velocidade" title="Velocidade – portugesa" lang="pt" hreflang="pt" data-title="Velocidade" data-language-autonym="Português" data-language-local-name="portugesa" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Utqa_kay" title="Utqa kay – kitxua" lang="qu" hreflang="qu" data-title="Utqa kay" data-language-autonym="Runa Simi" data-language-local-name="kitxua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Vitez%C4%83" title="Viteză – errumaniera" lang="ro" hreflang="ro" data-title="Viteză" data-language-autonym="Română" data-language-local-name="errumaniera" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%BA%D0%BE%D1%80%D0%BE%D1%81%D1%82%D1%8C" title="Скорость – errusiera" lang="ru" hreflang="ru" data-title="Скорость" data-language-autonym="Русский" data-language-local-name="errusiera" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A8%D0%B2%D1%8B%D0%B4%D0%BA%D0%BE%D1%81%D1%82%D1%8C" title="Швыдкость – Rusyn" lang="rue" hreflang="rue" data-title="Швыдкость" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sc badge-Q17437796 badge-featuredarticle mw-list-item" title="artikulu nabarmenduak"><a href="https://sc.wikipedia.org/wiki/Velotzidade" title="Velotzidade – sardiniera" lang="sc" hreflang="sc" data-title="Velotzidade" data-language-autonym="Sardu" data-language-local-name="sardiniera" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D9%88%D9%8A%D9%84%D8%A7%D8%B3%D9%BD%D9%8A" title="ويلاسٽي – sindhia" lang="sd" hreflang="sd" data-title="ويلاسٽي" data-language-autonym="سنڌي" data-language-local-name="sindhia" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Brzina" title="Brzina – serbokroaziera" lang="sh" hreflang="sh" data-title="Brzina" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroaziera" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%80%E0%B7%9A%E0%B6%9C%E0%B6%BA" title="ප්‍රවේගය – sinhala" lang="si" hreflang="si" data-title="ප්‍රවේගය" data-language-autonym="සිංහල" data-language-local-name="sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Velocity" title="Velocity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Velocity" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/R%C3%BDchlos%C5%A5_(fyzik%C3%A1lna_veli%C4%8Dina)" title="Rýchlosť (fyzikálna veličina) – eslovakiera" lang="sk" hreflang="sk" data-title="Rýchlosť (fyzikálna veličina)" data-language-autonym="Slovenčina" data-language-local-name="eslovakiera" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Hitrost" title="Hitrost – esloveniera" lang="sl" hreflang="sl" data-title="Hitrost" data-language-autonym="Slovenščina" data-language-local-name="esloveniera" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-smn mw-list-item"><a href="https://smn.wikipedia.org/wiki/Li%C3%A4htu" title="Liähtu – Inariko samiera" lang="smn" hreflang="smn" data-title="Liähtu" data-language-autonym="Anarâškielâ" data-language-local-name="Inariko samiera" class="interlanguage-link-target"><span>Anarâškielâ</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Muchacha" title="Muchacha – shonera" lang="sn" hreflang="sn" data-title="Muchacha" data-language-autonym="ChiShona" data-language-local-name="shonera" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Shpejt%C3%ABsia_(fizik%C3%AB)" title="Shpejtësia (fizikë) – albaniera" lang="sq" hreflang="sq" data-title="Shpejtësia (fizikë)" data-language-autonym="Shqip" data-language-local-name="albaniera" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D1%80%D0%B7%D0%B8%D0%BD%D0%B0" title="Брзина – serbiera" lang="sr" hreflang="sr" data-title="Брзина" data-language-autonym="Српски / srpski" data-language-local-name="serbiera" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Hastighet" title="Hastighet – suediera" lang="sv" hreflang="sv" data-title="Hastighet" data-language-autonym="Svenska" data-language-local-name="suediera" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Kasimwelekeo" title="Kasimwelekeo – swahilia" lang="sw" hreflang="sw" data-title="Kasimwelekeo" data-language-autonym="Kiswahili" data-language-local-name="swahilia" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AE%BF%E0%AE%9A%E0%AF%88%E0%AE%B5%E0%AF%87%E0%AE%95%E0%AE%AE%E0%AF%8D" title="திசைவேகம் – tamilera" lang="ta" hreflang="ta" data-title="திசைவேகம்" data-language-autonym="தமிழ்" data-language-local-name="tamilera" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B5%E0%B1%87%E0%B0%97%E0%B0%82" title="వేగం – telugua" lang="te" hreflang="te" data-title="వేగం" data-language-autonym="తెలుగు" data-language-local-name="telugua" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A1%D1%83%D1%80%D1%8A%D0%B0%D1%82" title="Суръат – tajikera" lang="tg" hreflang="tg" data-title="Суръат" data-language-autonym="Тоҷикӣ" data-language-local-name="tajikera" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B9%80%E0%B8%A3%E0%B9%87%E0%B8%A7" title="ความเร็ว – thailandiera" lang="th" hreflang="th" data-title="ความเร็ว" data-language-autonym="ไทย" data-language-local-name="thailandiera" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Tulin" title="Tulin – tagaloa" lang="tl" hreflang="tl" data-title="Tulin" data-language-autonym="Tagalog" data-language-local-name="tagaloa" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/H%C4%B1z" title="Hız – turkiera" lang="tr" hreflang="tr" data-title="Hız" data-language-autonym="Türkçe" data-language-local-name="turkiera" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A2%D0%B8%D0%B7%D0%BB%D0%B5%D0%BA" title="Тизлек – tatarera" lang="tt" hreflang="tt" data-title="Тизлек" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarera" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A8%D0%B2%D0%B8%D0%B4%D0%BA%D1%96%D1%81%D1%82%D1%8C" title="Швидкість – ukrainera" lang="uk" hreflang="uk" data-title="Швидкість" data-language-autonym="Українська" data-language-local-name="ukrainera" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%88%D9%84%D8%A7%D8%B3%D9%B9%DB%8C" title="ولاسٹی – urdua" lang="ur" hreflang="ur" data-title="ولاسٹی" data-language-autonym="اردو" data-language-local-name="urdua" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Tezlik" title="Tezlik – uzbekera" lang="uz" hreflang="uz" data-title="Tezlik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekera" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Piguz" title="Piguz – Veps" lang="vep" hreflang="vep" data-title="Piguz" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/V%E1%BA%ADn_t%E1%BB%91c" title="Vận tốc – vietnamera" lang="vi" hreflang="vi" data-title="Vận tốc" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamera" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Belosidad" title="Belosidad – warayera" lang="war" hreflang="war" data-title="Belosidad" data-language-autonym="Winaray" data-language-local-name="warayera" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%80%9F%E5%BA%A6" title="速度 – wu txinera" lang="wuu" hreflang="wuu" data-title="速度" data-language-autonym="吴语" data-language-local-name="wu txinera" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-velocity" title="I-velocity – xhosera" lang="xh" hreflang="xh" data-title="I-velocity" data-language-autonym="IsiXhosa" data-language-local-name="xhosera" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%92%D7%99%D7%9B%D7%A7%D7%99%D7%99%D7%98" title="גיכקייט – yiddisha" lang="yi" hreflang="yi" data-title="גיכקייט" data-language-autonym="ייִדיש" data-language-local-name="yiddisha" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%80%9F%E5%BA%A6" title="速度 – txinera" lang="zh" hreflang="zh" data-title="速度" data-language-autonym="中文" data-language-local-name="txinera" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E9%80%9F%E5%BA%A6" title="速度 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="速度" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Sok-t%C5%8D%CD%98" title="Sok-tō͘ – Minnan" lang="nan" hreflang="nan" data-title="Sok-tō͘" data-language-autonym="閩南語 / 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class="mw-empty-elt"> </p> <table class="infobox" style="width:22em"><tbody><tr><th colspan="2" style="text-align:center;font-size:125%;font-weight:bold">Abiadura</th></tr><tr><td colspan="2" class="infobox-full-data infobox-data" style="text-align:center"><span typeof="mw:File"><a href="/wiki/Fitxategi:Vector_snelheid-Plain.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Vector_snelheid-Plain.svg/285px-Vector_snelheid-Plain.svg.png" decoding="async" width="285" height="276" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Vector_snelheid-Plain.svg/428px-Vector_snelheid-Plain.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Vector_snelheid-Plain.svg/570px-Vector_snelheid-Plain.svg.png 2x" data-file-width="234" data-file-height="227" /></a></span></td></tr><tr><th scope="row" class="infobox-label" style="text-align:left">Formula</th><td class="infobox-data"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}={\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}={\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a3c633dc08536080125fe28c5df1e025cc55a4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.775ex; height:5.509ex;" alt="{\displaystyle {\boldsymbol {v}}={\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}}"></span></td></tr><tr><th scope="row" class="infobox-label" style="text-align:left">Formulako ikurra</th><td class="infobox-data"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b2c2d3aac4213f3996d828c6aa8f4eb464a05cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.318ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {v}}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6a5e169814762d75ef0dd3a3d0bc99b4a5a06e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {r}}}"></span> eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span></td></tr><tr><th scope="row" class="infobox-label" style="text-align:left">Ohiko ikurra</th><td class="infobox-data"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b2c2d3aac4213f3996d828c6aa8f4eb464a05cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.318ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {v}}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85820588abd7333ef4d0c56539cb31c20e730753" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.175ex; height:2.343ex;" alt="{\displaystyle {\vec {v}}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {u}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">u</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {u}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d60e374e33b2c1d75888c0e8759f9e770e718f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {u}}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {w}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">w</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {w}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a36660d03c65332b9ce8b29d7869818762cb970" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.931ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {w}}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {w}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>w</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {w}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b6c48cdaecf8d81481ea21b1d0c046bf34b68ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:2.343ex;" alt="{\displaystyle {\vec {w}}}"></span> eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {u}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {u}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89c41e9cf70c5e5b56e2128a136985a75f90ba43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:2.343ex;" alt="{\displaystyle {\vec {u}}}"></span></td></tr><tr><th scope="row" class="infobox-label" style="text-align:left">Neurtzeko unitatea</th><td class="infobox-data"><a href="/wiki/Metro_segundoko" title="Metro segundoko">metro segundoko</a> eta <a href="/wiki/Kilometro_orduko" title="Kilometro orduko">kilometro orduko</a></td></tr><tr><th scope="row" class="infobox-label" style="text-align:left">Dimentsioa</th><td class="infobox-data"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {L}}{\mathsf {T}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">T</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {L}}{\mathsf {T}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3185f766c8cc4ee9f9779720b4d9f66da6a6541a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.176ex; height:2.676ex;" alt="{\displaystyle {\mathsf {L}}{\mathsf {T}}^{-1}}"></span></td></tr><tr><th scope="row" class="infobox-label" style="text-align:left">Aurkitzailea edo asmatzailea</th><td class="infobox-data"><a href="/wiki/Pierre_Varignon" title="Pierre Varignon">Pierre Varignon</a></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r9236167">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output 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data-mw-deduplicate="TemplateStyles:r9249993">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:#f8f9fa;border:1px solid #aaa;padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output 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.sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:720px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Artikulu sorta honen partea:</td></tr><tr><th class="sidebar-title-with-pretitle" style="padding-left:0.9em;padding-right:0.9em;"><a href="/wiki/Mekanika_klasiko" title="Mekanika klasiko">Mekanika klasikoa</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {F}}=m{\boldsymbol {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">F</mi> </mrow> <mo>=</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">a</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {F}}=m{\boldsymbol {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0e889207254cfbfab613b8beba214f5e4d2430d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.49ex; height:2.176ex;" alt="{\displaystyle {\boldsymbol {F}}=m{\boldsymbol {a}}}"></span><div class="sidebar-caption" style="font-size:90%;padding:0.6em 0;font-style:italic;"><a href="/wiki/Newtonen_legeak" title="Newtonen legeak">Newtonen legeak</a></div></td></tr><tr><th class="sidebar-heading" style="background:#ddf; display:block;margin-bottom:1.0em;"> <div class="hlist"> <ul><li><a href="/wiki/Mekanika_klasikoaren_historia" title="Mekanika klasikoaren historia">Historia</a></li> <li><a href="/wiki/Mekanika_Klasikoaren_kronologia" class="mw-redirect" title="Mekanika Klasikoaren kronologia">Kronologia</a></li></ul> </div></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Adarrak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Mekanika_aplikatua" title="Mekanika aplikatua">Aplikatua</a></li> <li><a href="/wiki/Dinamika" title="Dinamika">Dinamika</a></li> <li><a href="/wiki/Estatika" title="Estatika">Estatika</a></li> <li><a href="/wiki/Zeruko_mekanika" title="Zeruko mekanika">Zerukoa</a></li> <li><a href="/wiki/Zinematika" title="Zinematika">Zinematika</a></li> <li><a href="/wiki/Medio_jarraituen_mekanika" title="Medio jarraituen mekanika">Medio jarraituak</a></li> <li><a href="/w/index.php?title=Zinetika_(fisika)&action=edit&redlink=1" class="new" title="Zinetika (fisika) (sortu gabe)">Zinetika</a></li> <li><a href="/w/index.php?title=Fisika_estatistiko&action=edit&redlink=1" class="new" title="Fisika estatistiko (sortu gabe)">Estatistikoa</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Oinarriak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a class="mw-selflink selflink">Abiadura</a></li> <li><a href="/wiki/Azelerazio" title="Azelerazio">Azelerazioa</a></li> <li><a href="/wiki/Abiadura-modulu" class="mw-redirect" title="Abiadura-modulu">Abiadura-modulua</a></li> <li><a href="/wiki/Bulkada_(fisika)" title="Bulkada (fisika)">Bulkada</a></li> <li><a href="/w/index.php?title=D%27Alembert-en_printzipioa&action=edit&redlink=1" class="new" title="D'Alembert-en printzipioa (sortu gabe)">D'Alembert-en printzipioa</a></li> <li><a href="/wiki/Denbora" title="Denbora">Denbora</a></li> <li><a href="/wiki/Energia" title="Energia">Energia</a> <ul><li><a href="/wiki/Energia_potentzial" title="Energia potentzial">potentziala</a></li> <li><a href="/wiki/Energia_zinetiko" title="Energia