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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">Inhoud</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">verbergen</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">Top</div> </a> </li> <li id="toc-Impuls_in_de_klassieke_natuurkunde:_stoot" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Impuls_in_de_klassieke_natuurkunde:_stoot"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Impuls in de klassieke natuurkunde: stoot</span> </div> </a> <ul id="toc-Impuls_in_de_klassieke_natuurkunde:_stoot-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wet_van_behoud_van_impuls" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Wet_van_behoud_van_impuls"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Wet van behoud van impuls</span> </div> </a> <ul id="toc-Wet_van_behoud_van_impuls-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Impuls_en_relativiteit" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Impuls_en_relativiteit"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Impuls en relativiteit</span> </div> </a> <ul id="toc-Impuls_en_relativiteit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Impuls_in_de_kwantummechanica" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Impuls_in_de_kwantummechanica"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Impuls in de kwantummechanica</span> </div> </a> <ul id="toc-Impuls_in_de_kwantummechanica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gegeneraliseerde_impuls" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Gegeneraliseerde_impuls"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Gegeneraliseerde impuls</span> </div> </a> <ul id="toc-Gegeneraliseerde_impuls-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zie_ook" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zie_ook"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Zie ook</span> </div> </a> <ul id="toc-Zie_ook-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nota_bene" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Nota_bene"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Nota bene</span> </div> </a> <ul id="toc-Nota_bene-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="Inhoud" 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="Inhoudsopgave omschakelen" > <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">Inhoudsopgave omschakelen</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">Impuls (natuurkunde)</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="Ga naar een artikel in een andere taal. Beschikbaar in 97 talen" > <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-97" 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">97 talen</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/Momentum" title="Momentum – Afrikaans" lang="af" hreflang="af" data-title="Momentum" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" 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/Impuls_(Physik)" title="Impuls (Physik) – Zwitserduits" lang="gsw" hreflang="gsw" data-title="Impuls (Physik)" data-language-autonym="Alemannisch" data-language-local-name="Zwitserduits" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B2%D8%AE%D9%85_%D8%A7%D9%84%D8%AD%D8%B1%D9%83%D8%A9" title="زخم الحركة – Arabisch" lang="ar" hreflang="ar" data-title="زخم الحركة" data-language-autonym="العربية" data-language-local-name="Arabisch" 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%AD%E0%A7%B0%E0%A6%AC%E0%A7%87%E0%A6%97" title="ভৰবেগ – Assamees" lang="as" hreflang="as" data-title="ভৰবেগ" data-language-autonym="অসমীয়া" data-language-local-name="Assamees" 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/Cantid%C3%A1_de_movimientu" title="Cantidá de movimientu – Asturisch" lang="ast" hreflang="ast" data-title="Cantidá de movimientu" data-language-autonym="Asturianu" data-language-local-name="Asturisch" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C4%B0mpuls" title="İmpuls – Azerbeidzjaans" lang="az" hreflang="az" data-title="İmpuls" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidzjaans" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Momentum" title="Momentum – Central Bikol" lang="bcl" hreflang="bcl" data-title="Momentum" 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%86%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81" title="Імпульс – Belarussisch" lang="be" hreflang="be" data-title="Імпульс" data-language-autonym="Беларуская" data-language-local-name="Belarussisch" 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%86%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81" title="Імпульс – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Імпульс" 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%98%D0%BC%D0%BF%D1%83%D0%BB%D1%81_(%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0)" title="Импулс (механика) – Bulgaars" lang="bg" hreflang="bg" data-title="Импулс (механика)" data-language-autonym="Български" data-language-local-name="Bulgaars" 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%E0%A4%AE%E0%A4%BE%E0%A4%A8" title="वेगमान – Bhojpuri" lang="bh" hreflang="bh" data-title="वेगमान" 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%AD%E0%A6%B0%E0%A6%AC%E0%A7%87%E0%A6%97" title="ভরবেগ – Bengaals" lang="bn" hreflang="bn" data-title="ভরবেগ" data-language-autonym="বাংলা" data-language-local-name="Bengaals" 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/Koli%C4%8Dina_kretanja" title="Količina kretanja – Bosnisch" lang="bs" hreflang="bs" data-title="Količina kretanja" data-language-autonym="Bosanski" data-language-local-name="Bosnisch" 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%98%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81" title="Импульс – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Импульс" 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/Quantitat_de_moviment" title="Quantitat de moviment – Catalaans" lang="ca" hreflang="ca" data-title="Quantitat de moviment" data-language-autonym="Català" data-language-local-name="Catalaans" 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/%DA%95%D8%A7%D9%88%DB%95%D8%B4" title="ڕاوەش – Soranî" lang="ckb" hreflang="ckb" data-title="ڕاوەش" data-language-autonym="کوردی" data-language-local-name="Soranî" 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/Hybnost" title="Hybnost – Tsjechisch" lang="cs" hreflang="cs" data-title="Hybnost" data-language-autonym="Čeština" data-language-local-name="Tsjechisch" 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%98%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81" title="Импульс – Tsjoevasjisch" lang="cv" hreflang="cv" data-title="Импульс" data-language-autonym="Чӑвашла" data-language-local-name="Tsjoevasjisch" 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/Momentwm" title="Momentwm – Welsh" lang="cy" hreflang="cy" data-title="Momentwm" data-language-autonym="Cymraeg" data-language-local-name="Welsh" 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/Impuls_(fysik)" title="Impuls (fysik) – Deens" lang="da" hreflang="da" data-title="Impuls (fysik)" data-language-autonym="Dansk" data-language-local-name="Deens" 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/Impuls" title="Impuls – Duits" lang="de" hreflang="de" data-title="Impuls" data-language-autonym="Deutsch" data-language-local-name="Duits" 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%9F%CF%81%CE%BC%CE%AE" title="Ορμή – Grieks" lang="el" hreflang="el" data-title="Ορμή" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" 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/Momentum" title="Momentum – Engels" lang="en" hreflang="en" data-title="Momentum" data-language-autonym="English" data-language-local-name="Engels" 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/Movokvanto" title="Movokvanto – Esperanto" lang="eo" hreflang="eo" data-title="Movokvanto" 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/Cantidad_de_movimiento" title="Cantidad de movimiento – Spaans" lang="es" hreflang="es" data-title="Cantidad