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Rotacija – Wikipedija/Википедија

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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">premjesti na bočnu traku</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</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">Početak</div> </a> </li> <li id="toc-Jednoliko_kružno_gibanje" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Jednoliko_kružno_gibanje"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Jednoliko kružno gibanje</span> </div> </a> <button aria-controls="toc-Jednoliko_kružno_gibanje-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>Uključi/isključi podsekciju Jednoliko kružno gibanje</span> </button> <ul id="toc-Jednoliko_kružno_gibanje-sublist" class="vector-toc-list"> <li id="toc-Obodna_brzina" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Obodna_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Obodna brzina</span> </div> </a> <ul id="toc-Obodna_brzina-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kutna_brzina" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kutna_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Kutna brzina</span> </div> </a> <ul id="toc-Kutna_brzina-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Nejednoliko_kružno_gibanje" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Nejednoliko_kružno_gibanje"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Nejednoliko kružno gibanje</span> </div> </a> <button aria-controls="toc-Nejednoliko_kružno_gibanje-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>Uključi/isključi podsekciju Nejednoliko kružno gibanje</span> </button> <ul id="toc-Nejednoliko_kružno_gibanje-sublist" class="vector-toc-list"> <li id="toc-Energija_vrtnje" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Energija_vrtnje"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Energija vrtnje</span> </div> </a> <ul id="toc-Energija_vrtnje-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Vlastita_vrtnja_ili_rotacija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vlastita_vrtnja_ili_rotacija"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Vlastita vrtnja ili rotacija</span> </div> </a> <button aria-controls="toc-Vlastita_vrtnja_ili_rotacija-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>Uključi/isključi podsekciju Vlastita vrtnja ili rotacija</span> </button> <ul id="toc-Vlastita_vrtnja_ili_rotacija-sublist" class="vector-toc-list"> <li id="toc-Zemljina_vrtnja" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zemljina_vrtnja"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Zemljina vrtnja</span> </div> </a> <ul id="toc-Zemljina_vrtnja-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Diferencijalna_rotacija" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Diferencijalna_rotacija"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Diferencijalna rotacija</span> </div> </a> <ul id="toc-Diferencijalna_rotacija-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Poveznice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Poveznice"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Poveznice</span> </div> </a> <ul id="toc-Poveznice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Izvori" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Izvori"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Izvori</span> </div> </a> <ul id="toc-Izvori-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="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" lang="sh-Latn" dir="ltr"> <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="Prikaži/sakrij sadržaj" > <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">Prikaži/sakrij sadržaj</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" lang="sh-Latn" dir="ltr"><span class="mw-page-title-main">Rotacija</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" lang="sh-Latn" dir="ltr"> <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="Prijedi na druge jezične varijante članka. Dostupno je na 76 jezika" > <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-76" 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">76 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D9%88%D8%B1%D8%A7%D9%86" title="دوران — Arapski" lang="ar" hreflang="ar" data-title="دوران" data-language-autonym="العربية" data-language-local-name="Arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Rotaci%C3%B3n" title="Rotación — Asturijski" lang="ast" hreflang="ast" data-title="Rotación" data-language-autonym="Asturianu" data-language-local-name="Asturijski" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%92%D1%8A%D1%80%D1%82%D0%B5%D0%BD%D0%B5" title="Въртене — Bugarski" lang="bg" hreflang="bg" data-title="Въртене" data-language-autonym="Български" data-language-local-name="Bugarski" 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%98%E0%A5%82%E0%A4%B0%E0%A5%8D%E0%A4%A3%E0%A4%A8" title="घूर्णन — Biharski" lang="bh" hreflang="bh" data-title="घूर्णन" data-language-autonym="भोजपुरी" data-language-local-name="Biharski" 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%98%E0%A7%82%E0%A6%B0%E0%A7%8D%E0%A6%A3%E0%A6%A8" title="ঘূর্ণন — Bengalski" lang="bn" hreflang="bn" data-title="ঘূর্ণন" data-language-autonym="বাংলা" data-language-local-name="Bengalski" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%A0%E0%BD%81%E0%BD%BC%E0%BD%A2%E0%BC%8B%E0%BD%A0%E0%BD%82%E0%BE%B2%E0%BD%BC%E0%BD%A6%E0%BC%8D" title="འཁོར་འགྲོས། — Tibetanski" lang="bo" hreflang="bo" data-title="འཁོར་འགྲོས།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetanski" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Rotacija" title="Rotacija — Bosanski" lang="bs" hreflang="bs" data-title="Rotacija" data-language-autonym="Bosanski" data-language-local-name="Bosanski" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Rotaci%C3%B3" title="Rotació — Katalonski" lang="ca" hreflang="ca" data-title="Rotació" data-language-autonym="Català" data-language-local-name="Katalonski" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AE%D9%88%D9%84%D8%A7%D9%86%DB%95%D9%88%DB%95" title="خولانەوە — centralnokurdski" lang="ckb" hreflang="ckb" data-title="خولانەوە" data-language-autonym="کوردی" data-language-local-name="centralnokurdski" 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/Ot%C3%A1%C4%8Den%C3%AD" title="Otáčení — Češki" lang="cs" hreflang="cs" data-title="Otáčení" data-language-autonym="Čeština" data-language-local-name="Češki" 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/%C3%87%D0%B0%D0%B2%D1%80%C4%83%D0%BD%D1%83" title="Çаврăну — Čuvaški" lang="cv" hreflang="cv" data-title="Çаврăну" data-language-autonym="Чӑвашла" data-language-local-name="Čuvaški" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Rotation" title="Rotation — Danski" lang="da" hreflang="da" data-title="Rotation" data-language-autonym="Dansk" data-language-local-name="Danski" 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/Rotation_(Physik)" title="Rotation (Physik) — Nemački" lang="de" hreflang="de" data-title="Rotation (Physik)" data-language-autonym="Deutsch" data-language-local-name="Nemački" 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%A0%CE%B5%CF%81%CE%B9%CF%83%CF%84%CF%81%CE%BF%CF%86%CE%AE" title="Περιστροφή — Grčki" lang="el" hreflang="el" data-title="Περιστροφή" data-language-autonym="Ελληνικά" data-language-local-name="Grčki" 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/Rotation" title="Rotation — Engleski" lang="en" hreflang="en" data-title="Rotation" data-language-autonym="English" data-language-local-name="Engleski" 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/Rotacio" title="Rotacio — Esperanto" lang="eo" hreflang="eo" data-title="Rotacio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" 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/Movimiento_de_rotaci%C3%B3n" title="Movimiento de rotación — Španski" lang="es" hreflang="es" data-title="Movimiento de rotación" data-language-autonym="Español" data-language-local-name="Španski" 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/P%C3%B6%C3%B6rlemine" title="Pöörlemine — Estonski" lang="et" hreflang="et" data-title="Pöörlemine" data-language-autonym="Eesti" data-language-local-name="Estonski" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Errotazio" title="Errotazio — Baskijski" lang="eu" hreflang="eu" data-title="Errotazio" data-language-autonym="Euskara" data-language-local-name="Baskijski" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D9%88%D8%B1%D8%A7%D9%86_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="دوران (هندسه) — Persijski" lang="fa" hreflang="fa" data-title="دوران (هندسه)" data-language-autonym="فارسی" data-language-local-name="Persijski" 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/Py%C3%B6rimisliike" title="Pyörimisliike — Finski" lang="fi" hreflang="fi" data-title="Pyörimisliike" data-language-autonym="Suomi" data-language-local-name="Finski" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Rotation_(physique)" title="Rotation (physique) — Francuski" lang="fr" hreflang="fr" data-title="Rotation (physique)" data-language-autonym="Français" data-language-local-name="Francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Rothl%C3%BA" title="Rothlú — Irski" lang="ga" hreflang="ga" data-title="Rothlú" data-language-autonym="Gaeilge" data-language-local-name="Irski" 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/Rotaci%C3%B3n" title="Rotación — Galski" lang="gl" hreflang="gl" data-title="Rotación" data-language-autonym="Galego" data-language-local-name="Galski" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%99%D7%91%D7%95%D7%91" title="סיבוב — Hebrejski" lang="he" hreflang="he" data-title="סיבוב" data-language-autonym="עברית" data-language-local-name="Hebrejski" 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%98%E0%A5%82%E0%A4%B0%E0%A5%8D%E0%A4%A3%E0%A4%A8" title="घूर्णन — Hindi" lang="hi" hreflang="hi" data-title="घूर्णन" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Vrtnja" title="Vrtnja — Hrvatski" lang="hr" hreflang="hr" data-title="Vrtnja" data-language-autonym="Hrvatski" data-language-local-name="Hrvatski" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Forg%C3%B3mozg%C3%A1s" title="Forgómozgás — Mađarski" lang="hu" hreflang="hu" data-title="Forgómozgás" data-language-autonym="Magyar" data-language-local-name="Mađarski" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Perputaran" title="Perputaran — Indonezijski" lang="id" hreflang="id" data-title="Perputaran" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonezijski" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Rotaco" title="Rotaco — Ido" lang="io" hreflang="io" data-title="Rotaco" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Rotazione" title="Rotazione — Italijanski" lang="it" hreflang="it" data-title="Rotazione" data-language-autonym="Italiano" data-language-local-name="Italijanski" 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/%E5%9B%9E%E8%BB%A2" title="回転 — Japanski" lang="ja" hreflang="ja" data-title="回転" data-language-autonym="日本語" data-language-local-name="Japanski" 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/Rotasi" title="Rotasi — Javanski" lang="jv" hreflang="jv" data-title="Rotasi" data-language-autonym="Jawa" data-language-local-name="Javanski" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D0%B9%D0%BD%D0%B0%D0%BB%D1%83" title="Айналу — Kozački" lang="kk" hreflang="kk" data-title="Айналу" data-language-autonym="Қазақша" data-language-local-name="Kozački" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AA%E0%B2%B0%E0%B2%BF%E0%B2%AD%E0%B3%8D%E0%B2%B0%E0%B2%AE%E0%B2%A3" title="ಪರಿಭ್ರಮಣ — Kanada" lang="kn" hreflang="kn" data-title="ಪರಿಭ್ರಮಣ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kanada" 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/%ED%9A%8C%EC%A0%84" title="회전 — Korejski" lang="ko" hreflang="ko" data-title="회전" data-language-autonym="한국어" data-language-local-name="Korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Rotatio" title="Rotatio — Latinski" lang="la" hreflang="la" data-title="Rotatio" data-language-autonym="Latina" data-language-local-name="Latinski" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Rot%C4%81cija" title="Rotācija — Letonski" lang="lv" hreflang="lv" data-title="Rotācija" data-language-autonym="Latviešu" data-language-local-name="Letonski" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%92%D1%80%D1%82%D0%B5%D1%9A%D0%B5" title="Вртење — Makedonski" lang="mk" hreflang="mk" data-title="Вртење" data-language-autonym="Македонски" data-language-local-name="Makedonski" 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%AD%E0%B5%8D%E0%B4%B0%E0%B4%AE%E0%B4%A3%E0%B4%82" title="ഭ്രമണം — Malajalam" lang="ml" hreflang="ml" data-title="ഭ്രമണം" data-language-autonym="മലയാളം" data-language-local-name="Malajalam" 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%AD%D1%80%D0%B3%D1%8D%D0%BB%D1%82" title="Эргэлт — Mongolski" lang="mn" hreflang="mn" data-title="Эргэлт" data-language-autonym="Монгол" data-language-local-name="Mongolski" 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%85%E0%A4%95%E0%A5%8D%E0%A4%B7" title="अक्ष — Marati" lang="mr" hreflang="mr" data-title="अक्ष" data-language-autonym="मराठी" data-language-local-name="Marati" 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/Putaran" title="Putaran — Malajski" lang="ms" hreflang="ms" data-title="Putaran" data-language-autonym="Bahasa Melayu" data-language-local-name="Malajski" 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%9C%E1%80%BE%E1%80%8A%E1%80%B7%E1%80%BA%E1%80%9C%E1%80%8A%E1%80%BA%E1%80%99%E1%80%BE%E1%80%AF" title="လှည့်လည်မှု — Burmanski" lang="my" hreflang="my" data-title="လှည့်လည်မှု" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmanski" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Rotatschoon_(Physik)" title="Rotatschoon (Physik) — Niski nemački" lang="nds" hreflang="nds" data-title="Rotatschoon (Physik)" data-language-autonym="Plattdüütsch" data-language-local-name="Niski nemački" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Rotatie_(natuurkunde)" title="Rotatie (natuurkunde) — Holandski" lang="nl" hreflang="nl" data-title="Rotatie (natuurkunde)" data-language-autonym="Nederlands" data-language-local-name="Holandski" 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/Rotasjon" title="Rotasjon — Norveški njorsk" lang="nn" hreflang="nn" data-title="Rotasjon" data-language-autonym="Norsk nynorsk" data-language-local-name="Norveški njorsk" 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/Rotasjon" title="Rotasjon — Norveški bokmål" lang="nb" hreflang="nb" data-title="Rotasjon" data-language-autonym="Norsk bokmål" data-language-local-name="Norveški bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Sochiin_Maraamarto" title="Sochiin Maraamarto — Oromo" lang="om" hreflang="om" data-title="Sochiin Maraamarto" data-language-autonym="Oromoo" data-language-local-name="Oromo" 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%97%E0%A9%87%E0%A9%9C%E0%A8%BE" title="ਗੇੜਾ — Pandžabski" lang="pa" hreflang="pa" data-title="ਗੇੜਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Pandžabski" 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/Obr%C3%B3t" title="Obrót — Poljski" lang="pl" hreflang="pl" data-title="Obrót" data-language-autonym="Polski" data-language-local-name="Poljski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Movimento_de_rota%C3%A7%C3%A3o" title="Movimento de rotação — Portugalski" lang="pt" hreflang="pt" data-title="Movimento de rotação" data-language-autonym="Português" data-language-local-name="Portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Rota%C8%9Bie" title="Rotație — Rumunski" lang="ro" hreflang="ro" data-title="Rotație" data-language-autonym="Română" data-language-local-name="Rumunski" 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%92%D1%80%D0%B0%D1%89%D0%B5%D0%BD%D0%B8%D0%B5" title="Вращение — Ruski" lang="ru" hreflang="ru" data-title="Вращение" data-language-autonym="Русский" data-language-local-name="Ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Rutazzioni" title="Rutazzioni — Sicilijanski" lang="scn" hreflang="scn" data-title="Rutazzioni" data-language-autonym="Sicilianu" data-language-local-name="Sicilijanski" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B7%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%B8%E0%B6%AB%E0%B6%BA" title="භ්‍රමණය — Singaleski" lang="si" hreflang="si" data-title="භ්‍රමණය" data-language-autonym="සිංහල" data-language-local-name="Singaleski" 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/Rotation" title="Rotation — Simple English" lang="en-simple" hreflang="en-simple" data-title="Rotation" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Vrtenje" title="Vrtenje — Slovenački" lang="sl" hreflang="sl" data-title="Vrtenje" data-language-autonym="Slovenščina" data-language-local-name="Slovenački" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Dendera" title="Dendera — Šona" lang="sn" hreflang="sn" data-title="Dendera" data-language-autonym="ChiShona" data-language-local-name="Šona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Wareega_Meere" title="Wareega Meere — Somalski" lang="so" hreflang="so" data-title="Wareega Meere" data-language-autonym="Soomaaliga" data-language-local-name="Somalski" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Rotaciono_kretanje_%C4%8Dvrstog_tela" title="Rotaciono kretanje čvrstog tela — Srpski" lang="sr" hreflang="sr" data-title="Rotaciono kretanje čvrstog tela" data-language-autonym="Српски / srpski" data-language-local-name="Srpski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Puteran" title="Puteran — Sudanski" lang="su" hreflang="su" data-title="Puteran" data-language-autonym="Sunda" data-language-local-name="Sudanski" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Rotation" title="Rotation — Švedski" lang="sv" hreflang="sv" data-title="Rotation" data-language-autonym="Svenska" data-language-local-name="Švedski" 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/Kujizungusha" title="Kujizungusha — Svahili" lang="sw" hreflang="sw" data-title="Kujizungusha" data-language-autonym="Kiswahili" data-language-local-name="Svahili" 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%9A%E0%AF%81%E0%AE%B4%E0%AE%B1%E0%AF%8D%E0%AE%9A%E0%AE%BF" title="சுழற்சி — Tamilski" lang="ta" hreflang="ta" data-title="சுழற்சி" data-language-autonym="தமிழ்" data-language-local-name="Tamilski" 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%AD%E0%B1%8D%E0%B0%B0%E0%B0%AE%E0%B0%A3%E0%B0%82" title="భ్రమణం — Telugu" lang="te" hreflang="te" data-title="భ్రమణం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%AB%E0%B8%A1%E0%B8%B8%E0%B8%99" title="การหมุน — Tajlandski" lang="th" hreflang="th" data-title="การหมุน" data-language-autonym="ไทย" data-language-local-name="Tajlandski" 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/Pag-ikot" title="Pag-ikot — Tagalski" lang="tl" hreflang="tl" data-title="Pag-ikot" data-language-autonym="Tagalog" data-language-local-name="Tagalski" 