zinetiko">zinetikoa</a></li></ul></li> <li><a href="/wiki/Erreferentzia-sistema" title="Erreferentzia-sistema">Erreferentzia-sistema</a></li> <li><a href="/wiki/Erreferentzia-sistema_inertzial" title="Erreferentzia-sistema inertzial">Erreferentzia-sistema inertziala</a></li> <li><a href="/wiki/Erreferentzia-sistema_ez-inertzial" title="Erreferentzia-sistema ez-inertzial">Erreferentzia-sistema ez-inertziala</a></li> <li><a href="/wiki/Espazio" title="Espazio">Espazioa</a></li> <li><a href="/wiki/Indar-pare" title="Indar-pare">Indar-parea</a></li> <li><a href="/wiki/Indar" title="Indar">Indarra</a></li> <li><span style="white-space:nowrap"><a href="/wiki/Inertzia" title="Inertzia">Inertzia</a> / <a href="/wiki/Inertzia-momentu" title="Inertzia-momentu">Inertzia-momentua</a></span></li> <li><a href="/wiki/Lan_(fisika)" title="Lan (fisika)">Lana</a></li> <li><a href="/w/index.php?title=Lan_birtual&action=edit&redlink=1" class="new" title="Lan birtual (sortu gabe)">Lan birtuala</a></li> <li><a href="/wiki/Masa" title="Masa">Masa</a></li> <li><a href="/w/index.php?title=Momentu_(fisika)&action=edit&redlink=1" class="new" title="Momentu (fisika) (sortu gabe)">Momentua</a></li> <li><a href="/wiki/Momentu_angeluar" title="Momentu angeluar">Momentu angeluarra</a></li> <li><a href="/wiki/Momentu_lineal" title="Momentu lineal">Momentu lineala</a></li> <li><a href="/wiki/Potentzia" title="Potentzia">Potentzia</a></li> <li><a href="/wiki/Torke" class="mw-redirect" title="Torke">Torkea</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Zientzialariak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a></li> <li><a href="/w/index.php?title=Jeremiah_Horrocks&action=edit&redlink=1" class="new" title="Jeremiah Horrocks (sortu gabe)">Horrocks</a></li> <li><a href="/wiki/Edmond_Halley" title="Edmond Halley">Halley</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/wiki/Jean_le_Rond_d%27Alembert" title="Jean le Rond d'Alembert">d'Alembert</a></li> <li><a href="/wiki/Alexis_Clairaut" title="Alexis Clairaut">Clairaut</a></li> <li><a href="/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange">Lagrange</a></li> <li><a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Laplace</a></li> <li><a href="/wiki/William_Rowan_Hamilton" title="William Rowan Hamilton">Hamilton</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a></li> <li><a href="/wiki/Johann_Bernoulli" title="Johann Bernoulli">Johann Bernoulli</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Muinekoak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Bibrazio" title="Bibrazio">Bibrazioa</a></li> <li><a href="/wiki/Desplazamendu_(fisika)" title="Desplazamendu (fisika)">Desplazamendua</a></li> <li><a href="/wiki/Erreferentzia-sistema" title="Erreferentzia-sistema">Erreferentzia-sistema</a></li> <li><a href="/wiki/Erreferentzia-sistema_inertzial" title="Erreferentzia-sistema inertzial">Erreferentzia-sistema inertziala</a></li> <li><a href="/wiki/Erreferentzia-sistema_ez-inertzial" title="Erreferentzia-sistema ez-inertzial">Erreferentzia-sistema ez-inertziala</a></li> <li><a href="/wiki/Gorputz_zurrun" title="Gorputz zurrun">Gorputz zurruna</a> <ul><li><a href="/w/index.php?title=Eulerren_ekuazio&action=edit&redlink=1" class="new" title="Eulerren ekuazio (sortu gabe)">Eulerren ekuazioa</a></li> <li><a href="/w/index.php?title=Solido_zurrunaren_mekanika&action=edit&redlink=1" class="new" title="Solido zurrunaren mekanika (sortu gabe)">Solido zurrunaren mekanika</a></li></ul></li> <li><a href="/wiki/Grabitazio_unibertsalaren_legea" title="Grabitazio unibertsalaren legea"><span style="white-space: normal;">Grabitazio unibertsalaren legea</span></a></li> <li><a href="/wiki/Higidura_zuzen" title="Higidura zuzen">Higidura zuzena</a></li> <li><a href="/wiki/Higidura" title="Higidura">Higidura</a></li> <li><a href="/wiki/Marruskadura-indar" title="Marruskadura-indar">Marruskadura-indarra</a></li> <li><a href="/wiki/Newtonen_legeak" title="Newtonen legeak">Newtonen legeak</a></li> <li><a href="/wiki/Osziladore_harmoniko" title="Osziladore harmoniko">Osziladore harmonikoa</a></li> <li><a href="/w/index.php?title=Moteltze&action=edit&redlink=1" class="new" title="Moteltze (sortu gabe)">Moteltze</a>(<a href="/w/index.php?title=Moteltze_ratio&action=edit&redlink=1" class="new" title="Moteltze ratio (sortu gabe)">Moteltze ratio</a>)</li> <li><a href="/w/index.php?title=Higiduraren_ekuazio&action=edit&redlink=1" class="new" title="Higiduraren ekuazio (sortu gabe)">Higiduraren ekuazioa</a></li> <li><a href="/w/index.php?title=Eulerren_higiduraren_legeak&action=edit&redlink=1" class="new" title="Eulerren higiduraren legeak (sortu gabe)"><span style="white-space: normal;">Eulerren higiduraren legeak</span></a></li> <li><a href="/w/index.php?title=Itxurazko_indar&action=edit&redlink=1" class="new" title="Itxurazko indar (sortu gabe)">Itxurazko indarra</a></li> <li><a href="/w/index.php?title=Partikula_planarraren_higadura-mekanika&action=edit&redlink=1" class="new" title="Partikula planarraren higadura-mekanika (sortu gabe)">Partikula planarraren higadura-mekanika</a></li> <li><a href="/w/index.php?title=Abiadura_erlatibo&action=edit&redlink=1" class="new" title="Abiadura erlatibo (sortu gabe)">Abiadura erlatiboa</a></li> <li><a href="/wiki/Higidura_harmoniko_sinple" title="Higidura harmoniko sinple">Higidura harmoniko sinple</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;"><a href="/wiki/Biraketa-ardatz" title="Biraketa-ardatz">Biraketa</a></div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Abiadura_angeluar" title="Abiadura angeluar">Abiadura angeluarra</a></li> <li><a class="mw-selflink selflink">Abiadura tangentziala</a></li> <li><a href="/w/index.php?title=Azelerazio_angeluar&action=edit&redlink=1" class="new" title="Azelerazio angeluar (sortu gabe)">Azelerazio angeluarra</a></li> <li><a href="/w/index.php?title=Biraketa-abiadura&action=edit&redlink=1" class="new" title="Biraketa-abiadura (sortu gabe)">Biraketa-abiadura</a></li> <li><a href="/wiki/Coriolis_efektua" title="Coriolis efektua">Coriolis efektua</a></li> <li><a href="/w/index.php?title=Desplazamendu_angeluar&action=edit&redlink=1" class="new" title="Desplazamendu angeluar (sortu gabe)">Desplazamendua</a></li> <li><a href="/wiki/Erreferentzia-sistema" title="Erreferentzia-sistema">Erreferentzia-sistema</a></li> <li><a href="/wiki/Higidura_zirkular" title="Higidura zirkular">Higidura zirkular</a></li> <li><a href="/wiki/Indar_zentripetu" title="Indar zentripetu">Indar zentripetu</a></li> <li><a href="/wiki/Indar_zentrifugo" title="Indar zentrifugo">Indar zentrifugo</a></li> <li><a href="/w/index.php?title=Maiztasun_angeluar&action=edit&redlink=1" class="new" title="Maiztasun angeluar (sortu gabe)">Maiztasuna</a></li> <li><a href="/wiki/Pendulu_(matematika)" class="mw-redirect" title="Pendulu (matematika)">Pendulua</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Formulazioak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Newtonen_legeak" title="Newtonen legeak">Newtonen legeak</a></li> <li><a href="/wiki/Mekanika_analitiko" title="Mekanika analitiko">Mekanika analitikoa</a></li> <li><a href="/wiki/Lagrangeren_mekanika" title="Lagrangeren mekanika">Mekanika Lagrangiar</a></li> <li><a href="/w/index.php?title=Mekanika_Hamiltoniar&action=edit&redlink=1" class="new" title="Mekanika Hamiltoniar (sortu gabe)">Mekanika Hamiltoniar</a></li> <li><a href="/w/index.php?title=Mekanika_Routhiar&action=edit&redlink=1" class="new" title="Mekanika Routhiar (sortu gabe)">Mekanika Routhiar</a></li> <li><a href="/w/index.php?title=Hamilton%E2%80%93Jacobi_ekuazioa&action=edit&redlink=1" class="new" title="Hamilton–Jacobi ekuazioa (sortu gabe)">Hamilton–Jacobi ekuazioa</a></li> <li><a href="/w/index.php?title=Appellen_higidura-ekuazioa&action=edit&redlink=1" class="new" title="Appellen higidura-ekuazioa (sortu gabe)">Appellen higidura-ekuazioa</a></li> <li><a href="/w/index.php?title=Koopman%E2%80%93von_Neumann_mekanika_klasiko&action=edit&redlink=1" class="new" title="Koopman–von Neumann mekanika klasiko (sortu gabe)">Koopman–von Neumann mekanika</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;text-align:center;">Kategoriak</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"><div class="CategoryTreeTag" data-ct-options="{"mode":0,"hideprefix":20,"showcount":false,"namespaces":false,"notranslations":false}"><div class="CategoryTreeSection"><div class="CategoryTreeItem"><span class="CategoryTreeBullet"><a class="CategoryTreeToggle" data-ct-title="Mekanika_klasikoa" aria-expanded="false"></a> </span> <bdi dir="ltr"><a href="/wiki/Kategoria:Mekanika_klasikoa" title="Kategoria:Mekanika klasikoa">Mekanika klasikoa</a></bdi></div><div class="CategoryTreeChildren" style="display:none"></div></div></div> </div></div></div></td> </tr><tr><td class="sidebar-navbar" style="padding-top:0.15em;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9236167"><style data-mw-deduplicate="TemplateStyles:r9235565">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-ikusi"><a href="/wiki/Txantiloi:Mekanika_klasikoa" title="Txantiloi:Mekanika klasikoa"><abbr title="Txantiloi hau ikusi">i</abbr></a></li><li class="nv-eztabaida"><a href="/w/index.php?title=Txantiloi_eztabaida:Mekanika_klasikoa&action=edit&redlink=1" class="new" title="Txantiloi eztabaida:Mekanika klasikoa (sortu gabe)"><abbr title="Txantiloi hau eztabaidatu">e</abbr></a></li><li class="nv-aldatu"><a class="external text" href="https://eu.wikipedia.org/w/index.php?title=Txantiloi:Mekanika_klasikoa&action=edit"><abbr title="Txantiloi hau aldatu">a</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Abiadura</b> <a href="/wiki/Magnitude_fisiko" title="Magnitude fisiko">magnitude fisikoak</a> puntu material batek norabide jakin batean denbora-unitateko duen <a href="/wiki/Desplazamendu_(fisika)" title="Desplazamendu (fisika)">desplazamendua</a> adierazten du. Magnitude hau <a href="/wiki/Bektore_(argipena)" class="mw-disambig" title="Bektore (argipena)">bektorea</a> da, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b2c2d3aac4213f3996d828c6aa8f4eb464a05cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.318ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {v}}}"></span> (edo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85820588abd7333ef4d0c56539cb31c20e730753" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.175ex; height:2.343ex;" alt="{\displaystyle {\vec {v}}}"></span>) sinboloaz adierazi ohi da, eta <a href="/wiki/Denbora" title="Denbora">denborarekiko</a> <a href="/wiki/Posizio" class="mw-redirect" title="Posizio">posizio</a>-aldaketa adierazten du. </p><p>Analisi dimentsionalean, hauxek dira abiaduraren <a href="/wiki/Dimentsio" title="Dimentsio">dimentsio</a>ak oinarrizko magnitudeen funtzioan: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [{\boldsymbol {v}}]={\text{L T}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo stretchy="false">]</mo> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>L T</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [{\boldsymbol {v}}]={\text{L T}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2614742edc5e6621d7fc07dac40dd6ade6707b47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.754ex; height:3.176ex;" alt="{\displaystyle [{\boldsymbol {v}}]={\text{L T}}^{-1}}"></span>. Hortaz, nazioarteko <a href="/wiki/Nazioarteko_Unitate_Sistema" title="Nazioarteko Unitate Sistema">SI sistema</a>n, abiaduraren unitatea <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{m s}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>m s</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{m s}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a22a144deca3d6c851d0820a7e37b5d742f96008" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.766ex; height:2.676ex;" alt="{\displaystyle {\text{m s}}^{-1}}"></span> edo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{m/s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>m/s</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{m/s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51a8fc65a4a8b3ba3a0904e1f4ac1051d6365618" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.015ex; height:2.843ex;" alt="{\displaystyle {\text{m/s}}}"></span> da («metro segundoko» edo «metro zati segundo» irakurtzen da). </p><p>Beti ere, abiadura bektorea <a href="/wiki/Erreferentzia-sistema" title="Erreferentzia-sistema">erreferentzia-sistema</a> batekiko definitzen da. Hortaz, abiadura oro erlatiboa da, erreferentzia-sistema jakin bati baitagokio, <a href="/wiki/Erlatibitate_berezi" class="mw-redirect" title="Erlatibitate berezi">erlatibitate bereziak</a> postulatu gisa hartzen duen argiaren abiadura (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9ec1e8ae921e8df868d35d61a2b704c6a5523f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.032ex; height:1.676ex;" alt="{\displaystyle {\text{c}}}"></span>) izan ezik, zeinak balio berbera duen sistema guztietan. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Abiadura_kontzeptuaren_historia">Abiadura kontzeptuaren historia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=1" title="Aldatu atal hau: «Abiadura kontzeptuaren historia»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=1" title="Edit section's source code: Abiadura kontzeptuaren historia"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nahiz eta gaur egun, abiadura kontzeptua nahikoa barneraturik daukagun irakaskuntzan eta gizartean, oso prozesu luzea behar izan zen, lehenik, naturan presente dagoen etengabeko <i><a href="/wiki/Higidura" title="Higidura">higidura</a></i>ren ulermenera iristeko, eta gero, gaur egun <a href="/wiki/Fisika" title="Fisika">fisika</a>n erabiltzen ditugun <i>abiadura</i> eta <i><a href="/wiki/Azelerazio" title="Azelerazio">azelerazioa</a></i> bezalako kontzeptuak zehazteko. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Aristotle_Altemps_Inv8575.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Aristotle_Altemps_Inv8575.jpg/175px-Aristotle_Altemps_Inv8575.jpg" decoding="async" width="175" height="234" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Aristotle_Altemps_Inv8575.jpg/262px-Aristotle_Altemps_Inv8575.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Aristotle_Altemps_Inv8575.jpg/350px-Aristotle_Altemps_Inv8575.jpg 2x" data-file-width="1700" data-file-height="2275" /></a><figcaption>Aristotelesen bustoa Erroman.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Aristoteles">Aristoteles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=2" title="Aldatu atal hau: «Aristoteles»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=2" title="Edit section's source code: Aristoteles"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Grezia zaharreko <i>naturaren filosofoak</i> K.a. VII. mendearen inguruan hasi ziren <a href="/wiki/Natura" title="Natura">Natura</a>n gertatzen ziren higiduren izaerari buruzko ideiak lantzen.enbait mende geroago, haien lanen sintesia egin zuen <a href="/wiki/Aristoteles" title="Aristoteles">Aristoteles</a>-ek (K.a. 384-322). Berak idatzitako <i>Fisika</i> izeneko lanean adierazi zuenez, Naturako materia orok du higidura-printzipio bat —ohar gisa diogun ezen «physis» (<i><b>φύσις</b>,</i> grezieraz idatzita) hitzak  “natura” esan nahi zuela greziera zaharrean—, eta printzipio horren arabera sorturiko higidura naturalak aztertu zituen. Beraren iritziz, berez erortzen ari zen gorputz orok abiadura jakin bat lortzen zuen, eta gorputzaren pisuak zerikusi funtsezkoa zuen abiaduraren balioan, honelakoa hain zuzen: pisu desberdineko bi gorputz kontsideraturik, batak bestearen pisu bikoitza bazuen, abiadura ere bikoitza izango zuen. Bistan denez, ez zuen ondo ulertu abiadura kontzeptua, eta ez zuen neurketa zehatzik egin gorputzen abiaduren balioa zenbatesteko; aitzitik, Aristotelesek deskribatu egin zituen higiduraren inguruko fenomenoak, baina matematika erabili gabe; eta zehaztasunik gabe. </p> <div class="mw-heading mw-heading3"><h3 id="Erdi_Aroko_aurrerapausoak">Erdi Aroko aurrerapausoak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=3" title="Aldatu atal hau: «Erdi Aroko aurrerapausoak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=3" title="Edit section's source code: Erdi Aroko aurrerapausoak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Aristotelesengandik poliki-poliki aldenduz, Erdi Aroan asko aurreratu zen abiadura kontzeptua ulertzeko ahaleginean, denbora neurtzeko erlojuetan eginiko aurrerapenak baliatuz, besteak beste. Horrela, abiaduraren balioen estimazioak egiten hasi ziren, eta horregatik, gaur egungo zenbait ikertzailek Galileo-ren lanen ikusi dituzte <a href="/wiki/Oxfordeko_Unibertsitatea" title="Oxfordeko Unibertsitatea">Oxford</a>-eko eta <a href="/wiki/Parisko_Unibertsitatea" title="Parisko Unibertsitatea">Paris</a>ko unibertsitateetan garai haietan eginiko lanetan. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Galileo.arp.300pix.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Galileo.arp.300pix.jpg/175px-Galileo.arp.300pix.jpg" decoding="async" width="175" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Galileo.arp.300pix.jpg/263px-Galileo.arp.300pix.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Galileo.arp.300pix.jpg/350px-Galileo.arp.300pix.jpg 2x" data-file-width="1180" data-file-height="1448" /></a><figcaption>Galileo Galilei (1564-1642)</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Galileo">Galileo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=4" title="Aldatu atal hau: «Galileo»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=4" title="Edit section's source code: Galileo"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a> (1564-1642) izan zen <i>abiadura</i> kontzeptua zehazki eta sistematikoki aztertu zuen lehena<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>. Horretarako, esperimentu egokiak diseinatu zituen abiadura neurtu ahal izateko. Funtsezkoak izan ziren <i><a href="/wiki/Plano_inklinatu" title="Plano inklinatu">plano inklinatu</a>a</i>n erortzen ziren gorputzekin eginiko saiakuntzak. Haietan, Galileo gai izan zen denbora zehazki neurtzeko <a href="/wiki/Pendulu" title="Pendulu">pendulua</a>ren bidez, baita denbora-tarte zehatz batean solidoek ibilitako bidea edo <i>distantzia</i> neurtzeko ere. Era horretan zehaztu eta definitu zuen abiadura kontzeptua, esanez ezen abiadura «<i>gorputzek denbora-unitatean ibilitako distantzia</i>» dela.   </p><p>Definizio horrek aurrerapen handia ekarri zuen, baina mugaturik egon zen hasieran, garai hartako matematikaren gaitasun mugatuagatik. Kasurako, posible —eta erraz— zen <i>abiadura konstanteaz</i> higitzen ari zen <i><a rel="nofollow" class="external text" href="https://zthiztegia.elhuyar.eus/terminoa/eu/higikari">higikari</a></i> baten abiadura kalkulatzea. Halaber posible zen <i>azelerazio konstanteaz</i> ari zen higikariaren abiadura kalkulatzea, hala nola Galileok berak aztertu zituen <a href="/wiki/Erorketa_aske" title="Erorketa aske">erorketa aske</a>ko kasuetako abiadurak lortzea. Nolanahi ere, higikariaren abiadura modu korapilatsuagoan aldatzen zenean, garai hartan ez zegoen tresna matematiko egokirik kalkuluak egiteko. </p> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Isaac_Newton,_English_School,_1715-20.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Isaac_Newton%2C_English_School%2C_1715-20.jpg/175px-Isaac_Newton%2C_English_School%2C_1715-20.jpg" decoding="async" width="175" height="213" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Isaac_Newton%2C_English_School%2C_1715-20.jpg/263px-Isaac_Newton%2C_English_School%2C_1715-20.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/48/Isaac_Newton%2C_English_School%2C_1715-20.jpg/351px-Isaac_Newton%2C_English_School%2C_1715-20.jpg 2x" data-file-width="2160" data-file-height="2624" /></a><figcaption>Isaac Newton (1643-1726)</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Christoph_Bernhard_Francke_-_Bildnis_des_Philosophen_Leibniz_(ca._1695).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Christoph_Bernhard_Francke_-_Bildnis_des_Philosophen_Leibniz_%28ca._1695%29.jpg/175px-Christoph_Bernhard_Francke_-_Bildnis_des_Philosophen_Leibniz_%28ca._1695%29.jpg" decoding="async" width="175" height="216" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Christoph_Bernhard_Francke_-_Bildnis_des_Philosophen_Leibniz_%28ca._1695%29.jpg/262px-Christoph_Bernhard_Francke_-_Bildnis_des_Philosophen_Leibniz_%28ca._1695%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Christoph_Bernhard_Francke_-_Bildnis_des_Philosophen_Leibniz_%28ca._1695%29.jpg/350px-Christoph_Bernhard_Francke_-_Bildnis_des_Philosophen_Leibniz_%28ca._1695%29.jpg 2x" data-file-width="4486" data-file-height="5538" /></a><figcaption>Gottfried Wilhelm Leibniz (1646-1716)</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Newton_eta_Leibnitz">Newton eta Leibnitz</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=5" title="Aldatu atal hau: «Newton eta Leibnitz»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=5" title="Edit section's source code: Newton eta Leibnitz"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Horretarako, XVII. mendearen bukaera aldera itxaron behar izan zen, Newton eta Leibinitzen lanen emaitzak ezagutu arte. Biek ala biek, ia aldi berean eta modu independentean garatu zuten <i>kalkulu infinitesimala</i>, eta horrela ebatzita geratu zen higikari batean <i>aldiuneko abiadura</i> kalkulatzeko problema. Labur esanda, kalkulu infinitesimalean bi arlo bereizten dira <a href="/wiki/Kalkulu_diferentzial" title="Kalkulu diferentzial">kalkulu diferentziala</a>, <i><a href="/wiki/Deribatu" title="Deribatu">deribatua</a></i>k aztertzen dituena, eta <a href="/wiki/Kalkulu_integral" class="mw-redirect" title="Kalkulu integral">kalkulu integrala</a>, <i><a href="/wiki/Integral" title="Integral">integral</a></i>en izaeraz ari dena, biak elkarrekin koherenteak izanik. Hain zuzen, Newtonen irakasle izandako <a href="/wiki/Isaac_Barrow" title="Isaac Barrow">Isaac Barrow</a>-ek (1630-1677) frogatu zuenez, <a href="/wiki/Deribazio" class="mw-redirect" title="Deribazio">deribazioa</a> eta <a href="/wiki/Integrazio_(argipena)" class="mw-disambig" title="Integrazio (argipena)">integrazioa</a> alderantzizko eragiketak dira. </p><p>Ordutik aurrera esan dezakegu «<i>abiadura higikariaren posizioaren denborarekiko deribatua</i>» dela. Eta bide beretik aurrera eginez, XVIII. mendearen hasierakin, 1700ean, <a href="/wiki/Pierre_Varignon" title="Pierre Varignon">Pierre Varignon</a>-ek (1654-1722) formalizatu egin zuen azelerazioaren definizioa hain zuzen ere «<i>azelerazioa abiaduraren denborarekiko deribatua</i>» zela zehaztuz<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>. </p><p><br /> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Higiduraren_elementuak.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Higiduraren_elementuak.png/330px-Higiduraren_elementuak.png" decoding="async" width="330" height="263" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Higiduraren_elementuak.png/495px-Higiduraren_elementuak.png 1.5x, //upload.wikimedia.org/wikipedia/commons/b/b8/Higiduraren_elementuak.png 2x" data-file-width="524" data-file-height="417" /></a><figcaption>Partikula puntualaren higidura deskribatzeko elementuak.</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Partikula_puntualaren_higidura">Partikula puntualaren higidura</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=6" title="Aldatu atal hau: «Partikula puntualaren higidura»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=6" title="Edit section's source code: Partikula puntualaren higidura"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Alboko irudian marrazturik ageri dira partikula puntual baten higidura definitzen duten elementuak: <a href="/wiki/Erreferentzia-sistema" title="Erreferentzia-sistema">erreferentzia-sistema</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Oxyz}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>x</mi> <mi>y</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Oxyz}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be27c2ad2be5d640cfc2a530df87d9b7b4ebf615" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.347ex; height:2.509ex;" alt="{\displaystyle Oxyz}"></span>), behatzailea (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>), <a href="/wiki/Ibilbide_(fisika)" title="Ibilbide (fisika)">ibilbidea</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{0}AA'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>A</mi> <msup> <mi>A</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{0}AA'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d559cff84be1c5b5b18e358931bbc8381bca00ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.968ex; height:2.843ex;" alt="{\displaystyle A_{0}AA'}"></span> kurba), hasierako posizioa (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c98dbd929292d464de6942e95db306b8b8a6fca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.797ex; height:2.509ex;" alt="{\displaystyle A_{0}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43469ec032d858feae5aa87029e22eaaf0109e9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.101ex; height:2.176ex;" alt="{\displaystyle t=0}"></span> aldiuneari dagokiona), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> aldiuneko posizioa (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> puntua), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>t</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a69b623f18f6b111645f0ec200b3271729fa99af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.524ex; height:2.509ex;" alt="{\displaystyle t'}"></span>aldiuneko posizioa (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98a12527148d6ed68adc91d9b419eb4b92d58ef6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.428ex; height:2.509ex;" alt="{\displaystyle A'}"></span> puntua), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> puntuaren posizio-bektorea (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6a5e169814762d75ef0dd3a3d0bc99b4a5a06e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {r}}}"></span>), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98a12527148d6ed68adc91d9b419eb4b92d58ef6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.428ex; height:2.509ex;" alt="{\displaystyle A'}"></span> puntuaren posizio-bektorea (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0f8cdfd9572599ee1a7b101c0053d512799f24d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.915ex; height:2.509ex;" alt="{\displaystyle {\boldsymbol {r}}'}"></span>), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AA'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <msup> <mi>A</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle AA'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc978cd14ba43f8c2ced54fa6748b909e8aa638b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.171ex; height:2.509ex;" alt="{\displaystyle AA'}"></span> ibilbide-tartearen arku-luzera (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd7783a6d29d2ca4d9f1e0f501c4c6483fc058bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.026ex; height:2.176ex;" alt="{\displaystyle \Delta s}"></span>), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {AA'}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>A</mi> <msup> <mi>A</mi> <mo>′</mo> </msup> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {AA'}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b4ee4c0357c86e2eee021bcde511a926207f24d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.171ex; height:4.009ex;" alt="{\displaystyle {\vec {AA'}}}"></span> bektorea (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta {\boldsymbol {r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta {\boldsymbol {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b11a6000fdc6eb50e0f73fb2611ba1d81bab1cce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.166ex; height:2.176ex;" alt="{\displaystyle \Delta {\boldsymbol {r}}}"></span>), (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t'-t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>−</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t'-t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfad3e560914fa97042eb79f063ed6859d72050a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.204ex; height:2.676ex;" alt="{\displaystyle t'-t}"></span>) denbora tartea (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c28867ecd34e2caed12cf38feadf6a81a7ee542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.775ex; height:2.176ex;" alt="{\displaystyle \Delta t}"></span>). </p> <div class="mw-heading mw-heading2"><h2 id="Batez_besteko_abiadurak">Batez besteko abiadurak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=7" title="Aldatu atal hau: «Batez besteko abiadurak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=7" title="Edit section's source code: Batez besteko abiadurak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lehenik, bi eratan definituko ditugu batez besteko abiadurak: </p> <ul><li>Eskalarki: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {v}}={\Delta s \over \Delta t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>s</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {v}}={\Delta s \over \Delta t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dc3bfbdab9e79cc8e0eea3031c075fa6ac959bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.188ex; height:5.509ex;" alt="{\displaystyle {\bar {v}}={\Delta s \over \Delta t}}"></span>. <i>Batez besteko abiadura eskalar</i> hau da ibilbidearen arkutik ibilitako bidearen eta pasatutako tartearen arteko zatidura, ibilbide osoa kontuan izanik.</li> <li>Bektorialki: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle {\boldsymbol {v}}\rangle ={\Delta {\boldsymbol {r}} \over \Delta t}={\Delta ({\boldsymbol {r}}'-{\boldsymbol {r}}) \over {t'-t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>′</mo> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>−</mo> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle {\boldsymbol {v}}\rangle ={\Delta {\boldsymbol {r}} \over \Delta t}={\Delta ({\boldsymbol {r}}'-{\boldsymbol {r}}) \over {t'-t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abbad9ccb38a9cf91f1d72686a86548d60046963" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:23.892ex; height:5.843ex;" alt="{\displaystyle \langle {\boldsymbol {v}}\rangle ={\Delta {\boldsymbol {r}} \over \Delta t}={\Delta ({\boldsymbol {r}}'-{\boldsymbol {r}}) \over {t'-t}}}"></span> . Izatez, balio honek ez dauka interpretazio orokorrik, ibilbidearen formaren araberakoa baita. Dena den, aurrerago aldiuneko abiadura definitzeko erabiliko dugu.