de movimiento" data-language-autonym="Español" data-language-local-name="Spaans" 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/Impulss" title="Impulss – Estisch" lang="et" hreflang="et" data-title="Impulss" data-language-autonym="Eesti" data-language-local-name="Estisch" 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/Momentu_lineal" title="Momentu lineal – Baskisch" lang="eu" hreflang="eu" data-title="Momentu lineal" data-language-autonym="Euskara" data-language-local-name="Baskisch" 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%AA%DA%A9%D8%A7%D9%86%D9%87" title="تکانه – Perzisch" lang="fa" hreflang="fa" data-title="تکانه" data-language-autonym="فارسی" data-language-local-name="Perzisch" 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/Liikem%C3%A4%C3%A4r%C3%A4" title="Liikemäärä – Fins" lang="fi" hreflang="fi" data-title="Liikemäärä" data-language-autonym="Suomi" data-language-local-name="Fins" 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/Quantit%C3%A9_de_mouvement" title="Quantité de mouvement – Frans" lang="fr" hreflang="fr" data-title="Quantité de mouvement" data-language-autonym="Français" data-language-local-name="Frans" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Ympuls_(natuerkunde)" title="Ympuls (natuerkunde) – Fries" lang="fy" hreflang="fy" data-title="Ympuls (natuerkunde)" data-language-autonym="Frysk" data-language-local-name="Fries" 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/M%C3%B3iminteam" title="Móiminteam – Iers" lang="ga" hreflang="ga" data-title="Móiminteam" data-language-autonym="Gaeilge" data-language-local-name="Iers" 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/Cantidade_de_movemento" title="Cantidade de movemento – Galicisch" lang="gl" hreflang="gl" data-title="Cantidade de movemento" data-language-autonym="Galego" data-language-local-name="Galicisch" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%B5%E0%AB%87%E0%AA%97%E0%AA%AE%E0%AA%BE%E0%AA%A8_%E0%AA%B8%E0%AA%82%E0%AA%B0%E0%AA%95%E0%AB%8D%E0%AA%B7%E0%AA%A3%E0%AA%A8%E0%AB%8B_%E0%AA%A8%E0%AA%BF%E0%AA%AF%E0%AA%AE" title="વેગમાન સંરક્ષણનો નિયમ – Gujarati" lang="gu" hreflang="gu" data-title="વેગમાન સંરક્ષણનો નિયમ" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%A0%D7%A2" title="תנע – Hebreeuws" lang="he" hreflang="he" data-title="תנע" data-language-autonym="עברית" data-language-local-name="Hebreeuws" 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%B8%E0%A4%82%E0%A4%B5%E0%A5%87%E0%A4%97_(%E0%A4%AD%E0%A5%8C%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80)" title="संवेग (भौतिकी) – Hindi" lang="hi" hreflang="hi" data-title="संवेग (भौतिकी)" 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/Koli%C4%8Dina_gibanja" title="Količina gibanja – Kroatisch" lang="hr" hreflang="hr" data-title="Količina gibanja" data-language-autonym="Hrvatski" data-language-local-name="Kroatisch" 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/Elan" title="Elan – Haïtiaans Creools" lang="ht" hreflang="ht" data-title="Elan" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haïtiaans Creools" 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/Lend%C3%BClet" title="Lendület – Hongaars" lang="hu" hreflang="hu" data-title="Lendület" data-language-autonym="Magyar" data-language-local-name="Hongaars" 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%BB%D5%B4%D5%BA%D5%B8%D6%82%D5%AC%D5%BD_(%D5%B7%D5%A1%D6%80%D5%AA%D5%B4%D5%A1%D5%B6_%D6%84%D5%A1%D5%B6%D5%A1%D5%AF)" title="Իմպուլս (շարժման քանակ) – Armeens" lang="hy" hreflang="hy" data-title="Իմպուլս (շարժման քանակ)" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Momentum" title="Momentum – Indonesisch" lang="id" hreflang="id" data-title="Momentum" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Skri%C3%B0%C3%BEungi" title="Skriðþungi – IJslands" lang="is" hreflang="is" data-title="Skriðþungi" data-language-autonym="Íslenska" data-language-local-name="IJslands" 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/Quantit%C3%A0_di_moto" title="Quantità di moto – Italiaans" lang="it" hreflang="it" data-title="Quantità di moto" data-language-autonym="Italiano" data-language-local-name="Italiaans" 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%81%8B%E5%8B%95%E9%87%8F" title="運動量 – Japans" lang="ja" hreflang="ja" data-title="運動量" data-language-autonym="日本語" data-language-local-name="Japans" 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/Mom%C3%A8ntum" title="Momèntum – Javaans" lang="jv" hreflang="jv" data-title="Momèntum" data-language-autonym="Jawa" data-language-local-name="Javaans" 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%98%E1%83%9B%E1%83%9E%E1%83%A3%E1%83%9A%E1%83%A1%E1%83%98" title="იმპულსი – Georgisch" lang="ka" hreflang="ka" data-title="იმპულსი" data-language-autonym="ქართული" data-language-local-name="Georgisch" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%94%D0%B5%D0%BD%D0%B5_%D0%B8%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81%D1%96" title="Дене импульсі – Kazachs" lang="kk" hreflang="kk" data-title="Дене импульсі" data-language-autonym="Қазақша" data-language-local-name="Kazachs" 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%86%E0%B2%B5%E0%B3%87%E0%B2%97_(%E0%B2%AD%E0%B3%8C%E0%B2%A4%E0%B2%B6%E0%B2%BE%E0%B2%B8%E0%B3%8D%E0%B2%A4%E0%B3%8D%E0%B2%B0)" title="ಆವೇಗ (ಭೌತಶಾಸ್ತ್ರ) – Kannada" lang="kn" hreflang="kn" data-title="ಆವೇಗ (ಭೌತಶಾಸ್ತ್ರ)" 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%9A%B4%EB%8F%99%EB%9F%89" title="운동량 – Koreaans" lang="ko" hreflang="ko" data-title="운동량" data-language-autonym="한국어" data-language-local-name="Koreaans" 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/Momentum" title="Momentum – Latijn" lang="la" hreflang="la" data-title="Momentum" data-language-autonym="Latina" data-language-local-name="Latijn" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Judesio_kiekis" title="Judesio kiekis – Litouws" lang="lt" hreflang="lt" data-title="Judesio kiekis" data-language-autonym="Lietuvių" data-language-local-name="Litouws" 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/Impulss" title="Impulss – Lets" lang="lv" hreflang="lv" data-title="Impulss" data-language-autonym="Latviešu" data-language-local-name="Lets" 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%98%D0%BC%D0%BF%D1%83%D0%BB%D1%81_(%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0)" title="Импулс (механика) – Macedonisch" lang="mk" hreflang="mk" data-title="Импулс (механика)" data-language-autonym="Македонски" data-language-local-name="Macedonisch" 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%86%E0%B4%95%E0%B5%8D%E0%B4%95%E0%B4%82" title="ആക്കം – Malayalam" lang="ml" hreflang="ml" data-title="ആക്കം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" 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%9C%D0%BE%D0%BC%D0%B5%D0%BD%D1%82" title="Момент – Mongools" lang="mn" hreflang="mn" data-title="Момент" data-language-autonym="Монгол" data-language-local-name="Mongools" 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%B8%E0%A4%82%E0%A4%B5%E0%A5%87%E0%A4%97" title="संवेग – Marathi" lang="mr" hreflang="mr" data-title="संवेग" data-language-autonym="मराठी" data-language-local-name="Marathi" 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/Momentum" title="Momentum – Maleis" lang="ms" hreflang="ms" data-title="Momentum" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" 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%9F%E1%80%AF%E1%80%94%E1%80%BA" title="အဟုန် – Birmaans" lang="my" hreflang="my" data-title="အဟုန်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Birmaans" 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/Impuls_(Physik)" title="Impuls (Physik) – Nedersaksisch" lang="nds" hreflang="nds" data-title="Impuls (Physik)" data-language-autonym="Plattdüütsch" data-language-local-name="Nedersaksisch" 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%AA%E0%A4%B0%E0%A4%BF%E0%A4%B5%E0%A5%87%E0%A4%97" title="परिवेग – Nepalees" lang="ne" hreflang="ne" data-title="परिवेग" data-language-autonym="नेपाली" data-language-local-name="Nepalees" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/R%C3%B8rslemengd" title="Rørslemengd – Noors - Nynorsk" lang="nn" hreflang="nn" data-title="Rørslemengd" data-language-autonym="Norsk nynorsk" data-language-local-name="Noors - Nynorsk" 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/Bevegelsesmengde" title="Bevegelsesmengde – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Bevegelsesmengde" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - Bokmål" 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/Quantitat_de_movement" title="Quantitat de movement – Occitaans" lang="oc" hreflang="oc" data-title="Quantitat de movement" data-language-autonym="Occitan" data-language-local-name="Occitaans" 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/Furguga" title="Furguga – Afaan Oromo" lang="om" hreflang="om" data-title="Furguga" data-language-autonym="Oromoo" data-language-local-name="Afaan 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%B8%E0%A9%B0%E0%A8%B5%E0%A9%87%E0%A8%97" title="ਸੰਵੇਗ – Punjabi" lang="pa" hreflang="pa" data-title="ਸੰਵੇਗ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" 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/P%C4%99d_(fizyka)" title="Pęd (fizyka) – Pools" lang="pl" hreflang="pl" data-title="Pęd (fizyka)" data-language-autonym="Polski" data-language-local-name="Pools" 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/Quantit%C3%A0_%C3%ABd_moviment" title="Quantità ëd moviment – Piëmontees" lang="pms" hreflang="pms" data-title="Quantità ëd moviment" data-language-autonym="Piemontèis" data-language-local-name="Piëmontees" 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%85%D9%88%D9%85%D9%86%D9%B9%D9%85" title="مومنٹم – Western Punjabi" lang="pnb" hreflang="pnb" data-title="مومنٹم" 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/Momento_linear" title="Momento linear – Portugees" lang="pt" hreflang="pt" data-title="Momento linear" data-language-autonym="Português" data-language-local-name="Portugees" 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/Impuls" title="Impuls – Roemeens" lang="ro" hreflang="ro" data-title="Impuls" data-language-autonym="Română" data-language-local-name="Roemeens" 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%98%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81" title="Импульс – Russisch" lang="ru" hreflang="ru" data-title="Импульс" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Impuls" title="Impuls – Servo-Kroatisch" lang="sh" hreflang="sh" data-title="Impuls" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Servo-Kroatisch" 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%9C%E0%B6%B8%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B6%AD%E0%B7%8F%E0%B7%80%E0%B6%BA" title="ගම්‍යතාවය – Singalees" lang="si" hreflang="si" data-title="ගම්‍යතාවය" data-language-autonym="සිංහල" data-language-local-name="Singalees" 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/Momentum" title="Momentum – Simple English" lang="en-simple" hreflang="en-simple" data-title="Momentum" 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/Hybnos%C5%A5" title="Hybnosť – Slowaaks" lang="sk" hreflang="sk" data-title="Hybnosť" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" 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/Gibalna_koli%C4%8Dina" title="Gibalna količina – Sloveens" lang="sl" hreflang="sl" data-title="Gibalna količina" data-language-autonym="Slovenščina" data-language-local-name="Sloveens" 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/Runhanhira" title="Runhanhira – Shona" lang="sn" hreflang="sn" data-title="Runhanhira" data-language-autonym="ChiShona" data-language-local-name="Shona" 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/Vrulli" title="Vrulli – Albanees" lang="sq" hreflang="sq" data-title="Vrulli" data-language-autonym="Shqip" data-language-local-name="Albanees" 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%98%D0%BC%D0%BF%D1%83%D0%BB%D1%81" title="Импулс – Servisch" lang="sr" hreflang="sr" data-title="Импулс" data-language-autonym="Српски / srpski" data-language-local-name="Servisch" 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/Mom%C3%A9ntum" title="Moméntum – Soendanees" lang="su" hreflang="su" data-title="Moméntum" data-language-autonym="Sunda" data-language-local-name="Soendanees" 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/R%C3%B6relsem%C3%A4ngd" title="Rörelsemängd – Zweeds" lang="sv" hreflang="sv" data-title="Rörelsemängd" data-language-autonym="Svenska" data-language-local-name="Zweeds" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%89%E0%AE%A8%E0%AF%8D%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="உந்தம் – Tamil" lang="ta" hreflang="ta" data-title="உந்தம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" 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%A6%E0%B1%8D%E0%B0%B0%E0%B0%B5%E0%B1%8D%E0%B0%AF%E0%B0%B5%E0%B1%87%E0%B0%97%E0%B0%82" title="ద్రవ్యవేగం – Telugu" lang="te" hreflang="te" data-title="ద్రవ్యవేగం" 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%B9%82%E0%B8%A1%E0%B9%80%E0%B8%A1%E0%B8%99%E0%B8%95%E0%B8%B1%E0%B8%A1" title="โมเมนตัม – Thai" lang="th" hreflang="th" data-title="โมเมนตัม" data-language-autonym="ไทย" data-language-local-name="Thai" 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/Momentum" title="Momentum – Tagalog" lang="tl" hreflang="tl" data-title="Momentum" data-language-autonym="Tagalog" data-language-local-name="Tagalog" 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/Momentum" title="Momentum – Turks" lang="tr" hreflang="tr" data-title="Momentum" data-language-autonym="Türkçe" data-language-local-name="Turks" 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/%C4%B0mpuls" title="İmpuls – Tataars" lang="tt" hreflang="tt" data-title="İmpuls" data-language-autonym="Татарча / tatarça" data-language-local-name="Tataars" 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%86%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81_(%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0)" title="Імпульс (механіка) – Oekraïens" lang="uk" hreflang="uk" data-title="Імпульс (механіка)" data-language-autonym="Українська" data-language-local-name="Oekraïens" 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%85%D8%B9%DB%8C%D8%A7%D8%B1_%D8%AD%D8%B1%DA%A9%D8%AA" title="معیار حرکت – Urdu" lang="ur" hreflang="ur" data-title="معیار حرکت" data-language-autonym="اردو" data-language-local-name="Urdu" 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/Impuls" title="Impuls – Oezbeeks" lang="uz" hreflang="uz" data-title="Impuls" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oezbeeks" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BB%99ng_l%C6%B0%E1%BB%A3ng" title="Động lượng – Vietnamees" lang="vi" hreflang="vi" data-title="Động lượng" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamees" 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/%E5%8A%A8%E9%87%8F" title="动量 – Wuyu" lang="wuu" hreflang="wuu" data-title="动量" data-language-autonym="吴语" data-language-local-name="Wuyu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%99%D7%9E%D7%A4%D7%A2%D7%98" title="אימפעט – Jiddisch" lang="yi" hreflang="yi" data-title="אימפעט" data-language-autonym="ייִדיש" data-language-local-name="Jiddisch" 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/%E5%8A%A8%E9%87%8F" title="动量 – Chinees" lang="zh" hreflang="zh" data-title="动量" data-language-autonym="中文" data-language-local-name="Chinees" 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/%E5%8B%95%E9%87%8F" title="動量 – Klassiek Chinees" lang="lzh" hreflang="lzh" data-title="動量" data-language-autonym="文言" data-language-local-name="Klassiek Chinees" 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/%C5%AAn-t%C5%8Dng-li%C5%8Dng" title="Ūn-tōng-liōng – Minnanyu" lang="nan" hreflang="nan" 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(natuurkunde)">stoot</a>)) een <a href="/wiki/Natuurkundige_grootheid" title="Natuurkundige grootheid">grootheid</a> die