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/D%C3%B6nme" title="Dönme — Turski" lang="tr" hreflang="tr" data-title="Dönme" data-language-autonym="Türkçe" data-language-local-name="Turski" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9E%D0%B1%D0%B5%D1%80%D1%82%D0%B0%D0%BD%D0%BD%D1%8F" title="Обертання — Ukrajinski" lang="uk" hreflang="uk" data-title="Обертання" data-language-autonym="Українська" data-language-local-name="Ukrajinski" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Quay" title="Quay — Vijetnamski" lang="vi" hreflang="vi" data-title="Quay" data-language-autonym="Tiếng Việt" data-language-local-name="Vijetnamski" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%BD%AC%E5%8A%A8" title="转动 — Wu kineski" lang="wuu" hreflang="wuu" data-title="转动" data-language-autonym="吴语" data-language-local-name="Wu kineski" 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/Ukujikeleza_ndawonye" title="Ukujikeleza ndawonye — Khosa" lang="xh" hreflang="xh" data-title="Ukujikeleza ndawonye" data-language-autonym="IsiXhosa" data-language-local-name="Khosa" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%BD%AC%E5%8A%A8" title="转动 — Kineski" lang="zh" hreflang="zh" data-title="转动" data-language-autonym="中文" data-language-local-name="Kineski" 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/%E8%87%AA%E8%BD%89" title="自轉 — Literary Chinese" lang="lzh" hreflang="lzh" data-title="自轉" 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-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%BD%89%E5%8B%95" title="轉動 — kantonski" lang="yue" hreflang="yue" data-title="轉動" data-language-autonym="粵語" data-language-local-name="kantonski" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q107617#sitelinks-wikipedia" title="Uredi međujezične poveznice" class="wbc-editpage">Uredi veze</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" lang="sh-Latn" dir="ltr"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Rotacija" title="Vidi stranicu sadržaja [c]" accesskey="c"><span>Stranica</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Razgovor:Rotacija&amp;action=edit&amp;redlink=1" rel="discussion" class="new" title="Razgovarajte o sadržini ove stranice (stranica ne postoji) [t]" accesskey="t"><span>Razgovor</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " lang="sh-Latn" dir="ltr"> <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Promijeni jezičnu varijantu" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Latinica</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants" lang="sh-Latn" dir="ltr"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-varlang-0" class="selected ca-variants-sh-Latn mw-list-item"><a href="/w/index.php?title=Rotacija&amp;variant=sh-latn" lang="sh-Latn" hreflang="sh-Latn"><span>Latinica</span></a></li><li id="ca-varlang-1" class="ca-variants-sh-Cyrl mw-list-item"><a href="/w/index.php?title=Rotacija&amp;variant=sh-cyrl" lang="sh-Cyrl" hreflang="sh-Cyrl"><span>Ћирилица</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Teme"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" lang="sh-Latn" dir="ltr"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Rotacija"><span>Prikaži</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Rotacija&amp;veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Rotacija&amp;action=edit" title="Uredite izvorni kod ove stranice [e]" accesskey="e"><span>Uredi kod</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Rotacija&amp;action=history" title="Pogledajte prethodne verzije ove stranice [h]" accesskey="h"><span>Historija</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" lang="sh-Latn" dir="ltr"> <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" 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class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Rotacija&amp;action=edit" title="Uredite izvorni kod ove stranice [e]" accesskey="e"><span>Uredi kod</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Rotacija&amp;action=history"><span>Historija</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" lang="sh-Latn" dir="ltr"> <div class="vector-menu-heading"> Opšte </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Posebno:%C5%A0to_vodi_ovdje/Rotacija" title="Pogledajte listu svih stranica koje vode ovamo [j]" accesskey="j"><span>Šta vodi ovamo</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Posebno:Povezane_izmjene/Rotacija" rel="nofollow" title="Prelistajte nedavne izmjene stranica koje su povezane s ovom [k]" accesskey="k"><span>Povezane izmjene</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Posebno:Posebne_stranice" title="Pregledajte listu svih posebnih stranica [q]" accesskey="q"><span>Posebne stranice</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Rotacija&amp;oldid=41038347" title="Nabavite trajnu vezu do ove verzije stranice"><span>Trajna veza</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Rotacija&amp;action=info" title="Pronađite više informacija o ovoj stranici"><span>Podaci o stranici</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Posebno:Citiraj&amp;page=Rotacija&amp;id=41038347&amp;wpFormIdentifier=titleform" title="Saznajte kako da citirate ovu stranicu"><span>Citiraj stranicu</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Posebno:Skra%C4%87iva%C4%8D_adresa&amp;url=https%3A%2F%2Fsh.wikipedia.org%2Fwiki%2FRotacija"><span>Skrati URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Posebno:QrCode&amp;url=https%3A%2F%2Fsh.wikipedia.org%2Fwiki%2FRotacija"><span>Preuzmi QR kod</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" lang="sh-Latn" dir="ltr"> <div class="vector-menu-heading"> Štampanje/izvoz </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Posebno:Kolekcija&amp;bookcmd=book_creator&amp;referer=Rotacija"><span>Napravi knjigu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Posebno:DownloadAsPdf&amp;page=Rotacija&amp;action=show-download-screen"><span>Preuzmi kao PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Rotacija&amp;printable=yes" title="Odštampajte ovu stranicu [p]" accesskey="p"><span>Odštampaj</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" lang="sh-Latn" dir="ltr"> <div class="vector-menu-heading"> Na drugim projektima </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Rotation" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q107617" title="Pogledajte povezanu stavku u skladištu podataka [g]" accesskey="g"><span>Stavka na Wikipodacima</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Izgled"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti na bočnu traku</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Izvor: Wikipedija</div> </div> <div id="contentSub" lang="sh-Latn" dir="ltr"><div id="mw-content-subtitle" lang="sh-Latn" dir="ltr"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sh-Latn" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Rotating_Sphere.