</li></ul> <figure typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Ford_Mondeo_MK3_ST220_-_Speedometer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Ford_Mondeo_MK3_ST220_-_Speedometer.jpg/250px-Ford_Mondeo_MK3_ST220_-_Speedometer.jpg" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Ford_Mondeo_MK3_ST220_-_Speedometer.jpg/375px-Ford_Mondeo_MK3_ST220_-_Speedometer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Ford_Mondeo_MK3_ST220_-_Speedometer.jpg/500px-Ford_Mondeo_MK3_ST220_-_Speedometer.jpg 2x" data-file-width="1640" data-file-height="1640" /></a><figcaption><i>Ford</i> markako automobil baten abiadura-neurgailua, aldiuneko abiadura <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{km/h}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>km/h</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{km/h}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/711ea572a64b0d5668770b3cfa9051f1c398b9d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.618ex; height:2.843ex;" alt="{\displaystyle {\text{km/h}}}"></span> eta<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{mph}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>mph</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{mph}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e83df31a73eeb4f61decf5e8ac294588316056c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.521ex; height:2.509ex;" alt="{\displaystyle {\text{mph}}}"></span> unitatetan adieraztekoa. </figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Aldiuneko_abiadurak">Aldiuneko abiadurak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=8" title="Aldatu atal hau: «Aldiuneko abiadurak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=8" title="Edit section's source code: Aldiuneko abiadurak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Honetan ere bi modutara definituko ditugu: </p> <ul><li><i>Aldiuneko abiadura eskalarra</i> batez besteko abiadura eskarralaren limite modura definituko dugu, denbora-tartea zerorantz doanean:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=\lim _{\Delta t\to 0}{\bar {v}}=\lim _{\Delta t\to 0}{\Delta s \over \Delta t}={\operatorname {d} \!s \over \operatorname {d} \!t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>s</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>s</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=\lim _{\Delta t\to 0}{\bar {v}}=\lim _{\Delta t\to 0}{\Delta s \over \Delta t}={\operatorname {d} \!s \over \operatorname {d} \!t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/baece9ec10c3c86341b9bd8ee4307e78ac29d45e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:28.361ex; height:5.676ex;" alt="{\displaystyle v=\lim _{\Delta t\to 0}{\bar {v}}=\lim _{\Delta t\to 0}{\Delta s \over \Delta t}={\operatorname {d} \!s \over \operatorname {d} \!t}}"></span>Abiadura hau da automobilen abiadura-neurgailuan adierazten dena</li></ul> <ul><li><i>Aldiuneko abiadura bektoriala</i> ere antzera definitzen da, baina kasu honetan batez besteko abiadura bektorialaren limite modura:<br /><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}=\lim _{\Delta t\to 0}\langle {\boldsymbol {v}}\rangle =\lim _{\Delta t\to 0}{\Delta {\boldsymbol {r}} \over \Delta t}={\operatorname {d} {\boldsymbol {r}} \over \operatorname {d} \!t}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}=\lim _{\Delta t\to 0}\langle {\boldsymbol {v}}\rangle =\lim _{\Delta t\to 0}{\Delta {\boldsymbol {r}} \over \Delta t}={\operatorname {d} {\boldsymbol {r}} \over \operatorname {d} \!t}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00bedbf79a9734e9c41547b735eb39123c5c4f7c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:31.378ex; height:5.676ex;" alt="{\displaystyle {\boldsymbol {v}}=\lim _{\Delta t\to 0}\langle {\boldsymbol {v}}\rangle =\lim _{\Delta t\to 0}{\Delta {\boldsymbol {r}} \over \Delta t}={\operatorname {d} {\boldsymbol {r}} \over \operatorname {d} \!t}.}"></span><br /><figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:3.5_irudia.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/3.5_irudia.png/330px-3.5_irudia.png" decoding="async" width="330" height="271" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/3.5_irudia.png/495px-3.5_irudia.png 1.5x, //upload.wikimedia.org/wikipedia/commons/7/76/3.5_irudia.png 2x" data-file-width="508" data-file-height="417" /></a><figcaption>Puntu bakoitzeko abiaduraren norabidea ibilbidearen ukitzailearena da.</figcaption></figure>Ezkerraldeko irudian ikus daitekeenez, aldiuneko abiadura bektorialaren norabidea ibilbidearen <i><a href="/wiki/Zuzen_ukitzaile" title="Zuzen ukitzaile">zuzen ukitzailea</a></i>rena da. Hauxe da <i>abiadura</i> <i>bektorea</i>.</li></ul> <p>Ondorioz, era honetan adieraz daiteke aldiuneko abiadura bektorea, ibilbideko puntu bakoitzeko lerro ukitzailearen norabideko <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {u}}_{t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">u</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {u}}_{t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d8e8ed33581cd11921fd1c64fbe3619495a9834" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.409ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {u}}_{t}}"></span> bektore unitarioaren bidez:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}=v{\boldsymbol {u}}_{t}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>=</mo> <mi>v</mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">u</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}=v{\boldsymbol {u}}_{t}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e224edfb0eeadbcf409eebf4d4245b57b5507e27" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.6ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {v}}=v{\boldsymbol {u}}_{t}.}"></span>Bestetik, aldiuneko abiadura bektorea posizio-bektorearen osagaien bidez ere adieraz daiteke, honelaxe:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}={\frac {{\text{d}}{\boldsymbol {r}}}{{\text{d}}t}}={\frac {{\text{d}}(x{\boldsymbol {i}}+y{\boldsymbol {j}}+z{\boldsymbol {k}})}{{\text{d}}t}}={\frac {{\text{d}}x}{{\text{d}}t}}{\boldsymbol {i}}+{\frac {{\text{d}}y}{{\text{d}}t}}{\boldsymbol {j}}+{\frac {{\text{d}}z}{{\text{d}}t}}{\boldsymbol {k}}=v_{x}{\boldsymbol {i}}+v_{y}{\boldsymbol {j}}+v_{z}{\boldsymbol {k}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">i</mi> </mrow> <mo>+</mo> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">j</mi> </mrow> <mo>+</mo> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">k</mi> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">i</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>y</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">j</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>z</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">k</mi> </mrow> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">i</mi> </mrow> <mo>+</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">j</mi> </mrow> <mo>+</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">k</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}={\frac {{\text{d}}{\boldsymbol {r}}}{{\text{d}}t}}={\frac {{\text{d}}(x{\boldsymbol {i}}+y{\boldsymbol {j}}+z{\boldsymbol {k}})}{{\text{d}}t}}={\frac {{\text{d}}x}{{\text{d}}t}}{\boldsymbol {i}}+{\frac {{\text{d}}y}{{\text{d}}t}}{\boldsymbol {j}}+{\frac {{\text{d}}z}{{\text{d}}t}}{\boldsymbol {k}}=v_{x}{\boldsymbol {i}}+v_{y}{\boldsymbol {j}}+v_{z}{\boldsymbol {k}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9399b88d539282a59938f9c75d875903200c4fcc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:69.159ex; height:5.843ex;" alt="{\displaystyle {\boldsymbol {v}}={\frac {{\text{d}}{\boldsymbol {r}}}{{\text{d}}t}}={\frac {{\text{d}}(x{\boldsymbol {i}}+y{\boldsymbol {j}}+z{\boldsymbol {k}})}{{\text{d}}t}}={\frac {{\text{d}}x}{{\text{d}}t}}{\boldsymbol {i}}+{\frac {{\text{d}}y}{{\text{d}}t}}{\boldsymbol {j}}+{\frac {{\text{d}}z}{{\text{d}}t}}{\boldsymbol {k}}=v_{x}{\boldsymbol {i}}+v_{y}{\boldsymbol {j}}+v_{z}{\boldsymbol {k}}.}"></span>Adierazpen horretan, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{x},v_{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{x},v_{y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ca8038742ae055fd7a30d62a91f457911926605" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.511ex; height:2.343ex;" alt="{\displaystyle v_{x},v_{y}}"></span>eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{z}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{z}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b553b9ecda9fc7f5c9da6f14a870e219080984e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.129ex; height:2.009ex;" alt="{\displaystyle v_{z}}"></span> abiadura bektorearen hiru osagai kartesiarrak dira. Osagaiok kontuan izanik, hauxe da aldiuneko abiadura bektorearen modulua:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=\left\vert {\boldsymbol {v}}\right\vert =\left\vert {\operatorname {d} {\boldsymbol {r}} \over \operatorname {d} \!t}\right\vert ={\operatorname {d} \!s \over \operatorname {d} \!t}={\sqrt {v_{x}^{2}+v_{y}^{2}+v_{z}^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>s</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=\left\vert {\boldsymbol {v}}\right\vert =\left\vert {\operatorname {d} {\boldsymbol {r}} \over \operatorname {d} \!t}\right\vert ={\operatorname {d} \!s \over \operatorname {d} \!t}={\sqrt {v_{x}^{2}+v_{y}^{2}+v_{z}^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dc46e3bca63bff1b421a49cb23a2cf5336288c6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:39.707ex; height:5.843ex;" alt="{\displaystyle v=\left\vert {\boldsymbol {v}}\right\vert =\left\vert {\operatorname {d} {\boldsymbol {r}} \over \operatorname {d} \!t}\right\vert ={\operatorname {d} \!s \over \operatorname {d} \!t}={\sqrt {v_{x}^{2}+v_{y}^{2}+v_{z}^{2}}}.}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Posizioaren_adierazpena_abiadura_eta_denboraren_funtzioan">Posizioaren adierazpena abiadura eta denboraren funtzioan</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=9" title="Aldatu atal hau: «Posizioaren adierazpena abiadura eta denboraren funtzioan»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=9" title="Edit section's source code: Posizioaren adierazpena abiadura eta denboraren funtzioan"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Aldiuneko abiaduraren definiziotik abiaturik, eta hasierako posizioa (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}_{\text{0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}_{\text{0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2366faad85f230bdb77e4934e164dc753a96f189" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {r}}_{\text{0}}}"></span>) eta abiadurak denboraren funtzioa daukan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/086caf81c101a6c4ed9a9f3415b6cb01ff082f31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.967ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {v}}(t)}"></span> balioa zein diren jakinik, modu errazean kalkula daiteke zein izango den partikularen posizioa, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa34186c096c01921320d71c58317ee7253c84fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.879ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {r}}(t)}"></span>, edozein <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> aldiunetan. Era honetan egin daitezke kalkuluak:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}(t)={\frac {{\mbox{d}}{\boldsymbol {r}}(t)}{{\mbox{d}}t}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>d</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>d</mtext> </mstyle> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}(t)={\frac {{\mbox{d}}{\boldsymbol {r}}(t)}{{\mbox{d}}t}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/134c55420fbbe4c793c54f56030b601986c3fb04" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.72ex; height:5.843ex;" alt="{\displaystyle {\boldsymbol {v}}(t)={\frac {{\mbox{d}}{\boldsymbol {r}}(t)}{{\mbox{d}}t}},}"></span><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{d}}{\boldsymbol {r}}(t)={\boldsymbol {v}}(t){\mbox{d}}t,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>d</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>d</mtext> </mstyle> </mrow> <mi>t</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{d}}{\boldsymbol {r}}(t)={\boldsymbol {v}}(t){\mbox{d}}t,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2642cf74bd6a9270097a9c5e6772cb9cc9ddcffa" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.016ex; height:2.843ex;" alt="{\displaystyle {\mbox{d}}{\boldsymbol {r}}(t)={\boldsymbol {v}}(t){\mbox{d}}t,}"></span><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{{\boldsymbol {r}}_{0}}^{{\boldsymbol {r}}(t)}{\mbox{d}}{\boldsymbol {r}}={\boldsymbol {r}}(t)-{\boldsymbol {r}}_{0}=\int _{t_{0}}^{t}{\boldsymbol {v}}(t){\mbox{d}}t,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>d</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>d</mtext> </mstyle> </mrow> <mi>t</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{{\boldsymbol {r}}_{0}}^{{\boldsymbol {r}}(t)}{\mbox{d}}{\boldsymbol {r}}={\boldsymbol {r}}(t)-{\boldsymbol {r}}_{0}=\int _{t_{0}}^{t}{\boldsymbol {v}}(t){\mbox{d}}t,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48d256aa1ab00981769a9c818398c114e216f73a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:33.972ex; height:6.676ex;" alt="{\displaystyle \int _{{\boldsymbol {r}}_{0}}^{{\boldsymbol {r}}(t)}{\mbox{d}}{\boldsymbol {r}}={\boldsymbol {r}}(t)-{\boldsymbol {r}}_{0}=\int _{t_{0}}^{t}{\boldsymbol {v}}(t){\mbox{d}}t,}"></span><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}(t)={\boldsymbol {r}}_{0}+\int _{t_{0}}^{t}{\boldsymbol {v}}(t){\mbox{d}}t.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>d</mtext> </mstyle> </mrow> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}(t)={\boldsymbol {r}}_{0}+\int _{t_{0}}^{t}{\boldsymbol {v}}(t){\mbox{d}}t.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f1cd4728987496fc69681b08726467bf6eafdf3" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:22.525ex; height:6.509ex;" alt="{\displaystyle {\boldsymbol {r}}(t)={\boldsymbol {r}}_{0}+\int _{t_{0}}^{t}{\boldsymbol {v}}(t){\mbox{d}}t.}"></span>Integral hori kalkulatzeko, abiadura nola aldatzen den jakin behar da aldez aurretik, alegia, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/086caf81c101a6c4ed9a9f3415b6cb01ff082f31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.967ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {v}}(t)}"></span> funtzioa nolakoa den jakin behar da. Abiadura konstantea den kasuan, oso erraz lortzen da emaitza:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}(t)={\boldsymbol {r}}_{0}+{\boldsymbol {v}}(t-t_{0}).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>−</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}(t)={\boldsymbol {r}}_{0}+{\boldsymbol {v}}(t-t_{0}).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f8efadb3e65adbb2dc4488f8acfd6561d853af0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.45ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {r}}(t)={\boldsymbol {r}}_{0}+{\boldsymbol {v}}(t-t_{0}).}"></span><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Abiadura_kontzeptu_erlatiboa_da">Abiadura kontzeptu erlatiboa da</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=10" title="Aldatu atal hau: «Abiadura kontzeptu erlatiboa da»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=10" title="Edit section's source code: Abiadura kontzeptu erlatiboa da"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div><p> Zer gertatzen da <a href="/wiki/Erreferentzia-sistema" title="Erreferentzia-sistema">erreferentzia-sistema</a> aldatzen denean? Elkarrekiko higitzen ari diren behatzaile guztiek modu berean neurtzen ote dute puntu material jakin baten abiadura? Galdera hohriei erantzuteko, bi kasu sinpletan aztertuko dugu arazoa: elkarrekiko translazioko <a href="/wiki/Higidura_zuzen_uniforme" title="Higidura zuzen uniforme">higidura zuzen uniformea</a> duten bi erreferentzia-sistemaren kasuan, eta elkarrekiko <a href="/wiki/Errotazio" title="Errotazio">biraketa-higidura</a> konstantea duten sistemen kasuan.</p><figure typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:4.2._irudia.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/4.2._irudia.png/330px-4.2._irudia.png" decoding="async" width="330" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/4.2._irudia.png/495px-4.2._irudia.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/4.2._irudia.png/660px-4.2._irudia.png 2x" data-file-width="893" data-file-height="529" /></a><figcaption><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Ox'y'z'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <msup> <mi>x</mi> <mo>′</mo> </msup> <msup> <mi>y</mi> <mo>′</mo> </msup> <msup> <mi>z</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ox'y'z'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71746309c2b419fd19cc5f94603fd7118f0628ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.408ex; height:2.843ex;" alt="{\displaystyle Ox'y'z'}"></span>sistema <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span> abiadura konstantez higitzen ari da <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Oxyz}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>x</mi> <mi>y</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Oxyz}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be27c2ad2be5d640cfc2a530df87d9b7b4ebf615" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.347ex; height:2.509ex;" alt="{\displaystyle Oxyz}"></span> sistemarekiko.