gerelateerd is aan de <a href="/wiki/Snelheid" title="Snelheid">snelheid</a> en de <a href="/wiki/Massa_(natuurkunde)" title="Massa (natuurkunde)">massa</a> van een <a href="/wiki/Lichaam_(natuurkunde)" title="Lichaam (natuurkunde)">object</a>. Binnen de <a href="/wiki/Klassieke_mechanica" title="Klassieke mechanica">klassieke mechanica</a> is impuls <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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> gedefinieerd als: </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 {\vec {p}}=m{\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>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>m</mi> <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 {p}}=m{\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e41e3b934ccee493856c6caceb07f9a14013b86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:7.729ex; height:2.676ex;" alt="{\displaystyle {\vec {p}}=m{\vec {v}}}"></span>,</dd></dl> <p>dus als het product van de <a href="/wiki/Scalar#Fysica" class="mw-redirect" title="Scalar">scalaire</a> grootheid <a href="/wiki/Massa_(natuurkunde)" title="Massa (natuurkunde)">massa</a> en de <a href="/wiki/Vector_(wiskunde)" title="Vector (wiskunde)">vectoriële</a> grootheid <a href="/wiki/Snelheid" title="Snelheid">snelheid</a>. De impuls is dus ook een vectorgrootheid, met dezelfde richting als de snelheid. </p><p>De eenheid van impuls is <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 \mathrm {Ns} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">s</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Ns} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/780e063dfc913e1dcd92bf57b32670a00751d7a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.659ex; height:2.176ex;" alt="{\displaystyle \mathrm {Ns} }"></span> (newtonseconde), wat in <a href="/wiki/Syst%C3%A8me_International" class="mw-redirect" title="Système International">SI</a>-eenheden neerkomt op <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 \mathrm {\frac {kg\cdot m}{s}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> <mo>⋅</mo> <mi mathvariant="normal">m</mi> </mrow> <mi mathvariant="normal">s</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {\frac {kg\cdot m}{s}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ade923b4b4009d2e7cb6edafb1d5a6edcf6a2090" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.841ex; height:5.343ex;" alt="{\displaystyle \mathrm {\frac {kg\cdot m}{s}} }"></span>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Impuls_in_de_klassieke_natuurkunde:_stoot">Impuls in de klassieke natuurkunde: stoot</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impuls_(natuurkunde)&veaction=edit&section=1" title="Bewerk dit kopje: Impuls in de klassieke natuurkunde: stoot" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impuls_(natuurkunde)&action=edit&section=1" title="De broncode bewerken van de sectie: Impuls in de klassieke natuurkunde: stoot"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Billard.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Billard.JPG/260px-Billard.JPG" decoding="async" width="260" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Billard.JPG/390px-Billard.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/86/Billard.JPG/520px-Billard.JPG 2x" data-file-width="3456" data-file-height="2304" /></a><figcaption>Stoot bij pool. De impuls van de witte bal wordt over alle ballen verdeeld.</figcaption></figure> <p>De impuls is een belangrijke grootheid in de <a href="/wiki/Klassieke_mechanica" title="Klassieke mechanica">klassieke mechanica</a>: Als er een externe kracht werkt op een systeem, verandert de impuls. Volgens de <a href="/wiki/Tweede_wet_van_Newton" class="mw-redirect" title="Tweede wet van Newton">tweede wet van Newton</a> is: </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 {\vec {F}}={\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </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"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </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 {\vec {F}}={\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c4a8492d513b91c77f3e4f9025f0fb7640ce6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.323ex; height:5.676ex;" alt="{\displaystyle {\vec {F}}={\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}}"></span></dd></dl> <p>Als de massa <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> constant blijft, geldt dus: </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 {\vec {F}}=m\,{\vec {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>m</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}=m\,{\vec {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b57290638dfe755afbfbfc9ff9a9bfeadfc8afcb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.527ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}=m\,{\vec {a}}}"></span></dd></dl> <p>Wanneer de kracht constant is, neemt de impuls lineair toe in de tijd. Als dit niet het geval is neemt men de integraal van de uitgeoefende kracht in de tijd. De integraal van een kracht F over de tijd van tijdstip a naar tijdstip b is de <a href="/wiki/Stoot_(natuurkunde)" title="Stoot (natuurkunde)">stoot</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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span>: </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 {\vec {I}}=\int _{a}^{b}{\vec {F}}\,\mathrm {d} t=\int _{a}^{b}{\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}\,\mathrm {d} t=\int _{a}^{b}\mathrm {d} {\vec {p}}=\Delta {\vec {p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>I</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {I}}=\int _{a}^{b}{\vec {F}}\,\mathrm {d} t=\int _{a}^{b}{\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}\,\mathrm {d} t=\int _{a}^{b}\mathrm {d} {\vec {p}}=\Delta {\vec {p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcb1c3e6d194a9c79901098f4c37627f6c836542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:41.39ex; height:6.343ex;" alt="{\displaystyle {\vec {I}}=\int _{a}^{b}{\vec {F}}\,\mathrm {d} t=\int _{a}^{b}{\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}\,\mathrm {d} t=\int _{a}^{b}\mathrm {d} {\vec {p}}=\Delta {\vec {p}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Wet_van_behoud_van_impuls">Wet van behoud van impuls</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impuls_(natuurkunde)&veaction=edit&section=2" title="Bewerk dit kopje: Wet van behoud van impuls" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impuls_(natuurkunde)&action=edit&section=2" title="De broncode bewerken van de sectie: Wet van behoud van impuls"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De <i>wet van behoud van impuls</i> kan worden afgeleid uit <a href="/wiki/Wetten_van_Newton" title="Wetten van Newton">Newtons axioma's</a> voor de <a href="/wiki/Klassieke_mechanica" title="Klassieke mechanica">klassieke mechanica</a>: Als er geen externe <a href="/wiki/Kracht" title="Kracht">kracht</a> werkt op een systeem, blijft de totale impuls behouden; De krachten die verschillende <a href="/wiki/Massa_(natuurkunde)" title="Massa (natuurkunde)">massa</a>'s in een systeem op elkaar uitoefenen heffen elkaar op volgens het axioma <i>actie = −reactie</i>. Dit principe is bijvoorbeeld van toepassing bij het uitstoten van massa bij een kanon of een raket, bij aantrekking (bijvoorbeeld door gravitatie), en bij afstoting op afstand of bij een <a href="/wiki/Botsing_(natuurkunde)" title="Botsing (natuurkunde)">botsing</a> van twee objecten/deeltjes (in de natuurkundelessen vaak <a href="/wiki/Biljartbal" title="Biljartbal">biljartballen</a>). Neem aan dat twee voorwerpen <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> en <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> tegen elkaar botsen of op een andere manier een kracht op elkaar uitoefenen. Als er verder geen krachten zijn is de kracht <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 {F_{A}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F_{A}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c2d4ba06d1af9015c0bc3cc2cfe7aa3117196fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.959ex; height:4.009ex;" alt="{\displaystyle {\vec {F_{A}}}}"></span> op <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> volgens het principe van <i>actie = −reactie</i> tegengesteld gericht aan de kracht <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 {F_{B}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F_{B}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75bcdcab6fbbc41f917e0b23b908c89812bd848b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.974ex; height:4.009ex;" alt="{\displaystyle {\vec {F_{B}}}}"></span> op <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> en even groot: </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 {\vec {F_{A}}}=-{\vec {F_{B}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F_{A}}}=-{\vec {F_{B}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3f0f02ffd0e7a1fece7ef1f3156ddf618cbe979" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.84ex; height:4.009ex;" alt="{\displaystyle {\vec {F_{A}}}=-{\vec {F_{B}}}}"></span></dd></dl> <p>Voor de impuls geldt: </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 {\frac {\mathrm {d} {\vec {p_{A}}}}{\mathrm {d} t}}={\vec {F_{A}}}=-{\vec {F_{B}}}=-{\frac {\mathrm {d} {\vec {p_{B}}}}{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <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"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </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 {\frac {\mathrm {d} {\vec {p_{A}}}}{\mathrm {d} t}}={\vec {F_{A}}}=-{\vec {F_{B}}}=-{\frac {\mathrm {d} {\vec {p_{B}}}}{\mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87180c226de26a86561ffdca7483d1d3eba1bb87" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:28.386ex; height:6.343ex;" alt="{\displaystyle {\frac {\mathrm {d} {\vec {p_{A}}}}{\mathrm {d} t}}={\vec {F_{A}}}=-{\vec {F_{B}}}=-{\frac {\mathrm {d} {\vec {p_{B}}}}{\mathrm {d} t}}}"></span></dd></dl> <p>Voor de totale impuls <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 {p}}={\vec {p_{A}}}+{\vec {p_{B}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}={\vec {p_{A}}}+{\vec {p_{B}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db350ce8196f92326dbdeceef63c75d28ec9c2a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:12.637ex; height:3.343ex;" alt="{\displaystyle {\vec {p}}={\vec {p_{A}}}+{\vec {p_{B}}}}"></span> geldt dan: </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 {\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}={\frac {\mathrm {d} {\vec {p_{A}}}}{\mathrm {d} t}}+{\frac {\mathrm {d} {\vec {p_{B}}}}{\mathrm {d} t}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </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"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </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"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}={\frac {\mathrm {d} {\vec {p_{A}}}}{\mathrm {d} t}}+{\frac {\mathrm {d} {\vec {p_{B}}}}{\mathrm {d} t}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f89388defcef91fd67e7c31654606f4b07c07abe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:23.194ex; height:6.343ex;" alt="{\displaystyle {\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}={\frac {\mathrm {d} {\vec {p_{A}}}}{\mathrm {d} t}}+{\frac {\mathrm {d} {\vec {p_{B}}}}{\mathrm {d} t}}=0}"></span></dd></dl> <p>De totale impuls van het systeem kan niet veranderen tenzij er een externe kracht op werkt. Dit geldt ook als het systeem bestaat uit meer dan twee voorwerpen of zelfs een <a href="/wiki/Continu%C3%BCm_(natuurkunde)" title="Continuüm (natuurkunde)">continuüm</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Impuls_en_relativiteit">Impuls en relativiteit</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impuls_(natuurkunde)&veaction=edit&section=3" title="Bewerk dit kopje: Impuls en relativiteit" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impuls_(natuurkunde)&action=edit&section=3" title="De broncode bewerken van de sectie: Impuls en relativiteit"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Bestand:Collision_huygens.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Collision_huygens.gif/200px-Collision_huygens.gif" decoding="async" width="200" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Collision_huygens.gif/300px-Collision_huygens.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/4/49/Collision_huygens.gif 2x" data-file-width="304" data-file-height="225" /></a><figcaption>Twee referentiekaders bij Huygens: 1 waarnemer staat op de wal en de ander in een boot.</figcaption></figure> <p>Er wordt algemeen aangenomen dat de wetten van de natuurkunde <a href="/wiki/Invariantie_(natuurkunde)" title="Invariantie (natuurkunde)">invariant</a> zouden moeten zijn voor <a href="/wiki/Translatie_(meetkunde)" title="Translatie (meetkunde)">translatie</a>. Met andere woorden: het moet niet uitmaken of een verschijnsel wordt waargenomen in stilstand of terwijl het met een constante snelheid beweegt. <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a> leidde zijn botsingswetten af door eerst een eenvoudige botsing te bekijken waarbij twee biljartballen elkaar met gelijke snelheid raken, en de botsing daarna in gedachten plaats te laten vinden aan boord van varende trekschuiten. </p><p>Toen <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> met eenzelfde soort gedachtenexperiment zijn <a href="/wiki/Relativiteitstheorie" title="Relativiteitstheorie">relativiteitstheorie</a> ontwikkelde, bleek dat de klassieke impuls niet voor verschillende waarnemers behouden kon zijn. Het was daarom nodig de definitie van impuls aan te passen tot een <a href="/wiki/Relativistische_impuls" title="Relativistische impuls">relativistische impuls</a>: </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 {\vec {p}}=\gamma \,m_{0}\,{\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>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>γ</mi> <mspace width="thinmathspace" /> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <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 {p}}=\gamma \,m_{0}\,{\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdfcca78d765a65f01ed3b8ab2b8446561d10e80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:10.82ex; height:2.843ex;" alt="{\displaystyle {\vec {p}}=\gamma \,m_{0}\,{\vec {v}}}"></span></dd></dl> <p>Hierbij is <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> de <a href="/wiki/Rustmassa" title="Rustmassa">rustmassa</a> en <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> de <a href="/wiki/Lorentzfactor" title="Lorentzfactor">lorentzfactor</a> die afhangt van de verhouding tussen de snelheid en de lichtsnelheid in vacuüm. Bij snelheden die klein zijn ten opzichte van de lichtsnelheid is de lorentzfactor vrijwel gelijk aan 1. De definities van klassieke en relativistische impuls komen dan overeen. Maar, wanneer de snelheid in de buurt komt van de lichtsnelheid 'c' neemt de lorentzfactor toe en is de relativistische impuls groter dan de klassieke. De impuls nadert zelfs tot oneindig wanneer de snelheid van het voorwerp de lichtsnelheid nadert. Dit geeft aan waarom de lichtsnelheid nooit gehaald kan worden. Hiervoor is een oneindig grote stoot nodig en dus een kracht die oneindig groot is of oneindig lang werkt. </p><p>De <a href="/wiki/Relativistische_impuls" title="Relativistische impuls">relativistische impuls</a> wordt zelfs gebruikt om een relativistische massa <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=\gamma \,m_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mi>γ</mi> <mspace width="thinmathspace" /> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=\gamma \,m_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f6444897c4965304f2a88f8e9e1b675361f2f5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.883ex; height:2.176ex;" alt="{\displaystyle m=\gamma \,m_{0}}"></span> te definiëren. Bij deze