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/0/02/Rotating_Sphere.gif" decoding="async" width="100" height="121" class="mw-file-element" data-file-width="100" data-file-height="121" /></a><figcaption> Vrtnja <a href="/wiki/Kugla" class="mw-redirect" title="Kugla">kugle</a> oko svoje <a href="/wiki/Os" title="Os">osi</a>.</figcaption></figure> <p><b>Vrtnja</b> ili <b>rotacija</b> (<a href="/wiki/Latinski_jezik" title="Latinski jezik">lat</a>. <i>rotatio</i>: okretanje, obrtanje), u <a href="/wiki/Fizika" title="Fizika">fizici</a>, je okretanje krutoga <a href="/wiki/Tijelo_(fizika)" title="Tijelo (fizika)">tijela</a> oko <a href="/wiki/Os" title="Os">osi</a>. Točke tijela u vrtnji opisuju <a href="/wiki/Kru%C5%BEnica" title="Kružnica">kružnice</a> kojima je središte na osi vrtnje, miruju jedino točke na osi vrtnje. Vrtnja može biti jednolika, jednoliko ubrzana ili nepravilna. <sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Jednoliko_kružno_gibanje"><span id="Jednoliko_kru.C5.BEno_gibanje"></span>Jednoliko kružno gibanje</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotacija&amp;veaction=edit&amp;section=1" title="Uredi odjeljak Jednoliko kružno gibanje" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rotacija&amp;action=edit&amp;section=1" title="Uredi kôd odjeljka Jednoliko kružno gibanje"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Okreće li se neki <a href="/wiki/Kota%C4%8D" title="Kotač">kotač</a> uvijek istom <a href="/wiki/Brzina" title="Brzina">brzinom</a>, odnosno ako čini uvijek isti <a href="/wiki/Broj_okretaja" title="Broj okretaja">broj okretaja</a> u jednoj <a href="/wiki/Sekunda" class="mw-redirect" title="Sekunda">sekundi</a>, kažemo da taj kotač vrši jednoliko kružno gibanje. Jednoliko kružno gibanje je takvo gibanje kod kojeg se neko tijelo, odnosno neka materijalna točka, giba jednoliko po kružnici. Kod ovog gibanja moramo razlikovati dvije brzine: </p> <ul><li>obodna brzina (ili linearna brzina) - jedinica <a href="/wiki/Metar_u_sekundi" title="Metar u sekundi">metara u sekundi</a> (m/s)</li> <li>kutna brzina - jedinica <a href="/wiki/Radijan" title="Radijan">radijana</a> u sekundi (rad/s).</li></ul> <div class="mw-heading mw-heading3"><h3 id="Obodna_brzina">Obodna brzina</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotacija&amp;veaction=edit&amp;section=2" title="Uredi odjeljak Obodna brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rotacija&amp;action=edit&amp;section=2" title="Uredi kôd odjeljka Obodna brzina"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><div class="noprint relarticle mainarticle"><i>Glavni članak: <a href="/wiki/Orbitalna_brzina" title="Orbitalna brzina">Orbitalna brzina</a></i></div></dd></dl> <p>Ako neka točka učini <i>n</i> <a href="/wiki/Broj_okretaja" title="Broj okretaja">okretaja u sekundi</a> (oznaka okr/s, 1/s ili s<sup>-1</sup>), a za vrijeme jednog okreta učini put od <i>2 ∙ r ∙ π</i> (odnosno <i>d ∙ π</i>, gdje je <i>d</i> - <a href="/wiki/Promjer" title="Promjer">promjer</a> vrtnje), gdje je <i>r</i> - polumjer vrtnje, onda je prijeđeni put te točke <i>2 ∙ r ∙ π ∙ n</i>, a obodna brzina iznosi: </p> <dl><dd><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\cdot r\cdot \pi \cdot n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mn>2</mn> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>r</mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>&#x03C0;<!-- π --></mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=2\cdot r\cdot \pi \cdot n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/408cb6143f7c2c50d4a54e51ce777e47b0abdd58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.201ex; height:2.176ex;" alt="{\displaystyle v=2\cdot r\cdot \pi \cdot n}"></span></dd></dl> <p>odnosno: </p> <dl><dd><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=d\cdot \pi \cdot n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mi>d</mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>&#x03C0;<!-- π --></mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=d\cdot \pi \cdot n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a76929d1432b2d79aa0a8f65daaf7692c14992f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.527ex; height:2.176ex;" alt="{\displaystyle v=d\cdot \pi \cdot n}"></span></dd></dl> <p>Računamo li broj okretaja u jednoj <a href="/wiki/Minuta" class="mw-redirect" title="Minuta">minuti</a>, koja iznosi 60 sekundi, onda imamo izraze za obodnu brzinu: </p> <dl><dd><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={\frac {r\cdot \pi \cdot n}{30}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>r</mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>&#x03C0;<!-- π --></mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>n</mi> </mrow> <mn>30</mn> </mfrac> </mrow> <mtext>&#xA0;</mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={\frac {r\cdot \pi \cdot n}{30}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a738321d211953c97686bd95d861b87bd859679f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.776ex; height:4.676ex;" alt="{\displaystyle v={\frac {r\cdot \pi \cdot n}{30}}\ }"></span></dd></dl> <p>odnosno: </p> <dl><dd><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={\frac {d\cdot \pi \cdot n}{60}}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>&#x03C0;<!-- π --></mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>n</mi> </mrow> <mn>60</mn> </mfrac> </mrow> <mtext>&#xA0;</mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={\frac {d\cdot \pi \cdot n}{60}}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac894c94b104b992256a6039a7fcdf666ea90d94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.944ex; height:5.343ex;" alt="{\displaystyle v={\frac {d\cdot \pi \cdot n}{60}}\ }"></span></dd></dl> <p>Obodna brzina je brojčano jednaka duljini <a href="/wiki/Luk_(matematika)" title="Luk (matematika)">luka</a> što ga učini točka na obodu kružnice u jednoj sekundi. Ona u svakoj točki ima smjer tangente koji se stalno mijenja, ali joj veličina ostaje ista. <sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup> </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Angular_velocity.