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Elkarrekiko_translazio-higidura_zuzen_eta_uniformea_duten_bi_erreferentzia-sistemaren_kasua">Elkarrekiko translazio-higidura zuzen eta uniformea duten bi erreferentzia-sistemaren kasua</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=11" title="Aldatu atal hau: «Elkarrekiko translazio-higidura zuzen eta uniformea duten bi erreferentzia-sistemaren kasua»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=11" title="Edit section's source code: Elkarrekiko translazio-higidura zuzen eta uniformea duten bi erreferentzia-sistemaren kasua"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kontsidera dezagun bi erreferentzia-sistema paralelo ditugula, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Oxyz}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>x</mi> <mi>y</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Oxyz}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be27c2ad2be5d640cfc2a530df87d9b7b4ebf615" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.347ex; height:2.509ex;" alt="{\displaystyle Oxyz}"></span> eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O'x'y'z'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>O</mi> <mo>′</mo> </msup> <msup> <mi>x</mi> <mo>′</mo> </msup> <msup> <mi>y</mi> <mo>′</mo> </msup> <msup> <mi>z</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O'x'y'z'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1e1892103681a237424e77202f4875447b5eb2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.093ex; height:2.843ex;" alt="{\displaystyle O'x'y'z'}"></span> sistemak, bakoitza bere behatzailearekin, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>B</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b144e466a3757b4706daf24a45d4f1266700016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.449ex; height:2.509ex;" alt="{\displaystyle B'}"></span>, alboko irudian ageri den bezala. Bigarren sistema <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">V</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {V}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a960e1b6c3d5b28afcd5742709ebd498ca13be63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.059ex; height:2.176ex;" alt="{\displaystyle {\boldsymbol {V}}}"></span> abiadura konstantez higitzen ari da lehenarekiko, eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43469ec032d858feae5aa87029e22eaaf0109e9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.101ex; height:2.176ex;" alt="{\displaystyle t=0}"></span> aldiunean bi sistemak kointzidenteak izan direla onartuko dugu, hots, aldiune horretan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O=O'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo>=</mo> <msup> <mi>O</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O=O'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed811a941ce342ac12aef890984f5acf5474b6b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.33ex; height:2.509ex;" alt="{\displaystyle O=O'}"></span>izan dela. </p><p>Beraz, edozein <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> aldiunetan, bigarren sistemaren jatorriak lehenengo sisteman duen posizio-bektorea<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {R}}={\boldsymbol {V}}t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">R</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">V</mi> </mrow> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {R}}={\boldsymbol {V}}t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f37888f4384959f3e19d23ddf871048db737c563" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.044ex; height:2.176ex;" alt="{\displaystyle {\boldsymbol {R}}={\boldsymbol {V}}t}"></span>izango da. Hortaz, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> puntuaren posizioa neurtzean, bi behatzaileek bektore desberdinak neurtuko dituzte, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6a5e169814762d75ef0dd3a3d0bc99b4a5a06e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {r}}}"></span><b> </b>eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0f8cdfd9572599ee1a7b101c0053d512799f24d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.915ex; height:2.509ex;" alt="{\displaystyle {\boldsymbol {r}}'}"></span>, bi bektore horien artean erlazio hau izanik:  <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}={\boldsymbol {R}}+{\boldsymbol {r}}'={\boldsymbol {V}}t+{\boldsymbol {r}}'.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">R</mi> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">V</mi> </mrow> <mi>t</mi> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>′</mo> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}={\boldsymbol {R}}+{\boldsymbol {r}}'={\boldsymbol {V}}t+{\boldsymbol {r}}'.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20bf23a1f85afc091a8c1484325cfcef98348f5c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:22.529ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {r}}={\boldsymbol {R}}+{\boldsymbol {r}}'={\boldsymbol {V}}t+{\boldsymbol {r}}'.}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Abiaduren_batuketa_mekanika_klasikoan">Abiaduren batuketa mekanika klasikoan</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=12" title="Aldatu atal hau: «Abiaduren batuketa mekanika klasikoan»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=12" title="Edit section's source code: Abiaduren batuketa mekanika klasikoan"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Eta mekanika klasikoan denbora bi behatzaileentzat modu berean pasatzen denez, berdintza horren alde biak denborarekiko deribatuz, bi behatzaileek neurtzen dituzten abiaduren arteko erlazioa lortuko dugu:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\operatorname {d} {\boldsymbol {r}} \over \operatorname {d} \!t}={\operatorname {d} ({\boldsymbol {V}}{t}) \over \operatorname {d} \!t}+{\operatorname {d} {\boldsymbol {r}}' \over \operatorname {d} \!t},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>′</mo> </msup> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mspace width="negativethinmathspace" /> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\operatorname {d} {\boldsymbol {r}} \over \operatorname {d} \!t}={\operatorname {d} ({\boldsymbol {V}}{t}) \over \operatorname {d} \!t}+{\operatorname {d} {\boldsymbol {r}}' \over \operatorname {d} \!t},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0a506b2a2a6bf555cfd8ee2fda5d8b29261af54" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.598ex; height:5.843ex;" alt="{\displaystyle {\operatorname {d} {\boldsymbol {r}} \over \operatorname {d} \!t}={\operatorname {d} ({\boldsymbol {V}}{t}) \over \operatorname {d} \!t}+{\operatorname {d} {\boldsymbol {r}}' \over \operatorname {d} \!t},}"></span><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}={\boldsymbol {V}}+{\boldsymbol {v}}'.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">V</mi> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>′</mo> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}={\boldsymbol {V}}+{\boldsymbol {v}}'.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/451962459e7d9d6a78f253fe066afe1cbf160a1b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.966ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {v}}={\boldsymbol {V}}+{\boldsymbol {v}}'.}"></span>Ikus dezakegunez, bi behatzaileek neurtzen dituzten abiadurak desberdinak dira; hain zuzen, lehenengo behatzaileak neurturiko <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b2c2d3aac4213f3996d828c6aa8f4eb464a05cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.318ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {v}}}"></span> abiaduraren balioa beste bi <i><b>abiaduren batura</b></i> da, hots, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {V}}+{\boldsymbol {v}}'.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">V</mi> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>′</mo> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {V}}+{\boldsymbol {v}}'.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dd67b27fadfbd94776ada5e1fe2cfd82d6e6bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.549ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {V}}+{\boldsymbol {v}}'.}"></span> Agerikoa denez, abiaduraren balioa kontzeptu erlatiboa da, neurketako erreferentzia-sistemaren araberakoa. </p> <div class="mw-heading mw-heading3"><h3 id="Elkarrekiko_biraketa-higidura_duten_bi_erreferentzia-sistemaren_kasua">Elkarrekiko biraketa-higidura duten bi erreferentzia-sistemaren kasua</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=13" title="Aldatu atal hau: «Elkarrekiko biraketa-higidura duten bi erreferentzia-sistemaren kasua»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=13" title="Edit section's source code: Elkarrekiko biraketa-higidura duten bi erreferentzia-sistemaren kasua"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:4.4._irudia.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/4.4._irudia.png/330px-4.4._irudia.png" decoding="async" width="330" height="248" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/4.4._irudia.png/495px-4.4._irudia.png 1.5x, //upload.wikimedia.org/wikipedia/commons/1/15/4.4._irudia.png 2x" data-file-width="647" data-file-height="486" /></a><figcaption>Elkarrekiko biraka ari diren bi erreferentzia-sistemaren kasua.</figcaption></figure> <p>Oraingoan, alboko irudian ageri den moduko higidura erlatiboa duten bi erreferentzia-sistemaren kasua aztertuko dugu. Kontsideratuko dugu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Oxyz}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>x</mi> <mi>y</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Oxyz}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be27c2ad2be5d640cfc2a530df87d9b7b4ebf615" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.347ex; height:2.509ex;" alt="{\displaystyle Oxyz}"></span> sistema geldi dagoela eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Ox'y'z'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <msup> <mi>x</mi> <mo>′</mo> </msup> <msup> <mi>y</mi> <mo>′</mo> </msup> <msup> <mi>z</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ox'y'z'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71746309c2b419fd19cc5f94603fd7118f0628ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.408ex; height:2.843ex;" alt="{\displaystyle Ox'y'z'}"></span> sistema biraka ari dela <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span> puntutik pasatzen den ardatz baten inguruan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cb8af7a2f64af348e559652b6b1f0d2415ba444" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.669ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {\omega }}}"></span> <a href="/wiki/Abiadura_angeluar" title="Abiadura angeluar">abiadura angeluar</a> konstanteaz. </p><p>Jatorri bereko bi sistema direnez, posizio-bektoreak berberak izango dira denbora guztian, baina sistema bakoitzean osagai desberdinak izango dituzte:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}\equiv {\boldsymbol {r}}',}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>≡</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>′</mo> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}\equiv {\boldsymbol {r}}',}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12f7ff56d0e16437f32bb18c9adafbaf0d4c128d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.89ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {r}}\equiv {\boldsymbol {r}}',}"></span><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x{\boldsymbol {i}}+y{\boldsymbol {j}}+z{\boldsymbol {k}}=x'{\boldsymbol {i}}'+y'{\boldsymbol {j}}'+z'{\boldsymbol {k}}'.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">i</mi> </mrow> <mo>+</mo> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">j</mi> </mrow> <mo>+</mo> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">k</mi> </mrow> <mo>=</mo> <msup> <mi>x</mi> <mo>′</mo> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">i</mi> </mrow> <mo>′</mo> </msup> <mo>+</mo> <msup> <mi>y</mi> <mo>′</mo> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">j</mi> </mrow> <mo>′</mo> </msup> <mo>+</mo> <msup> <mi>z</mi> <mo>′</mo> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">k</mi> </mrow> <mo>′</mo> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x{\boldsymbol {i}}+y{\boldsymbol {j}}+z{\boldsymbol {k}}=x'{\boldsymbol {i}}'+y'{\boldsymbol {j}}'+z'{\boldsymbol {k}}'.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0e3b926b3ba4ff1e27a911e9dee328a7e241d0b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:33.251ex; height:2.843ex;" alt="{\displaystyle x{\boldsymbol {i}}+y{\boldsymbol {j}}+z{\boldsymbol {k}}=x'{\boldsymbol {i}}'+y'{\boldsymbol {j}}'+z'{\boldsymbol {k}}'.}"></span>Bi sistemetan partikulak dituen abiadurak kalkulatzeko, denborarekiko deribatuak kalkulatu behar dira. Dena den, hemen ez dugu deribazio-prozesua zehatz-mehatz aztertuko; bakarrik jarriko dugu azken emaitza:<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><br /><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}={\boldsymbol {v}}'+{\boldsymbol {\omega }}\times {\boldsymbol {r}}'.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>′</mo> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> <mo>×</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>′</mo> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}={\boldsymbol {v}}'+{\boldsymbol {\omega }}\times {\boldsymbol {r}}'.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0744cd41e9f361b8b16efea5bb6736d614944551" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:16.33ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {v}}={\boldsymbol {v}}'+{\boldsymbol {\omega }}\times {\boldsymbol {r}}'.}"></span>Bistan denez, bi behatzaileek neurtzen dituzten abiadurak desberdinak dira, eta horretan eragin zuzena du baita bigarren sistemaren <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cb8af7a2f64af348e559652b6b1f0d2415ba444" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.669ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {\omega }}}"></span> abiadura angeluarrak ere. </p> <div class="mw-heading mw-heading2"><h2 id="Abiadura_neurtzeko_unitateak">Abiadura neurtzeko unitateak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=14" title="Aldatu atal hau: «Abiadura neurtzeko unitateak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=14" title="Edit section's source code: Abiadura neurtzeko unitateak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Abiadura hainbat arlotan erabiltzen denez, ohitura dago unitate espezifikoak erabiltzeko bizimodu arrunteko arloan arloko praktikan. </p> <div class="mw-heading mw-heading3"><h3 id="Nazioarteko_SI_unitate-sistema">Nazioarteko SI unitate-sistema</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=15" title="Aldatu atal hau: «Nazioarteko SI unitate-sistema»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=15" title="Edit section's source code: Nazioarteko SI unitate-sistema"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Oro har, zientziaren arlo gehienetan unitate estandarrak erabiltzen dira, alegia, <a href="/wiki/Nazioarteko_Unitate_Sistema" title="Nazioarteko Unitate Sistema">SI sistema</a>ko zazpi oinarrizko unitateetatik eratorritakoak. Hortaz, abiaduraren dimentsio-ekuazioa, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [{\boldsymbol {v}}]={\text{L T}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo stretchy="false">]</mo> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>L T</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [{\boldsymbol {v}}]={\text{L T}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2614742edc5e6621d7fc07dac40dd6ade6707b47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.754ex; height:3.176ex;" alt="{\displaystyle [{\boldsymbol {v}}]={\text{L T}}^{-1}}"></span>, kontuan izanik, </p> <ul><li>zientzian erabili ohi den unitatea «metro zati segundo» (edo «metro segundo minus bat» edo «metro segundoko») da. Era sinbolikoan honelaxe adierazten da: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{m/s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>m/s</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{m/s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51a8fc65a4a8b3ba3a0904e1f4ac1051d6365618" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.015ex; height:2.843ex;" alt="{\displaystyle {\text{m/s}}}"></span> edo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{m s}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>m s</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{m s}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a22a144deca3d6c851d0820a7e37b5d742f96008" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.766ex; height:2.676ex;" alt="{\displaystyle {\text{m s}}^{-1}}"></span>.  </li></ul> <p>Nolanahi ere, SI sistemakoak izan gabe, unitate hauek ere erabiltzen dira askotan: </p> <ul><li>Ibilgailuen kasuan, ohikoena «kilometro orduko» unitatea da, eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{km/h}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>km/h</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{km/h}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/711ea572a64b0d5668770b3cfa9051f1c398b9d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.618ex; height:2.843ex;" alt="{\displaystyle {\text{km/h}}}"></span> sinboloaz adierazten da.</li> <li>Abiadura oso handien kasuan, argiarenean adibidez, «kilometro segundoko» unitatea, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{km/s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>km/s</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{km/s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e159dc0409388e3e30db0ad8248aa9740324d90d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.242ex; height:2.843ex;" alt="{\displaystyle {\text{km/s}}}"></span> sinboloaz adierazten dena.</li></ul> <div class="mw-heading mw-heading3"><h3 id="CGS_sistema_(sistema_zegesimala)"><span id="CGS_sistema_.28sistema_zegesimala.29"></span>CGS sistema (sistema zegesimala)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=16" title="Aldatu atal hau: «CGS sistema (sistema zegesimala)»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=16" title="Edit section's source code: CGS sistema (sistema zegesimala)"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Zientziaren zenbait arlotan ohitura dago, antzina arrunta zen CGS sistemako abiadura-unitatea erabiltzeko, alegia: </p> <ul><li>«zentimetro segundoko» unitatea da, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{cm/s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>cm/s</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{cm/s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5ab2d88d953a29c8752748d3c9be023d0a7ddf2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.047ex; height:2.843ex;" alt="{\displaystyle {\text{cm/s}}}"></span> sinboloaz adierazten dena.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Unitate-sistema_anglosaxoia">Unitate-sistema anglosaxoia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=17" title="Aldatu atal hau: «Unitate-sistema anglosaxoia»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=17" title="Edit section's source code: Unitate-sistema anglosaxoia"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lurralde anglosaxoietan beren tradiziozko unitate-sistema erabiltzen segitzen dute bizimodu arruntean, nahiz eta zientziaren arloan SI sistema nagusitzen ari den gero eta gehiago. Hona hemen sistema anglosaxoizko abiadura-unitateak: </p> <ul><li>«oin segundoko» unitatea, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{ft/s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>ft/s</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{ft/s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3bdb02e31a8f21be503170d1f147a558059144bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.695ex; height:2.843ex;" alt="{\displaystyle {\text{ft/s}}}"></span> sinboloduna.</li> <li>«milia orduko» unitatea, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{mph}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>mph</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{mph}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e83df31a73eeb4f61decf5e8ac294588316056c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.521ex; height:2.509ex;" alt="{\displaystyle {\text{mph}}}"></span> sinboloduna, ibilgailuetan ohikoena.</li> <li>«milia segundoko» unitatea, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{mps}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>mps</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{mps}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7e4c0a62718587057910c3bd9c0e5acad3575c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.145ex; height:2.009ex;" alt="{\displaystyle {\text{mps}}}"></span> sinboloduna.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Itsas_nabigazioko_unitatea">Itsas nabigazioko unitatea</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=18" title="Aldatu atal hau: «Itsas nabigazioko unitatea»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=18" title="Edit section's source code: Itsas nabigazioko unitatea"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Itsasoko nabigazioan «<a href="/wiki/Korapilo_(abiadura_unitatea)" title="Korapilo (abiadura unitatea)">korapiloa</a>» deritzon unitate berezia erabiltzen da; beraren sinboloa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{kn}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>kn</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{kn}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ba0e1c59bd26cfe61ba2cf3a3931c0037831064" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.52ex; height:2.176ex;" alt="{\displaystyle {\text{kn}}}"></span> da (ingelesezko «knot» hitzetik sortua) </p> <ul><li>Korapilo bateko abiadura ordubetean «<a href="/wiki/Itsas_milia" title="Itsas milia">itsas milia</a> bat ibiltzean eginiko» desplazamenduari  dagokio. Beraren sinboloa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{kn}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>kn</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{kn}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ba0e1c59bd26cfe61ba2cf3a3931c0037831064" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.52ex; height:2.176ex;" alt="{\displaystyle {\text{kn}}}"></span> da. Itsas milia bat («milia nautikoa» ere deitua) <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{1852 m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>1852 m</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{1852 m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8fea36e8f45afdd8ed75d92f38c767d1533476f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.166ex; height:2.176ex;" alt="{\displaystyle {\text{1852 m}}}"></span>-ren baliokidea denez, baliokidetza hau du: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{1 kn = 1,852 km/h}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>1 kn = 1,852 km/h</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{1 kn = 1,852 km/h}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0693b7d5fc3a2926c8360f7d0840e1c8885613" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.728ex; height:2.843ex;" alt="{\displaystyle {\text{1 kn = 1,852 km/h}}}"></span>Ohar gisa diogun ezen lehorrean erabili ohi den «<a href="/wiki/Milia" title="Milia">milia</a>»-aren balioa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{1609,344 m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>1609,344 m</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{1609,344 m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30bcf2357b0d4d27541fe8d4a1f8e7369b9b70a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.301ex; height:2.509ex;" alt="{\displaystyle {\text{1609,344 m}}}"></span> dela.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Aeronautikako_unitate_berezia">Aeronautikako unitate berezia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=19" title="Aldatu atal hau: «Aeronautikako unitate berezia»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=19" title="Edit section's source code: Aeronautikako unitate berezia"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Aeronautika" title="Aeronautika">Aeronautika</a>n, abiadura handiko <a href="/wiki/Hegazkin" title="Hegazkin">hegazkin</a>en kasuan, <a href="/wiki/Soinu" title="Soinu">soinua</a>k atmosferan baldintza berezietan duen abiadura hartzen da erreferentziatzat. Hain zuzen, itsas mailan airearen hezetasuna <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \%{\text{ 50}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">%</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> 50</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \%{\text{ 50}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6832498a3f96a480df38711bf5d3a12d9f6b7313" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.841ex; height:2.343ex;" alt="{\displaystyle \%{\text{ 50}}}"></span>-eko izanik eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{20 }}^{\circ }{\text{C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>20 </mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>C</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{20 }}^{\circ }{\text{C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0e3c193c3241b3f6a23bcbc7f89ee702bb856e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.638ex; height:2.343ex;" alt="{\displaystyle {\text{20 }}^{\circ }{\text{C}}}"></span>-eko tenperaturan neurturik, <a href="/wiki/Soinuaren_abiadura" class="mw-redirect" title="Soinuaren abiadura">soinuaren abiadura</a>k <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 343,2{\text{ m/s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>343</mn> <mo>,</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> m/s</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 343,2{\text{ m/s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c1fa054251e1bc922ceabfbca35ff9e03f0e285" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.279ex; height:2.843ex;" alt="{\displaystyle 343,2{\text{ m/s}}}"></span> <a href="/wiki/Metro_segundoko" title="Metro segundoko">m/s</a> balio du (hots, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{1235,52 km/h}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>1235,52 km/h</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{1235,52 km/h}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3be212a466d04df38ea119a5c7b5db8779dde365" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.821ex; height:2.843ex;" alt="{\displaystyle {\text{1235,52 km/h}}}"></span>). </p><p>Soinuaren abiadura hori oinarri hartuta, «<a href="/wiki/Mach_zenbakia" title="Mach zenbakia">Mach zenbakia</a>» izeneko abiadura erlatibo bat definitzen da, hegazkinaren abiaduraren, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span>, eta soinuaren abiaduraren, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b967b0fadf0e61501f222904f77e4f0bd87e67b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.008ex; height:2.009ex;" alt="{\displaystyle v_{\text{s}}}"></span>, zatidura modura. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{Mach zenbakia}}=M={\frac {v}{v_{\text{s}}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Mach zenbakia</mtext> </mrow> <mo>=</mo> <mi>M</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>v</mi> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{Mach zenbakia}}=M={\frac {v}{v_{\text{s}}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c543f6929e83b019405aafee8aab6e1c94d0eb60" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:27.178ex; height:5.009ex;" alt="{\displaystyle {\text{Mach zenbakia}}=M={\frac {v}{v_{\text{s}}}}.}"></span>Mach zenbakiaren osagai dimentsionalak kalkulatzean, emaitza hau lortzen da: </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:British_Airways_Concorde_G-BOAC_03.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/British_Airways_Concorde_G-BOAC_03.jpg/260px-British_Airways_Concorde_G-BOAC_03.jpg" decoding="async" width="260" height="172" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/British_Airways_Concorde_G-BOAC_03.jpg/390px-British_Airways_Concorde_G-BOAC_03.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/British_Airways_Concorde_G-BOAC_03.jpg/520px-British_Airways_Concorde_G-BOAC_03.jpg 2x" data-file-width="1024" data-file-height="679" /></a><figcaption><i>Concorde</i> hegazkin supertsonikoa airean.</figcaption></figure> <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [M]={\frac {[v]}{[v_{\text{s}}]}}={\frac {{\text{L T}}^{-1}}{{\text{L T}}^{-1}}}={\text{L}}^{0}{\text{T}}^{0}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mi>v</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mo stretchy="false">[</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>L T</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>L T</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>T</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [M]={\frac {[v]}{[v_{\text{s}}]}}={\frac {{\text{L T}}^{-1}}{{\text{L T}}^{-1}}}={\text{L}}^{0}{\text{T}}^{0}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91be9063b97f50c5064752eb4d5a5a92a28dcef2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:29.935ex; height:6.509ex;" alt="{\displaystyle [M]={\frac {[v]}{[v_{\text{s}}]}}={\frac {{\text{L T}}^{-1}}{{\text{L T}}^{-1}}}={\text{L}}^{0}{\text{T}}^{0}.}"></span> </p><p>Agerikoa denez, zenbaki adimentsionala da, logikoa dena bestalde, hegazkina soinuaren abiadura baino zenbat aldiz bizkorrago dabilen adierazten baitu soilik. Adibidez, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2801ac77396e68de0b640087e1531a2329067e9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.703ex; height:2.176ex;" alt="{\displaystyle M=2}"></span> abiaduraz doan hegazkina soinua baino bi aldiz bizkorragoan dabil, hots, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=2\times {\text{1235,52 km/h}}={\text{2471,04 km/h}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mn>2</mn> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>1235,52 km/h</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>2471,04 km/h</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=2\times {\text{1235,52 km/h}}={\text{2471,04 km/h}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b316af298d79e704ff8f58f1a9f126a27cf0dafb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.969ex; height:2.843ex;" alt="{\displaystyle v=2\times {\text{1235,52 km/h}}={\text{2471,04 km/h}}}"></span> abiaduran. Normalean, gerra-hegazkinak baino ez dabiltza tarte labur batzuetan soinua baino bizkorrago. Orain arte bi hegazkin komertzial supertsoniko baino ez dira fabrikatu eta erabili. Lehena <a href="/wiki/Tupolev_Tu-144" title="Tupolev Tu-144">Tupolev Tu-144a</a> hegazkin sobietarra izan zen, 1968-1978 bitartean erabili zena. Bigarrena <a href="/wiki/Frantzia" title="Frantzia">Frantzia</a>k eta <a href="/wiki/Erresuma_Batua" title="Erresuma Batua">Erresuma Batua</a>k fabrikaturiko <a href="/wiki/Concorde" title="Concorde">Concorde</a> izenekoa, 1969 eraikia, 1976an komertzialki erabiltzen hasia, eta 2000. urtean istripu bat izan ondoren, bere hegaldiak 2003an amaitu zituena. </p> <div class="mw-heading mw-heading3"><h3 id="Argiaren_abiadura">Argiaren abiadura</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=20" title="Aldatu atal hau: «Argiaren abiadura»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=20" title="Edit section's source code: Argiaren abiadura"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Erlatibitatearen_teoria" title="Erlatibitatearen teoria">Erlatibitatearen teoria</a>ren ondorioak kontuan izanik, argiaren abiadurak ezaugarri berezia du: argiak hutsean duen abiadura <i>konstante unibertsala</i> da. Pisu eta Neurrien Nazioarteko Batzordearen (frantsesez, <i>Comité international des poids et mesures</i>, CIPM)<a rel="nofollow" class="external autonumber" href="https://www.bipm.org/fr/committees/cipm/">[1]</a> azpibatzorde baten proposamena kontuan harturik, oinarrizko zazpi unitateen definizioa zazpi konstante unibertsalen bidez ematea erabaki zen 2018ko 26. Batzar Orokorrean. Aukeratutako zazpi konstante horietako bat argiaren abiadura da. Hain, zuzen argiak hutsean duen abiadurak <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle c={\text{299 792 458 m s}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>299 792 458 m s</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle c={\text{299 792 458 m