alternatieve rekenmethode in de relativistische mechanica wordt de regel <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 {p}}=m{\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>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>m</mi> <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 {p}}=m{\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e41e3b934ccee493856c6caceb07f9a14013b86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:7.729ex; height:2.676ex;" alt="{\displaystyle {\vec {p}}=m{\vec {v}}}"></span> behouden. </p><p>Met behulp van <a href="/wiki/Viervector" title="Viervector">viervectoren</a> ontstaat een nieuwe invariantie. Die geldt niet voor energie en zelfs niet voor massa, maar wel voor impuls. Zie <a href="/wiki/Behoudswet" title="Behoudswet">Behoudswet</a>. In de relativistische mechanica is de <i>4-impuls</i> de viervector </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 \gamma \,m_{0}\,{\frac {\mathrm {d} (ct,{\vec {r}})}{\mathrm {d} t}}=(E/c,{\vec {p}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mspace width="thinmathspace" /> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mi>t</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma \,m_{0}\,{\frac {\mathrm {d} (ct,{\vec {r}})}{\mathrm {d} t}}=(E/c,{\vec {p}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a85f2732bdc8aa6c34ff39307d2ef16ac125bbb0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:24.384ex; height:5.843ex;" alt="{\displaystyle \gamma \,m_{0}\,{\frac {\mathrm {d} (ct,{\vec {r}})}{\mathrm {d} t}}=(E/c,{\vec {p}})}"></span></dd></dl> <p>waarin <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=\gamma \,m_{0}\,c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>γ</mi> <mspace width="thinmathspace" /> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\gamma \,m_{0}\,c^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/992929f59873be1e5a40a62ca39d587e33b7f4ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.066ex; height:3.176ex;" alt="{\displaystyle E=\gamma \,m_{0}\,c^{2}}"></span> de totale energie in het systeem is en de <a href="/wiki/Relativistische_impuls" title="Relativistische impuls">relativistische impuls</a> gedefinieerd is als: </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 {\vec {p}}=\gamma \,m_{0}\,{\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>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>γ</mi> <mspace width="thinmathspace" /> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <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 {p}}=\gamma \,m_{0}\,{\vec {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdfcca78d765a65f01ed3b8ab2b8446561d10e80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:10.82ex; height:2.843ex;" alt="{\displaystyle {\vec {p}}=\gamma \,m_{0}\,{\vec {v}}}"></span></dd></dl> <p>De lengte van de 4-impuls blijft constant en is gelijk aan <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}c}"> <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> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{0}c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40e6b666bf4bf20e6c36bd33a3cf741c56ddbc7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.101ex; height:2.009ex;" alt="{\displaystyle m_{0}c}"></span>: </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/c,{\vec {p}})\|^{2}=E^{2}-{\vec {p}}\cdot {\vec {p}}=\gamma ^{2}m_{0}^{2}(c^{2}-v^{2})=(m_{0}c)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">‖</mo> <mo stretchy="false">(</mo> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <msup> <mo fence="false" stretchy="false">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">(</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <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/c,{\vec {p}})\|^{2}=E^{2}-{\vec {p}}\cdot {\vec {p}}=\gamma ^{2}m_{0}^{2}(c^{2}-v^{2})=(m_{0}c)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/367a6c2e79e0dd36acf19829bfcf9f13eed03871" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:52.092ex; height:3.343ex;" alt="{\displaystyle \|(E/c,{\vec {p}})\|^{2}=E^{2}-{\vec {p}}\cdot {\vec {p}}=\gamma ^{2}m_{0}^{2}(c^{2}-v^{2})=(m_{0}c)^{2}}"></span></dd></dl> <p>Massaloze deeltjes zoals <a href="/wiki/Foton" title="Foton">fotonen</a> hebben eveneens een impuls. Daarvoor geldt: </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 p={\frac {E}{c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>E</mi> <mi>c</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p={\frac {E}{c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/639a565140bc0f3895affeb689823187d4c235c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-left: -0.089ex; width:6.969ex; height:5.176ex;" alt="{\displaystyle p={\frac {E}{c}}}"></span></dd></dl> <p>waarin <var>E</var> de energie van het foton is. Met deze definitie geldt voor zowel deeltjes met massa als deeltjes zonder massa dat <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 p={\frac {Ev}{c^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>E</mi> <mi>v</mi> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p={\frac {Ev}{c^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0de20f6edbd1827966fd61bd1e759f25592ba724" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-left: -0.089ex; width:8.097ex; height:5.509ex;" alt="{\displaystyle p={\frac {Ev}{c^{2}}}}"></span>, waarin <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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> de lengte van de <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 {p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84fee53c81592db54e0fe6c6f9eba002bb1dc74b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.415ex; height:2.676ex;" alt="{\displaystyle {\vec {p}}}"></span> aangeeft en <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> de lengte van <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>. Massaloze deeltjes bewegen zich altijd met de lichtsnelheid. </p> <div class="mw-heading mw-heading2"><h2 id="Impuls_in_de_kwantummechanica">Impuls in de kwantummechanica</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impuls_(natuurkunde)&veaction=edit&section=4" title="Bewerk dit kopje: Impuls in de kwantummechanica" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impuls_(natuurkunde)&action=edit&section=4" title="De broncode bewerken van de sectie: Impuls in de kwantummechanica"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De twee bovenstaande beschrijvingen waren redelijk gelijksoortig, in de <a href="/wiki/Kwantummechanica" title="Kwantummechanica">kwantummechanica</a> ziet de wereld er echter anders uit. Alle meetbare grootheden worden daar voorgesteld door <a href="/wiki/Hermitische_operator" title="Hermitische operator">hermitische operatoren</a>. Zo ook de impuls. De operator voor de impuls is (in de positie-representatie): </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 {\frac {\hbar }{i}}{\frac {\mathrm {d} }{\mathrm {d} x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mi>i</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\hbar }{i}}{\frac {\mathrm {d} }{\mathrm {d} x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9379be57de3e6e1794565d10a6357d249830ddb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:5.601ex; height:5.509ex;" alt="{\displaystyle {\frac {\hbar }{i}}{\frac {\mathrm {d} }{\mathrm {d} x}}}"></span></dd></dl> <p>of in meerdere dimensies </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 {\frac {\hbar }{i}}\nabla }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mi>i</mi> </mfrac> </mrow> <mi mathvariant="normal">∇</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\hbar }{i}}\nabla }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44a780a450641b69eef43a766533d1fdffe4bdd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:4.078ex; height:5.343ex;" alt="{\displaystyle {\frac {\hbar }{i}}\nabla }"></span></dd></dl> <p>Wanneer met deze operator gewerkt wordt in de kwantummechanica, zijn de uitkomsten van de berekeningen (wanneer toegepast