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Angular_velocity.svg/250px-Angular_velocity.svg.png" decoding="async" width="250" height="189" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Angular_velocity.svg/375px-Angular_velocity.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Angular_velocity.svg/500px-Angular_velocity.svg.png 2x" data-file-width="352" data-file-height="266" /></a><figcaption><a href="/wiki/Vektor" title="Vektor">Vektor</a> <a href="/wiki/Kutna_brzina" title="Kutna brzina">kutne brzine</a> <i>ω</i> i <a href="/wiki/Radijvektor" class="mw-redirect" title="Radijvektor">radijvektor</a> <i>r</i></figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Kutna_brzina">Kutna brzina</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotacija&amp;veaction=edit&amp;section=3" title="Uredi odjeljak Kutna brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rotacija&amp;action=edit&amp;section=3" title="Uredi kôd odjeljka Kutna brzina"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><div class="noprint relarticle mainarticle"><i>Glavni članak: <a href="/wiki/Kutna_brzina" title="Kutna brzina">Kutna brzina</a></i></div></dd></dl> <p>Ako se točka vrti stalnom obodnom brzinom <i>v</i> po kružnici, <a href="/wiki/Radijvektor" class="mw-redirect" title="Radijvektor">radijvektor</a> te točke opisuje u svakoj sekundi jednak <a href="/wiki/Kut" class="mw-redirect" title="Kut">kut</a>. Kut što ga opiše radijvektor u jednoj sekundi zove se kutne brzina. Kutna brzina mjeri se u <a href="/wiki/Radijan" title="Radijan">radijanima</a> u sekundi (rad/s). Jedan radijan je luk koji je jednak <a href="/wiki/Polumjer" class="mw-redirect" title="Polumjer">polumjeru</a> (radijusu), a oba pripadaju istoj kružnici. Budući da je <a href="/wiki/Opseg" title="Opseg">opseg</a> kružnice <i>2 ∙ r ∙ π</i>, čitav opseg, odnosno puni <a href="/wiki/Kut" class="mw-redirect" title="Kut">kut</a> od 360° ima <i>2 ∙ π</i> radijana. </p> <dl><dd><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 360^{\circ }=2\pi \,\mathrm {rad} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>&#x2218;<!-- ∘ --></mo> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mi>&#x03C0;<!-- π --></mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 360^{\circ }=2\pi \,\mathrm {rad} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3acfb2df836c5ff487617d784fd08181d1d5e167" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.888ex; height:2.343ex;" alt="{\displaystyle 360^{\circ }=2\pi \,\mathrm {rad} }"></span></dd></dl> <p>ili: </p> <dl><dd><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 1\,\mathrm {rad} ={\frac {360^{\circ }}{2\pi }}\approx 57{,}29577951^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>&#x2218;<!-- ∘ --></mo> </mrow> </msup> <mrow> <mn>2</mn> <mi>&#x03C0;<!-- π --></mi> </mrow> </mfrac> </mrow> <mo>&#x2248;<!-- ≈ --></mo> <mn>57,295</mn> <msup> <mn>77951</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>&#x2218;<!-- ∘ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1\,\mathrm {rad} ={\frac {360^{\circ }}{2\pi }}\approx 57{,}29577951^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cee2326ff787458916a5239a6f1e167d391a0a49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:29.816ex; height:5.343ex;" alt="{\displaystyle 1\,\mathrm {rad} ={\frac {360^{\circ }}{2\pi }}\approx 57{,}29577951^{\circ }}"></span></dd></dl> <p>Budući da točka u jednom okretu prijeđe put od <i>2 ∙ π</i> radijana, to znači da za vrijeme jedne sekunde prijeđe put od <i>2 ∙ π ∙ n</i> radijana. Kako je brzina prijeđeni put u jednoj sekundi, dobivamo da je kutna brzina <i>ω</i>: </p> <dl><dd><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 \omega =2\cdot \pi \cdot n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C9;<!-- ω --></mi> <mo>=</mo> <mn>2</mn> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>&#x03C0;<!-- π --></mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega =2\cdot \pi \cdot n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b93f0fff59b1e0ea46f58a10043b66885edbf0e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.792ex; height:2.176ex;" alt="{\displaystyle \omega =2\cdot \pi \cdot n}"></span></dd></dl> <p>Računamo li broj okretaja u jednoj minuti, koja iznosi 60 sekundi, onda dobivamo izraze za kutnu brzinu: </p> <dl><dd><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 \omega ={{2\cdot \pi \cdot n} \over 60}={{\pi \cdot n} \over 30}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C9;<!-- ω --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>&#x03C0;<!-- π --></mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>n</mi> </mrow> <mn>60</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x03C0;<!-- π --></mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>n</mi> </mrow> <mn>30</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega ={{2\cdot \pi \cdot n} \over 60}={{\pi \cdot n} \over 30}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8856b89c05415ceedcf776d3f15e351225cfef5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.968ex; height:5.176ex;" alt="{\displaystyle \omega ={{2\cdot \pi \cdot n} \over 60}={{\pi \cdot n} \over 30}}"></span></dd></dl> <p>Uvrstimo li u izraz za obodnu brzinu gornji izraz za kutnu brzinu, dobivamo: </p> <dl><dd><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=r\cdot \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mi>r</mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>&#x03C9;<!