s}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62631b413f787cc1ebb2315b6eb3af80676485f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:22.075ex; height:2.676ex;" alt="{\textstyle c={\text{299 792 458 m s}}^{-1}}"></span>balio du. </p> <div class="mw-heading mw-heading2"><h2 id="Abiadura_mekanika_erlatibistan">Abiadura mekanika erlatibistan</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=21" title="Aldatu atal hau: «Abiadura mekanika erlatibistan»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=21" title="Edit section's source code: Abiadura mekanika erlatibistan"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><br />Mekanika erlatibistan, aldatu egin behar dira mekanika ez-erlatibistaren atalean esandako zenbait kontzeptu, bereziki goragoko atal batean elkarrekiko translazio-higidura zuzen eta uniformea duten bi erreferentzia-sistemaren kasuan azaldutako transformazioei buruzkoak. Izan ere, jadanik <a href="/wiki/Denbora" title="Denbora">denbora</a> eta <a href="/wiki/Lorentzen_uzkurdura" title="Lorentzen uzkurdura">espazioa</a> ez dira kontzeptu absolutuak, eta bi sistemetako behatzaileek (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>B</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b144e466a3757b4706daf24a45d4f1266700016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.449ex; height:2.509ex;" alt="{\displaystyle B'}"></span>) neurtzen dituzten abiaduren arteko transformazio-ekuazioak desberdinak baitira. </p><p>Ondorioz, abiaduren batuketa egitean, jadanik ez da betetzen mekanika klasikoaren ekuazio sinplea —alegia, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}={\boldsymbol {V}}+{\boldsymbol {v}}'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">V</mi> </mrow> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}={\boldsymbol {V}}+{\boldsymbol {v}}'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/285eb9eb04894621aeae96bb92f664f057759ac4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.319ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {v}}={\boldsymbol {V}}+{\boldsymbol {v}}'}"></span> batuketa—. Aitzitik, mekanika erlatibistan transformazio ekuazio hau hartu beharko dugu kontuan:<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v={\frac {V+v'}{1+{\frac {Vv'}{c^{2}}}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <mo>+</mo> <msup> <mi>v</mi> <mo>′</mo> </msup> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <msup> <mi>v</mi> <mo>′</mo> </msup> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={\frac {V+v'}{1+{\frac {Vv'}{c^{2}}}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aba7b986345132c48e8a6b419aa24b7341249f04" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:13.141ex; height:7.509ex;" alt="{\displaystyle v={\frac {V+v'}{1+{\frac {Vv'}{c^{2}}}}}.}"></span>Horrek mekanika ez-erlatibitaren arloan ulertu ezin diren ondorioak dauzka. </p><p>Adibidez, ikus dezagun zer gertatzen den <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9961844d1f539adee019e432dc18aa2a7ede59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.206ex; height:2.509ex;" alt="{\displaystyle S'}"></span> sistematik argia bera behatzean. Kasu horretan, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>B</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b144e466a3757b4706daf24a45d4f1266700016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.449ex; height:2.509ex;" alt="{\displaystyle B'}"></span> behatzaileak <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v'=c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>v</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v'=c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/170ec3cb01e8899af03f38fa91484c114e3df765" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.918ex; height:2.509ex;" alt="{\displaystyle v'=c}"></span> abiadura neurtuko du. Abiaduren batuketa erlatibistari dagokion formula aplikatuz gero, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> behatzaileak abiadura hau neurtuko du: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v={\frac {V+c}{1+{\frac {Vc}{c^{2}}}}}={\frac {V+c}{\frac {c^{2}+Vc}{c^{2}}}}={\frac {V+c}{\frac {c(c+V)}{c^{2}}}}=c.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <mo>+</mo> <mi>c</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <mi>c</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <mo>+</mo> <mi>c</mi> </mrow> <mfrac> <mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>V</mi> <mi>c</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <mo>+</mo> <mi>c</mi> </mrow> <mfrac> <mrow> <mi>c</mi> <mo stretchy="false">(</mo> <mi>c</mi> <mo>+</mo> <mi>V</mi> <mo stretchy="false">)</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mfrac> </mrow> <mo>=</mo> <mi>c</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={\frac {V+c}{1+{\frac {Vc}{c^{2}}}}}={\frac {V+c}{\frac {c^{2}+Vc}{c^{2}}}}={\frac {V+c}{\frac {c(c+V)}{c^{2}}}}=c.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3d5cd1ccdfe45da2f9c026fb2a767173e3594ba" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:36.214ex; height:7.509ex;" alt="{\displaystyle v={\frac {V+c}{1+{\frac {Vc}{c^{2}}}}}={\frac {V+c}{\frac {c^{2}+Vc}{c^{2}}}}={\frac {V+c}{\frac {c(c+V)}{c^{2}}}}=c.}"></span> </p><p>Alegia, argiaren abiadura <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d8f4833a2784cb7631b0d3853871d06cdfbafa0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.233ex; height:1.676ex;" alt="{\displaystyle v=c}"></span> izango da baita <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> sisteman ere. Emaitza hori guztiz ados dago erlatibitatearen teoriaren postulatuarekin: argiaren abiadura konstante unibertsala da. </p> <div class="mw-heading mw-heading2"><h2 id="Abiadura-modulua">Abiadura-modulua</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=22" title="Aldatu atal hau: «Abiadura-modulua»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=22" title="Edit section's source code: Abiadura-modulua"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Abiadura-</b> edo <b>lastertasun-modulua</b> egindako <a href="/wiki/Bitarte_(matematika)" class="mw-redirect" title="Bitarte (matematika)">bitartearen</a> eta bitartea osatzeko erabilitako denboraren arteko harremana da. Bere <a href="/wiki/Izari_fisiko" class="mw-redirect" title="Izari fisiko">izaria</a> <i>v</i> izendatzen da. Abiadura-modulua [<a href="/wiki/Luzera" class="mw-redirect" title="Luzera">L</a>]/[<a href="/wiki/Denbora" title="Denbora">t</a>] dimentsioko <a href="/w/index.php?title=Izari_eskalar&action=edit&redlink=1" class="new" title="Izari eskalar (sortu gabe)">izari eskalar</a> bat da. </p> <div class="mw-heading mw-heading2"><h2 id="Abiaduraren_bidez_definituriko_bi_magnitude_fisiko">Abiaduraren bidez definituriko bi magnitude fisiko</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=23" title="Aldatu atal hau: «Abiaduraren bidez definituriko bi magnitude fisiko»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=23" title="Edit section's source code: Abiaduraren bidez definituriko bi magnitude fisiko"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mekanika ez-erlatibistan, abiaduraren bidez definitzen dira bi magnitude hauek: </p> <ul><li><a href="/wiki/Momentu_lineal" title="Momentu lineal">Momentu lineala</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">p</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04cff366782c9fb192fc63992ef75ad59ee77695" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.052ex; width:1.449ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {p}}}"></span>) magnitude bektoriala da, partikularen <a href="/wiki/Masa" title="Masa">masa</a>ren eta abiaduraren biderkadura gisa definitua: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {p}}=m{\boldsymbol {v}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">p</mi> </mrow> <mo>=</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {p}}=m{\boldsymbol {v}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96c081943031dfa424d96fd458d74ae8b2e4a735" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.052ex; width:8.553ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {p}}=m{\boldsymbol {v}}.}"></span></li> <li><a href="/wiki/Energia_zinetiko" title="Energia zinetiko">Energia zinetikoa</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\text{k}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>k</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\text{k}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce71f608d367b0bb170515bcdb0cf74f7c6dcf73" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.815ex; height:2.509ex;" alt="{\displaystyle E_{\text{k}}}"></span>) magnitude eskalarra da: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\text{k}}={\frac {1}{2}}mv^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>k</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\text{k}}={\frac {1}{2}}mv^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ea528b71a10842a426decbd22527b9ba2c15551" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.782ex; height:5.176ex;" alt="{\displaystyle E_{\text{k}}={\frac {1}{2}}mv^{2}.}"></span></li></ul> <p>Gainera, partikularen masa konstantetzat hartzen da; hau da, beraren balioa ez da aldatzen abiadura handiagotzean, eta balio bera du erreferentzia-sisteman geldi egon zein <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span> abiaduraz ibili. </p><p><a href="/wiki/Erlatibitatearen_teoria" title="Erlatibitatearen teoria">Mekanika erlatibista</a>n, ordea, masa aldatu egiten da abiadurarekin, era honetan, hain zuzen: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {m_{0}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}=\gamma m_{0},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mfrac> </mrow> <mo>=</mo> <mi>γ</mi> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {m_{0}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}=\gamma m_{0},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b47f00763f0ace0b1317889dcc4c6726d7f2d4b1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:22.869ex; height:7.509ex;" alt="{\displaystyle m={\frac {m_{0}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}=\gamma m_{0},}"></span>non <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a6ff51ee949104fe6fae553cfbdfba29d5fac1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.095ex; height:2.009ex;" alt="{\displaystyle m_{0}}"></span> <i>pausaguneko masa</i> den, eta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }"></span> Lorentzen faktorea. Horrek momentu linealaren eta energiaren definizioen aldaketa dakar: </p> <ul><li>Momentu lineala honelaxe adierazten da pausaguneko masaren eta abiaduraren bidez: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {p}}=\gamma m_{0}{\boldsymbol {v}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">p</mi> </mrow> <mo>=</mo> <mi>γ</mi> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {p}}=\gamma m_{0}{\boldsymbol {v}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3341daa4d9193b45554f24be6f437ad0e6bb6c25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.052ex; width:10.87ex; height:2.176ex;" alt="{\displaystyle {\boldsymbol {p}}=\gamma m_{0}{\boldsymbol {v}}.}"></span></li> <li>Partikula geldi dagoela, hauxe da pausaguneko energia: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0}=m_{0}c^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}=m_{0}c^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f0a021357a032f1540e858738042215ead9657e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.67ex; height:3.009ex;" alt="{\displaystyle E_{0}=m_{0}c^{2}.}"></span></li> <li>Eta abiaduraz doan partikularen energia zinetikoa: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=mc^{2}=\gamma m_{0}c^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>m</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>γ</mi> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=mc^{2}=\gamma m_{0}c^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ee7d8a9460e663bf83a25a6546051d4095e097c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.139ex; height:3.176ex;" alt="{\displaystyle E=mc^{2}=\gamma m_{0}c^{2}.}"></span></li></ul> <p>Azkenik, energia osoaren adierazpena eta momentuaren definizioa konbinatzen baditugu,  faktore gabeko energia osoaren adierazpena lortuko dugu: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E^{2}=(m_{0}c^{2})^{2}+(pc)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mi>c</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E^{2}=(m_{0}c^{2})^{2}+(pc)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3968840308130f3dff5370666d11ec1f75c6694" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.846ex; height:3.176ex;" alt="{\displaystyle E^{2}=(m_{0}c^{2})^{2}+(pc)^{2}}"></span> </p><p>Masaren terminoa askatuta, honela geratzen da adierazpena: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E^{2}-p^{2}c^{2}={m_{0}}^{2}c^{4}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E^{2}-p^{2}c^{2}={m_{0}}^{2}c^{4}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ee90171b6bb422cf3882c1bb6b4a3d711cd95d8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.928ex; height:3.009ex;" alt="{\displaystyle E^{2}-p^{2}c^{2}={m_{0}}^{2}c^{4}.}"></span> </p><p>Eskuineko aldea konstantea denez, ezkerreko aldeak ere konstantea izan behar du, eta beraz, erreferentzia-sistema guztietan balio berbera izan behar du. Hau da, azken adierazpen hori aldaezin erlatibista da.<br /> </p> <div class="mw-heading mw-heading2"><h2 id="Ariketak"><figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/Fitxategi:Jakindun_logoa.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Jakindun_logoa.png/24px-Jakindun_logoa.png" decoding="async" width="24" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Jakindun_logoa.png/36px-Jakindun_logoa.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Jakindun_logoa.png/48px-Jakindun_logoa.png 2x" data-file-width="225" data-file-height="225" /></a><figcaption></figcaption></figure> Ariketak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=24" title="Aldatu atal hau: «Ariketak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=24" title="Edit section's source code: Ariketak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul class="gallery mw-gallery-packed" style="background-color: #fef6e7; margin-left: 0;"> <li class="gallerycaption">Distantzia, abiadura eta denbora</li> <li class="gallerybox" style="width: 215.33333333333px"> <div class="thumb" style="width: 213.33333333333px;"><span typeof="mw:File"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm/320px-seek%3D71-Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="214" height="120" data-durationhint="216" data-mwtitle="Distantzia,_abiadura,_denbora_ariketa_1.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/28/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/28/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/28/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/2/28/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm" type="video/webm; codecs="vp9, opus"" data-width="3840" data-height="2160" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/28/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/28/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/28/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/28/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_1.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span></span></div> <div class="gallerytext"><b>Distantzia, abiadura eta denbora</b> lantzeko ariketa.</div> </li> <li class="gallerybox" style="width: 215.33333333333px"> <div class="thumb" style="width: 213.33333333333px;"><span typeof="mw:File"><span><video id="mwe_player_1" poster="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm/320px-seek%3D71-Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="214" height="120" data-durationhint="218" data-mwtitle="Distantzia,_abiadura,_denbora_ariketa_2.