op voor de andere methoden gebruikelijke schaal) overigens wel gelijk aan de bovenstaande formules. </p><p>Zie ook <a href="/wiki/Impulsoperator" title="Impulsoperator">Impulsoperator</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Gegeneraliseerde_impuls">Gegeneraliseerde impuls</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impuls_(natuurkunde)&veaction=edit&section=5" title="Bewerk dit kopje: Gegeneraliseerde impuls" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impuls_(natuurkunde)&action=edit&section=5" title="De broncode bewerken van de sectie: Gegeneraliseerde impuls"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Gegeneraliseerde impuls</b> is een term die in de theoretische mechanica een belangrijke rol speelt. In het <a href="/wiki/Lagrangiaan" title="Lagrangiaan">Lagrangeformalisme</a> is die gedefinieerd als: </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 p_{i}\equiv {\frac {\partial L(q_{i},{\dot {q_{i}}})}{\partial {\dot {q_{i}}}}}\qquad (i=1,2,\ldots ,n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>≡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>L</mi> <mo stretchy="false">(</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>˙</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>˙</mo> </mover> </mrow> </mrow> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mo stretchy="false">(</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}\equiv {\frac {\partial L(q_{i},{\dot {q_{i}}})}{\partial {\dot {q_{i}}}}}\qquad (i=1,2,\ldots ,n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42e6632df41dc44534d397f2aab3c5dd95c776e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-left: -0.089ex; width:35.698ex; height:6.176ex;" alt="{\displaystyle p_{i}\equiv {\frac {\partial L(q_{i},{\dot {q_{i}}})}{\partial {\dot {q_{i}}}}}\qquad (i=1,2,\ldots ,n)}"></span>,</dd></dl> <p>waarin <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 q_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2752dcbff884354069fe332b8e51eb0a70a531b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.837ex; height:2.009ex;" alt="{\displaystyle q_{i}}"></span> een plaatscoördinaat en <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 {\dot {q_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {q_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/326955fb5b20bfb832bdd050f4081176833bc2a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.837ex; height:2.509ex;" alt="{\displaystyle {\dot {q_{i}}}}"></span> een snelheidscoördinaat is in een <a href="/wiki/Gegeneraliseerde_co%C3%B6rdinaten" title="Gegeneraliseerde coördinaten">gegeneraliseerd coördinatenstelsel</a>. Het nummer van de vrijheidsgraad wordt met i aangegeven. </p><p>In het <a href="/wiki/Hamiltonformalisme" title="Hamiltonformalisme">Hamiltonformalisme</a> zijn <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 q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.07ex; height:2.009ex;" alt="{\displaystyle q}"></span> en <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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> de onafhankelijke gegeneraliseerde coördinaten. Hierin geldt: </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 {\dot {q}}_{i}={\frac {\partial H(q_{i},p_{i})}{\partial p_{i}}},\qquad {\dot {p}}_{i}=-{\frac {\partial H(q_{i},p_{i})}{\partial q_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>q</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> <mo stretchy="false">(</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>,</mo> <mspace width="2em" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> <mo stretchy="false">(</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {q}}_{i}={\frac {\partial H(q_{i},p_{i})}{\partial p_{i}}},\qquad {\dot {p}}_{i}=-{\frac {\partial H(q_{i},p_{i})}{\partial q_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57fb80f3391910ad156b3b14d2c3aed1ad2fb877" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:39.754ex; height:6.176ex;" alt="{\displaystyle {\dot {q}}_{i}={\frac {\partial H(q_{i},p_{i})}{\partial p_{i}}},\qquad {\dot {p}}_{i}=-{\frac {\partial H(q_{i},p_{i})}{\partial q_{i}}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Zie_ook">Zie ook</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impuls_(natuurkunde)&veaction=edit&section=6" title="Bewerk dit kopje: Zie ook" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impuls_(natuurkunde)&action=edit&section=6" title="De broncode bewerken van de sectie: Zie ook"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Impulsmoment" title="Impulsmoment">Impulsmoment</a></li> <li><a href="/wiki/Wet_van_behoud_van_impulsmoment" title="Wet van behoud van impulsmoment">Wet van behoud van impulsmoment</a></li> <li><a href="/wiki/Stoot_(natuurkunde)" title="Stoot (natuurkunde)">Stoot</a></li> <li><a href="/wiki/Lagrangiaan#Geladen_deeltje_in_elektromagnetisch_veld" title="Lagrangiaan">Lagrangiaan#Geladen deeltje in elektromagnetisch veld</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Nota_bene">Nota bene</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impuls_(natuurkunde)&veaction=edit&section=7" title="Bewerk dit kopje: Nota bene" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impuls_(natuurkunde)&action=edit&section=7" title="De broncode bewerken van de sectie: Nota bene"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Let op!</b> Het Engelse woord <i>impulse</i> heeft dezelfde betekenis als het Nederlandse <i>stoot</i>, niet als impuls. Het Engelse woord voor impuls is <i>momentum</i>, niet te verwarren met het Nederlandse woord <i><a href="/wiki/Moment_(natuurkunde)" class="mw-redirect" title="Moment (natuurkunde)">moment</a></i>, dat in het Engels <i>torque</i> heet (en daarmee lijkt op het Nederlandse woord <a href="/wiki/Wringspanning" title="Wringspanning">torsie</a>, dat het gevolg kan zijn van een <i>moment</i>). </p> <style data-mw-deduplicate="TemplateStyles:r67837862">.mw-parser-output .navigatie{position:relative;clear:both;overflow:auto;margin:1em auto -0.5em;padding:2px;background-color:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);text-align:center;font-size:87%}.mw-parser-output .navigatie-bewerken{margin-left:0.5em}.mw-parser-output .navigatie-bewerken .mw-ui-icon::before{background-size:0.9em}.mw-parser-output .navigatie-afb-links,.mw-parser-output .navigatie-afb-rechts{position:absolute}.mw-parser-output .navigatie-afb-rechts{right:2px}.mw-parser-output .navigatie-afb-groot{float:right;padding-left:0.5em}.mw-parser-output .navigatie-titel{background-color:#ddeef8;padding:2px 5.5em;font-weight:bold}.mw-parser-output .navigatie-inhoud{padding:0.5em}.mw-parser-output .navigatie-inhoud p:first-child{margin:0}.mw-parser-output .navigatie div[style*="background-color"],.mw-parser-output .navigatie div[style*="background"]{color:inherit}@media screen{html.skin-theme-clientpref-night .mw-parser-output .navigatie-titel{background-color:var(--background-color-interactive,#eaecf0)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navigatie-titel{background-color:var(--background-color-interactive,#eaecf0)!important}}</style> <div class="navigatie mw-collapsible mw-collapsed" role="navigation" aria-labelledby="Grootheden_en_eenheden_in_de_(klassieke)_mechanica" data-expandtext="Uitklappen" data-collapsetext="Inklappen"> <div class="navigatie-afb-links noviewer"><div class="navigatie-bewerken show-autoconfirmed nomobile"><span class="nowrap skin-invert-image"><span typeof="mw:File"><a href="/wiki/Sjabloon:Grootheden_(mechanica)" title="Sjabloon:Grootheden (mechanica)"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/OOjs_UI_icon_article-ltr.svg/16px-OOjs_UI_icon_article-ltr.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/OOjs_UI_icon_article-ltr.svg/24px-OOjs_UI_icon_article-ltr.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/OOjs_UI_icon_article-ltr.svg/32px-OOjs_UI_icon_article-ltr.