-- ω --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=r\cdot \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c0a99fa0ed94eb8e5a92ce65711d09a5c320ee5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.4ex; height:1.676ex;" alt="{\displaystyle v=r\cdot \omega }"></span></dd></dl> <p>To znači što je veći polumjer vrtnje, to je i obodna brzina veća pri istoj kutnoj brzini. </p> <div class="mw-heading mw-heading2"><h2 id="Nejednoliko_kružno_gibanje"><span id="Nejednoliko_kru.C5.BEno_gibanje"></span>Nejednoliko kružno gibanje</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotacija&amp;veaction=edit&amp;section=4" title="Uredi odjeljak Nejednoliko kružno gibanje" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rotacija&amp;action=edit&amp;section=4" title="Uredi kôd odjeljka Nejednoliko kružno gibanje"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pri nejednolikoj vrtnji svaka točka u jedinici vremena prevali <a href="/wiki/Kut" class="mw-redirect" title="Kut">kut</a> <i>φ</i>, pa je kutna brzina: </p> <dl><dd><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 \omega ={\frac {\mathrm {d} \varphi }{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C9;<!-- ω --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>&#x03C6;<!-- φ --></mi> </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 \omega ={\frac {\mathrm {d} \varphi }{\mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cceb4a7273da6da58be11e3c682f98b8513cd6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.193ex; height:5.509ex;" alt="{\displaystyle \omega ={\frac {\mathrm {d} \varphi }{\mathrm {d} t}}}"></span></dd></dl> <p>a pri nejednoliko ubrzanoj vrtnji promjena kutne brzine u jedinici vremena nejednaka je i naziva se kutno <a href="/wiki/Ubrzanje" title="Ubrzanje">ubrzanje</a> ili kutna akceleracija: </p> <dl><dd><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 {\alpha }={\frac {d\omega }{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>&#x03B1;<!-- α --></mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>&#x03C9;<!-- ω --></mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\alpha }={\frac {d\omega }{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b094ce854968b287543c62fa1ee5a8b15784c4f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.084ex; height:5.509ex;" alt="{\displaystyle {\alpha }={\frac {d\omega }{dt}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Energija_vrtnje">Energija vrtnje</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotacija&amp;veaction=edit&amp;section=5" title="Uredi odjeljak Energija vrtnje" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rotacija&amp;action=edit&amp;section=5" title="Uredi kôd odjeljka Energija vrtnje"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Energija tijela u vrtnji jest: </p> <dl><dd><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={\frac {\omega ^{2}}{2}}I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>&#x03C9;<!-- ω --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>2</mn> </mfrac> </mrow> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E={\frac {\omega ^{2}}{2}}I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12aca95307cd93ea10cb0d7359ab01d64eedb314" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.382ex; height:5.676ex;" alt="{\displaystyle E={\frac {\omega ^{2}}{2}}I}"></span></dd></dl> <p>gdje je: <i>I</i> - <a href="/wiki/Moment_tromosti" class="mw-redirect" title="Moment tromosti">moment tromosti</a> ili moment inercije, <i>m</i> - <a href="/wiki/Masa" title="Masa">masa</a>, a <i>r</i> - udaljenost točke od osi vrtnje. </p><p><a href="/wiki/Kutna_koli%C4%8Dina_gibanja" class="mw-redirect" title="Kutna količina gibanja">kutna količina gibanja</a> određena je s: </p> <dl><dd><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 L=I\cdot \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mi>I</mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>&#x03C9;<!-- ω --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=I\cdot \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d008520600a44f2350e26929d1274b327db31d14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.978ex; height:2.176ex;" alt="{\displaystyle L=I\cdot \omega }"></span></dd></dl> <p>a <a href="/wiki/Moment_sile" class="mw-redirect" title="Moment sile">moment sile</a> s: </p> <dl><dd><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=I\cdot \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mi>I</mi> <mo>&#x22C5;<!-- ⋅ --></mo> <mi>&#x03B1;<!-- α --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M=I\cdot \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40ea458991d9f59bd609e81fd1e830e1d67d9ec6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.879ex; height:2.176ex;" alt="{\displaystyle M=I\cdot \alpha }"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Vlastita_vrtnja_ili_rotacija">Vlastita vrtnja ili rotacija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotacija&amp;veaction=edit&amp;section=6" title="Uredi odjeljak Vlastita vrtnja ili rotacija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rotacija&amp;action=edit&amp;section=6" title="Uredi kôd odjeljka Vlastita vrtnja ili rotacija"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kad se promatra <a href="/wiki/Gibanje" class="mw-redirect" title="Gibanje">gibanje</a> <a href="/wiki/Tijelo_(fizika)" title="Tijelo (fizika)">tijela</a> s utvrđenom točkom, na primjer gibanje <a href="/w/index.php?title=Zvrk&amp;action=edit&amp;redlink=1" class="new" title="Zvrk (stranica ne postoji)">zvrka</a>, <a href="/wiki/Os" title="Os">os</a> rotacije kojega može mijenjati smjer zbog učinka vanjskih <a href="/wiki/Sila" title="Sila">sila</a>, njegova rotacija oko osi naziva se vlastita, zato što tijelo tada može izvoditi složeno gibanje, to jest još i <a href="/wiki/Precesija" title="Precesija">precesiju</a> i <a href="/wiki/Nutacija" title="Nutacija">nutaciju</a>, koje se također mogu tumačiti kao rotacije oko određenih osi, ali koje nisu čvrsto spojene sa samim tijelom. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Praezession.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Praezession.svg/250px-Praezession.svg.png" decoding="async" width="250" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Praezession.svg/375px-Praezession.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Praezession.svg/500px-Praezession.svg.png 2x" data-file-width="500" data-file-height="600" /></a><figcaption><a href="/wiki/Nebeska_sfera" title="Nebeska sfera">Nebeski svod</a> se kreće po <a href="/wiki/Krivulja" title="Krivulja">krivulji</a>, koja je <a href="/wiki/Rezultanta" title="Rezultanta">rezultanta</a> uzajamnog djelovanja <a href="/wiki/Zemljina_rotacija" title="Zemljina rotacija">Zemljine vrtnje</a> (zeleno), <a href="/wiki/Zemljina_precesija" title="Zemljina precesija">Zemljine precesije</a> (plavo) i <a href="/wiki/Nutacija" title="Nutacija">nutacije</a> (crveno).