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a9/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a9/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a9/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/a/a9/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm" type="video/webm; codecs="vp9, opus"" data-width="3840" data-height="2160" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a9/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a9/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a9/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a9/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm/Distantzia%2C_abiadura%2C_denbora_ariketa_2.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span></span></div> <div class="gallerytext"><b>Distantzia, abiadura eta denbora</b> lantzeko ariketa II.</div> </li> <li class="gallerybox" style="width: 215.33333333333px"> <div class="thumb" style="width: 213.33333333333px;"><span typeof="mw:File"><span><video id="mwe_player_2" poster="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Higidura_eta_unitateak_Ariketa_1_DBH3.webm/320px-seek%3D71-Higidura_eta_unitateak_Ariketa_1_DBH3.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="214" height="120" data-durationhint="234" data-mwtitle="Higidura_eta_unitateak_Ariketa_1_DBH3.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/1f/Higidura_eta_unitateak_Ariketa_1_DBH3.webm/Higidura_eta_unitateak_Ariketa_1_DBH3.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/1f/Higidura_eta_unitateak_Ariketa_1_DBH3.webm/Higidura_eta_unitateak_Ariketa_1_DBH3.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/1f/Higidura_eta_unitateak_Ariketa_1_DBH3.webm/Higidura_eta_unitateak_Ariketa_1_DBH3.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/1/1f/Higidura_eta_unitateak_Ariketa_1_DBH3.webm" type="video/webm; codecs="vp9, opus"" data-width="3840" data-height="2160" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/1f/Higidura_eta_unitateak_Ariketa_1_DBH3.webm/Higidura_eta_unitateak_Ariketa_1_DBH3.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/1f/Higidura_eta_unitateak_Ariketa_1_DBH3.webm/Higidura_eta_unitateak_Ariketa_1_DBH3.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/1f/Higidura_eta_unitateak_Ariketa_1_DBH3.webm/Higidura_eta_unitateak_Ariketa_1_DBH3.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/1/1f/Higidura_eta_unitateak_Ariketa_1_DBH3.webm/Higidura_eta_unitateak_Ariketa_1_DBH3.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span></span></div> <div class="gallerytext"><b>Higidura</b>, <b>abiadura unitateak</b> eta <b>azelerazio unitateak</b> lantzeko ariketa I.</div> </li> <li class="gallerybox" style="width: 215.33333333333px"> <div class="thumb" style="width: 213.33333333333px;"><span typeof="mw:File"><span><video id="mwe_player_3" poster="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Higidura_eta_unitateak_Ariketa_2_DBH3.webm/320px-seek%3D71-Higidura_eta_unitateak_Ariketa_2_DBH3.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="214" height="120" data-durationhint="322" data-mwtitle="Higidura_eta_unitateak_Ariketa_2_DBH3.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e0/Higidura_eta_unitateak_Ariketa_2_DBH3.webm/Higidura_eta_unitateak_Ariketa_2_DBH3.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e0/Higidura_eta_unitateak_Ariketa_2_DBH3.webm/Higidura_eta_unitateak_Ariketa_2_DBH3.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e0/Higidura_eta_unitateak_Ariketa_2_DBH3.webm/Higidura_eta_unitateak_Ariketa_2_DBH3.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/e/e0/Higidura_eta_unitateak_Ariketa_2_DBH3.webm" type="video/webm; codecs="vp9, opus"" data-width="3840" data-height="2160" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e0/Higidura_eta_unitateak_Ariketa_2_DBH3.webm/Higidura_eta_unitateak_Ariketa_2_DBH3.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e0/Higidura_eta_unitateak_Ariketa_2_DBH3.webm/Higidura_eta_unitateak_Ariketa_2_DBH3.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e0/Higidura_eta_unitateak_Ariketa_2_DBH3.webm/Higidura_eta_unitateak_Ariketa_2_DBH3.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e0/Higidura_eta_unitateak_Ariketa_2_DBH3.webm/Higidura_eta_unitateak_Ariketa_2_DBH3.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span></span></div> <div class="gallerytext"><b>Higidura</b>, <b>abiadura unitateak</b> eta <b>azelerazio unitateak</b> lantzeko ariketa II.</div> </li> <li class="gallerybox" style="width: 215.33333333333px"> <div class="thumb" style="width: 213.33333333333px;"><span typeof="mw:File"><span><video id="mwe_player_4" poster="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Higidura_eta_unitateak_Ariketa_3_DBH3.webm/320px-seek%3D71-Higidura_eta_unitateak_Ariketa_3_DBH3.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="214" height="120" data-durationhint="242" data-mwtitle="Higidura_eta_unitateak_Ariketa_3_DBH3.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d5/Higidura_eta_unitateak_Ariketa_3_DBH3.webm/Higidura_eta_unitateak_Ariketa_3_DBH3.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d5/Higidura_eta_unitateak_Ariketa_3_DBH3.webm/Higidura_eta_unitateak_Ariketa_3_DBH3.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d5/Higidura_eta_unitateak_Ariketa_3_DBH3.webm/Higidura_eta_unitateak_Ariketa_3_DBH3.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/d/d5/Higidura_eta_unitateak_Ariketa_3_DBH3.webm" type="video/webm; codecs="vp9, opus"" data-width="3840" data-height="2160" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d5/Higidura_eta_unitateak_Ariketa_3_DBH3.webm/Higidura_eta_unitateak_Ariketa_3_DBH3.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d5/Higidura_eta_unitateak_Ariketa_3_DBH3.webm/Higidura_eta_unitateak_Ariketa_3_DBH3.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d5/Higidura_eta_unitateak_Ariketa_3_DBH3.webm/Higidura_eta_unitateak_Ariketa_3_DBH3.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/d/d5/Higidura_eta_unitateak_Ariketa_3_DBH3.webm/Higidura_eta_unitateak_Ariketa_3_DBH3.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span></span></div> <div class="gallerytext"><b>Higidura</b>, <b>abiadura unitateak</b> eta <b>azelerazio unitateak</b> lantzeko ariketa III.</div> </li> <li class="gallerybox" style="width: 215.33333333333px"> <div class="thumb" style="width: 213.33333333333px;"><span typeof="mw:File"><span><video id="mwe_player_5" poster="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Higidura_eta_unitateak_Ariketa_4_DBH3.webm/320px-seek%3D71-Higidura_eta_unitateak_Ariketa_4_DBH3.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="214" height="120" data-durationhint="282" data-mwtitle="Higidura_eta_unitateak_Ariketa_4_DBH3.webm" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/52/Higidura_eta_unitateak_Ariketa_4_DBH3.webm/Higidura_eta_unitateak_Ariketa_4_DBH3.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/52/Higidura_eta_unitateak_Ariketa_4_DBH3.webm/Higidura_eta_unitateak_Ariketa_4_DBH3.webm.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/52/Higidura_eta_unitateak_Ariketa_4_DBH3.webm/Higidura_eta_unitateak_Ariketa_4_DBH3.webm.1080p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/5/52/Higidura_eta_unitateak_Ariketa_4_DBH3.webm" type="video/webm; codecs="vp9, opus"" data-width="3840" data-height="2160" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/52/Higidura_eta_unitateak_Ariketa_4_DBH3.webm/Higidura_eta_unitateak_Ariketa_4_DBH3.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/52/Higidura_eta_unitateak_Ariketa_4_DBH3.webm/Higidura_eta_unitateak_Ariketa_4_DBH3.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/52/Higidura_eta_unitateak_Ariketa_4_DBH3.webm/Higidura_eta_unitateak_Ariketa_4_DBH3.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/5/52/Higidura_eta_unitateak_Ariketa_4_DBH3.webm/Higidura_eta_unitateak_Ariketa_4_DBH3.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span></span></div> <div class="gallerytext"><b>Higidura</b>, <b>abiadura unitateak</b> eta <b>azelerazio unitateak</b> lantzeko ariketa IV.</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Erreferentziak">Erreferentziak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=25" title="Aldatu atal hau: «Erreferentziak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=25" title="Edit section's source code: Erreferentziak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">↑</a> <span class="reference-text"><span class="citation"> <span style="cursor: help; font-size: 90%; font-family: bold; color: gray" title="Ingelesez dago aipu honen iturburua"><b>(Ingelesez)</b></span></span> <span class="citation" id="CITEREFCeccarelli2006-12">Ceccarelli, Marco.  (2006-12). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S0094114X06000553">«Early TMM in Le Mecaniche by Galileo Galilei in 1593»</a> <i>Mechanism and Machine Theory</i> 41 (12): 1401–1406.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1016%2Fj.mechmachtheory.2006.02.005">10.1016/j.mechmachtheory.2006.02.005</a></span>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2023-03-01)</small></span></span>.</span> </li> <li id="cite_note-2"><a href="#cite_ref-2">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFBlay2004">Blay, Michel.  (2004). Palmerino, Carla Rita ed. <a rel="nofollow" class="external text" href="http://link.springer.com/10.1007/978-1-4020-2455-9_12">«Mathematization of the Science of Motion at the Turn of the Seventeenth and Eighteenth Centuries: Pierre Varignon»</a> <i>The Reception of the Galilean Science of Motion in Seventeenth-Century Europe</i> (Springer Netherlands) 239: 243–259.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2F978-1-4020-2455-9_12">10.1007/978-1-4020-2455-9_12</a></span>. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/978-90-481-6658-9" title="Berezi:BookSources/978-90-481-6658-9">978-90-481-6658-9</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2023-03-01)</small></span></span>.</span> </li> <li id="cite_note-3"><a href="#cite_ref-3">↑</a> <span class="reference-text"><span class="citation"> </span> <span class="citation"> <i>Fisika Orokorra. </i> UEU <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/84-8434-045-9" title="Berezi:BookSources/84-8434-045-9">84-8434-045-9</a>.</span>.</span> </li> <li id="cite_note-4"><a href="#cite_ref-4">↑</a> <span class="reference-text"><span class="citation"> </span> <span class="citation"> <i>Mekanika eta Uhinak. </i> Udako Euskal Unibertsitatea, 214-218 or. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/84-86967-42-2" title="Berezi:BookSources/84-86967-42-2">84-86967-42-2</a>.</span>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=26" title="Aldatu atal hau: «Bibliografia»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=26" title="Edit section's source code: Bibliografia"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation"></span>Aguirregabiria, Juan María.. (2004). <i>Mekanika klasikoa.</i> Universidad del País Vasco <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/84-8373-631-4" title="Berezi:BookSources/84-8373-631-4">84-8373-631-4</a> <a href="/wiki/PubMed_Central" class="mw-redirect" title="PubMed Central">PMC</a> 932541663</li></ul> <ul><li>Fishbane, Paul (2008) <i>Fisika zientzialari eta ingeniarientzat. 1. bolumena, (1.etik-21.era Gaiak)</i> Universidad del País Vasco/Euskal Herriko Unibertsitatea <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a><a href="/wiki/Berezi:BookSources/9788490820308" title="Berezi:BookSources/9788490820308">9788490820308</a><a href="/wiki/PubMed_Central" class="mw-redirect" title="PubMed Central">PMC</a>932800438.</li> <li>Etxebarria Bilbao, Jose Ramon (arg.) <i>Fisika orokorra (2. argitalpena)</i> UEU, Bilbo (2003) <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/9788484380450" title="Berezi:BookSources/9788484380450">9788484380450</a>.</li> <li>Marcelo Alonso, Edward J. Finn (1976). <i>Física</i>. Fondo Educativo Interamericano. <small>ISBN 84-03-20234-</small></li> <li>J.R. Etxebarria & F. Plazaola (1992) Mekanika eta Uhinak, UEU, Bilbo, <a href="/wiki/Berezi:BookSources/84-86967-42-2" title="Berezi:BookSources/84-86967-42-2">ISBN 84-86967-42-2</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Ikus,_gainera"><span id="Ikus.2C_gainera"></span>Ikus, gainera</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=27" title="Aldatu atal hau: «Ikus, gainera»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Abiadura&action=edit&section=27" title="Edit section's source code: Ikus, gainera"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="-moz-column-width:20em;-webkit-column-width:20em;column-width:20em;-moz-column-gap:1em;-webkit-column-gap:1em;column-gap:1em;text-align:left;"> <ul><li><a href="/wiki/Abiadura_angeluar" title="Abiadura angeluar">Abiadura angeluarra</a>.</li> <li><a href="/wiki/Azelerazio" title="Azelerazio">Azelerazioa</a>.</li> <li><a href="/wiki/Bektore_(argipena)" class="mw-disambig" title="Bektore (argipena)">bektore</a>.</li> <li><a href="/wiki/Deribatu" title="Deribatu">Deribatu</a>.</li> <li><a href="/wiki/Energia_zinetiko" title="Energia zinetiko">Energia zinetikoa</a>.</li> <li><a href="/wiki/Erreferentzia-sistema" title="Erreferentzia-sistema">Erreferentzia-sistema</a>.</li> <li><a href="/wiki/Ihes-abiadura" title="Ihes-abiadura">Ihes-abiadura</a>.</li> <li><a href="/wiki/Posizio" class="mw-redirect" title="Posizio">Posizioa</a>.</li> <li><a href="/wiki/Zinematika" title="Zinematika">Zinematika</a>.</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Kanpo_estekak">Kanpo estekak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abiadura&veaction=edit&section=28" title="Aldatu atal hau: «Kanpo estekak»" 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aria-labelledby="Autoritate_kontrola" style="width: inherit;padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Autoritate_kontrola" scope="row" class="navbox-group" style="width:1%;width: 12%; text-align:center;"><a href="/wiki/Laguntza:Autoritate_kontrola" title="Laguntza:Autoritate kontrola">Autoritate kontrola</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><b>Wikimedia proiektuak</b></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, 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href="https://commons.wikimedia.org/wiki/Category:Velocity">Velocity</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q11465%22">Q11465</a></span></span></li></ul> <hr /> <ul><li><b>Identifikadoreak</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Biblioth%C3%A8que_nationale_de_France" class="mw-redirect" title="Bibliothèque nationale de France">BNF</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119762787">119762787</a> <a rel="nofollow" class="external text" href="http://data.bnf.fr/ark:/12148/cb119762787">(data)</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Integrated_Authority_File" class="mw-redirect" title="Integrated Authority File">GND</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4020574-5">4020574-5</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Library_of_Congress_Control_Number" title="Library of Congress Control Number">LCCN</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85126486">sh85126486</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/National_Library_of_the_Czech_Republic" class="mw-redirect" title="National Library of the Czech Republic">NKC</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph872791">ph872791</a></span></li> <li><b>Hiztegiak eta entziklopediak</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Britannica</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/velocity">url</a></span></li></ul> </div></td></tr></tbody></table></div><div class="mw-mf-linked-projects hlist"> <ul><li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datuak:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q11465" class="extiw" title="wikidata:Q11465">Q11465</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Velocity">Velocity</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q11465%22">Q11465</a></span></span></li></ul> </div></div> <p><br /> </p> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9236167"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9236165"></div><div role="navigation" class="navbox" aria-labelledby="Zinematika" style="padding:3px"><table class="nowraplinks mw-collapsible 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