</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Zemljina_vrtnja">Zemljina vrtnja</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotacija&amp;veaction=edit&amp;section=7" title="Uredi odjeljak Zemljina vrtnja" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rotacija&amp;action=edit&amp;section=7" title="Uredi kôd odjeljka Zemljina vrtnja"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><div class="noprint relarticle mainarticle"><i>Glavni članak: <a href="/wiki/Zemljina_putanja" title="Zemljina putanja">Zemljina putanja</a></i></div></dd></dl> <p><a href="/wiki/Zemlja" title="Zemlja">Zemlja</a> se okreće oko svoje osi (rotacija ili okretanje) od zapada prema istoku, te joj je za jedan puni okret potrebno oko 24 <a href="/wiki/Sat" class="mw-redirect" title="Sat">sata</a>, vremenski razmak koji se naziva Sunčevim danom (<a href="/w/index.php?title=Sinodi%C4%8Dki_dan&amp;action=edit&amp;redlink=1" class="new" title="Sinodički dan (stranica ne postoji)">sinodički dan</a>). Rotaciju Zemlje nije moguće osjetiti. Svaka Zemljina točka (osim sjevernog i južnog pola) sudjeluje u rotaciji Zemlje odnosno opisuje krugove oko Zemljine osi. Pritom najveće krugove prave točke na <a href="/wiki/Ekvator" title="Ekvator">ekvatoru</a>, koje se ujedno i najbrže kreću. Zbog rotacije događa se izmjenjivanje dana, noći i dnevne topline pa Sunce stoga u jednom trenutku obasjava samo jedan dio Zemlje. </p><p>Period Zemljine vrtnje jest 1 zvjezdani dan ili <a href="/wiki/Sideri%C4%8Dki_dan" class="mw-redirect" title="Siderički dan">siderički dan</a> (23 h 56 min 4,1 s), a srednji period vrtnje s obzirom na osunčenje jednak je jednomu srednjemu Sunčevu danu (1 dan). Period vrtnje nije stalan, već ovisi o sezonskim i sekularnim premještanjima masa na površini Zemlje i unutar nje; promjene se prate s pomoću <a href="/wiki/Radio_astronomija" class="mw-redirect" title="Radio astronomija">radioastronomskih</a> interferometrijskih sustava s velikom osnovicom (<a href="/wiki/Dugobazi%C4%8Dna_interferometrija" title="Dugobazična interferometrija">dugobazična interferometrija</a>). Zbog <a href="/wiki/Morske_mijene" class="mw-redirect" title="Morske mijene">plima i oseka</a>, period Zemljine vrtnje stalno se produljuje. Kao posljedica plimnog međudjelovanja (<a href="/wiki/Plimna_sila" title="Plimna sila">plimna sila</a>) <a href="/wiki/Mjesec" title="Mjesec">Mjeseca</a> i Zemlje, količina gibanja Mjeseca povećava se i on se udaljava od Zemlje, u sadašnjem trenutku gotovo 4 centimetra na godinu. Zemlja ima <a href="/wiki/Godi%C5%A1nja_doba" class="mw-redirect" title="Godišnja doba">godišnja doba</a> zbog nagiba <a href="/wiki/Ekvator" title="Ekvator">ekvatora</a> prema <a href="/wiki/Ekliptika" title="Ekliptika">ekliptici</a> od 23° 26'. Taj se nagib mijenja u periodu od 41 000 godina, od 22,1° do 24,5°. Sada se smanjuje 0,47" na godinu. Period promjene izduženosti staze, precesije ekvinokcija i nagiba ekvatora, astronomski su činitelji pojave <a href="/wiki/Ledeno_doba" title="Ledeno doba">ledenih doba</a> prema teoriji <a href="/wiki/Milutin_Milankovi%C4%87" title="Milutin Milanković">Milutina Milankovića</a> (<a href="/wiki/Milankovi%C4%87evi_ciklusi" title="Milankovićevi ciklusi">Milankovićevi ciklusi</a>). Toplinska ravnoteža Zemlje uvjetovana je dotokom energije Sunčevim zračenjem; <a href="/wiki/Sun%C4%8Deva_konstanta" title="Sunčeva konstanta">Sunčeva konstanta</a> iznosi 1 367,7 ± 6 W/m², a promjena je uvjetovana ciklusom Sunčeve aktivnosti (<a href="/wiki/Sun%C4%8Dev_ciklus" title="Sunčev ciklus">Sunčev ciklus</a>), koji se u prosjeku mijenja svakih 11 godina. <sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">&#91;</span>3<span class="cite-bracket">&#93;</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Diferencijalna_rotacija">Diferencijalna rotacija</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotacija&amp;veaction=edit&amp;section=8" title="Uredi odjeljak Diferencijalna rotacija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rotacija&amp;action=edit&amp;section=8" title="Uredi kôd odjeljka Diferencijalna rotacija"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Diferencijalna rotacija</b> je pojava različitih <a href="/wiki/Period" class="mw-redirect" title="Period">perioda</a> vrtnje dijelova <a href="/wiki/Nebesko_tijelo" title="Nebesko tijelo">nebeskog tijela</a> koje nije kruto, na primjer <a href="/wiki/Jupiter" title="Jupiter">Jupitera</a> i <a href="/wiki/Sunce" title="Sunce">Sunca</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Poveznice">Poveznice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotacija&amp;veaction=edit&amp;section=9" title="Uredi odjeljak Poveznice" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rotacija&amp;action=edit&amp;section=9" title="Uredi kôd odjeljka Poveznice"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Rotacija_polja" class="mw-redirect" title="Rotacija polja">rotacija polja</a>, vektorska operacija</li></ul> <div class="mw-heading mw-heading2"><h2 id="Izvori">Izvori</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotacija&amp;veaction=edit&amp;section=10" title="Uredi odjeljak Izvori" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Rotacija&amp;action=edit&amp;section=10" title="Uredi kôd odjeljka Izvori"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r41378145">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"> <b>rotacija ili vrtnja</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/Natuknica.aspx?ID=53453">[1]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2015.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"> Velimir Kruz: "Tehnička fizika za tehničke škole", "Školska knjiga" Zagreb, 1969.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"> <b>Zemlja</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/Natuknica.aspx?ID=67110">[2]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2014.</span> </li> </ol></div></div> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐7d588db968‐vh74x Cached time: 20241105003322 Cache expiry: 2592000 Reduced expiry: false Complications: [show‐toc] CPU time usage: 0.101 seconds Real time usage: 0.418 seconds Preprocessor visited node count: 356/1000000 Post‐expand include size: 648/2097152 bytes Template argument size: 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