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span> · <span typeof="mw:File"><a href="https://en.wikipedia.org/wiki/nl:Overleg_sjabloon:Grootheden_(mechanica)" title="Overleg sjabloon"><img alt="Overleg sjabloon" 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style="font-weight:normal;"></th> <th style="font-weight:normal;">'verheid' ('farness')</th> <th></th> </tr> <tr> <th style="font-weight:normal;font-size:80%;"><a href="/wiki/Dimensie_van_een_grootheid" title="Dimensie van een grootheid">Dimensie</a></th> <th style="font-weight:normal;">L<sup>−1</sup></th> <th style="font-weight:normal;">1</th> <th style="font-weight:normal;">L</th> <th style="font-weight:normal;">L<sup>2</sup></th> </tr> <tr> <th style="font-weight:normal;">T<sup>9</sup></th> <td><i>presrop</i> (Engels)<br />m<sup>−1</sup>·s<sup>9</sup></td> <td></td> <td><i>absrop</i> (Engels)<br />m·s<sup>9</sup></td> </tr> <tr> <th style="font-weight:normal;">T<sup>8</sup></th> <td><i>presock</i> (Engels)<br />m<sup>−1</sup>·s<sup>8</sup></td> <td></td> <td><i>absock</i> (Engels)<br />m·s<sup>8</sup></td> </tr> <tr> <th style="font-weight:normal;">T<sup>7</sup></th> <td><i>presop</i> (Engels)<br />m<sup>−1</sup>·s<sup>7</sup></td> <td></td> <td><i>absop</i> (Engels)<br />m·s<sup>7</sup></td> </tr> <tr> <th style="font-weight:normal;">T<sup>6</sup></th> <td><i>presackle</i> (Engels)<br />m<sup>−1</sup>·s<sup>6</sup></td> <td></td> <td><i>absrackle</i> (Engels)<br />m·s<sup>6</sup></td> </tr> <tr> <th style="font-weight:normal;">T<sup>5</sup></th> <td><i>presounce</i> (Engels)<br />m<sup>−1</sup>·s<sup>5</sup></td> <td></td> <td><i>absounce</i> (Engels)<br />m·s<sup>5</sup></td> </tr> <tr> <th style="font-weight:normal;">T<sup>4</sup></th> <td><i>preserk</i> (Engels)<br />m<sup>−1</sup>·s<sup>4</sup></td> <td></td> <td><i>abserk</i> (Engels): <b>D</b><br />m·s<sup>4</sup></td> </tr> <tr> <th style="font-weight:normal;">T<sup>3</sup></th> <td><i>preseleration</i> (Engels)<br />m<sup>−1</sup>·s<sup>3</sup></td> <td></td> <td><i>abseleration</i> (Engels): <b>C</b><br />m·s<sup>3</sup></td> <td></td> <td colspan="4" style="border:none;backgound:none; font-weight:bold;">hoek/rotatie grootheden</td> </tr> <tr> <th style="font-weight:normal;">T<sup>2</sup></th> <td><i>presity</i> (Engels)<br />m<sup>−1</sup>·s<sup>2</sup></td> <td></td> <td><i>absity</i> (Engels): <b>B</b><br />m·s<sup>2</sup></td> <td></td> <th style="font-weight:normal;font-size:80%;"><a href="/wiki/Dimensie_van_een_grootheid" title="Dimensie van een grootheid">Dimensie</a></th> <th style="font-weight:normal;">1</th> <th style="font-weight:normal;">geen (m·m<sup>−1</sup>)</th> <th style="font-weight:normal;">geen (m<sup>2</sup>·m<sup>−2</sup>)</th> </tr> <tr> <th style="font-weight:normal;">T</th> <td><i>presement</i> (Engels)<br />m<sup>−1</sup>·s</td> <td><a href="/wiki/Tijd" title="Tijd">tijd</a>: <i>t</i><br /><a href="/wiki/Seconde" title="Seconde">s</a></td> <td><i>absition/absement</i> (Engels): <b>A</b><br />m·s</td> <td></td> <th style="font-weight:normal;">T</th> <td><a href="/wiki/Tijd" title="Tijd">tijd</a>: <i>t</i><br /><a href="/wiki/Seconde" title="Seconde">s</a></td> <td></td> <td></td> </tr><tr> <th style="font-weight:normal;">1</th> <td><i>placement</i> (Engels)<br /><a href="/wiki/Golfgetal" title="Golfgetal">golfgetal</a><br />m<sup>−1</sup></td> <td></td> <td>afgelegde weg: <i>d</i><br /><span class="nowrap"><a href="/wiki/Plaatsvector" title="Plaatsvector">plaatsvector</a>: <b>r</b>, <b>s</b>, <b>x</b></span><br /><a href="/wiki/Afstand" title="Afstand">afstand</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 \Delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32769037c408874e1890f77554c65f39c523ebe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.176ex;" alt="{\displaystyle \Delta }"></span><b>s</b><br /><a href="/wiki/Meter" title="Meter">m</a></td> <td><a href="/wiki/Oppervlakte" title="Oppervlakte">oppervlakte</a>: <i>A</i><br /><a href="/wiki/Vierkante_meter" title="Vierkante meter">m<sup>2</sup></a></td> <th style="font-weight:normal;">1</th> <td></td> <td><a href="/wiki/Hoek_(meetkunde)" title="Hoek (meetkunde)">hoek</a>: <i>θ</i><br /><a href="/wiki/Radiaal_(wiskunde)" title="Radiaal (wiskunde)">rad</a></td> <td><span class="nowrap"><a href="/wiki/Ruimtehoek" title="Ruimtehoek">ruimtehoek</a>: <i>Ω</i><br /><a href="/wiki/Steradiaal" title="Steradiaal">rad<sup>2</sup>, sr</a></span></td> </tr> <tr> <th style="font-weight:normal;font-size:80%;">Wat meten tijdsafgeleiden?</th> <th style="font-weight:normal;"></th> <th style="font-weight:normal;"></th> <th style="font-weight:normal;">'rasheid' ('swiftness')</th> <th></th> </tr> <tr> <th style="font-weight:normal;">T<sup>−1</sup></th> <td></td> <td><span class="nowrap"><a href="/wiki/Frequentie" title="Frequentie">frequentie</a>: <i>f</i></span><br /><a href="/wiki/Hertz_(eenheid)" title="Hertz (eenheid)">s<sup>−1</sup>, Hz</a></td> <td><a href="/wiki/Snelheid" title="Snelheid">snelheid (scalar)</a>: <i>v</i><br /><a href="/wiki/Snelheid" title="Snelheid">snelheid (vector)</a>: <b>v</b><br /><a href="/wiki/Meter_per_seconde" title="Meter per seconde">m·s<sup>−1</sup></a></td> <td><a href="/wiki/Kinematische_viscositeit" class="mw-redirect" title="Kinematische viscositeit">kinematische viscositeit</a>: <span style="font-family:'Times New Roman', 'Nimbus Roman No9 L', Times, serif; font-size:118%; white-space:nowrap;"><i>ν</i></span><br /><a href="/wiki/Diffusieco%C3%ABffici%C3%ABnt" class="mw-redirect" title="Diffusiecoëfficiënt">diffusiecoëfficiënt</a>: <i>D</i><br /><a href="/wiki/Tweelichamenprobleem#Specifieke_baanenergie_en_specifiek_impulsmoment" title="Tweelichamenprobleem">specifiek impulsmoment</a>: <i>h</i><br />m<sup>2</sup>·s<sup>−1</sup></td> <th style="font-weight:normal;">T<sup>−1</sup></th> <td><span class="nowrap"><a href="/wiki/Frequentie" title="Frequentie">frequentie</a>: <i>f</i></span><br /><a href="/wiki/Hertz_(eenheid)" title="Hertz (eenheid)">s<sup>−1</sup>, Hz</a></td> <td><a href="/wiki/Hoeksnelheid" title="Hoeksnelheid">hoeksnelheid</a>: <i>ω</i>, <b>ω</b><br /><a href="/wiki/Radialen_per_seconde" title="Radialen per seconde">rad·s<sup>−1</sup></a></td> <td></td> </tr> <tr> <th style="font-weight:normal;">T<sup>−2</sup></th> <td></td> <td></td> <td><a href="/wiki/Versnelling_(natuurkunde)" title="Versnelling (natuurkunde)">versnelling</a>: <b>a</b><br />m·s<sup>−2</sup></td> <td><a href="/wiki/Verbrandingswarmte" title="Verbrandingswarmte">verbrandingswarmte</a><br /><a href="/wiki/Geabsorbeerde_dosis" title="Geabsorbeerde dosis">geabsorbeerde dosis</a>: D<br /><a href="/wiki/Radioactieve-dosisequivalent" title="Radioactieve-dosisequivalent">radioactieve-dosisequivalent</a><br />m<sup>2</sup>·s<sup>−2</sup>, <a href="/wiki/Joule" title="Joule">J</a>·kg<sup>−1</sup>, <a href="/wiki/Gray_(eenheid)" title="Gray (eenheid)">Gy</a>, <a href="/wiki/Sievert" title="Sievert">Sv</a></td> <th style="font-weight:normal;">T<sup>−2</sup></th> <td></td> <td><a href="/wiki/Hoekversnelling" title="Hoekversnelling">hoekversnelling</a>: <b>α</b><br />rad·s<sup>−2</sup></td> <td></td> </tr> <tr> <th style="font-weight:normal;">T<sup>−3</sup></th> <td></td> <td></td> <td><a href="/wiki/Jerk_(natuurkunde)" class="mw-redirect" title="Jerk (natuurkunde)">ruk</a>: <b>j</b><br />m·s<sup>−3</sup></td> <td></td> <th style="font-weight:normal;">T<sup>−3</sup></th> <td></td> <td>hoekruk: <b>ζ</b><br />rad·s<sup>−3</sup></td> <td></td> </tr> <tr> <th style="font-weight:normal;">T<sup>−4</sup></th> <td></td> <td></td> <td><i>jounce/snap</i> (Engels): <b>s</b> <br />m·s<sup>−4</sup></td> </tr> <tr> <th style="font-weight:normal;">T<sup>−5</sup></th> <td></td> <td></td> <td><i>crackle</i> (Engels): <b>c</b><br />m·s<sup>−5</sup></td> </tr> <tr> <th style="font-weight:normal;">T<sup>−6</sup></th> <td></td> <td></td> <td><i>pop</i> (Engels): <b>Po</b><br />m·s<sup>−6</sup></td> </tr> <tr> <th style="font-weight:normal;">T<sup>−7</sup></th> <td></td> <td></td> <td><i>lock</i> (Engels)<br />m·s<sup>−7</sup></td> </tr> <tr> <th style="font-weight:normal;">T<sup>−8</sup></th> <td></td> <td></td> <td><i>drop</i> (Engels)<br />m·s<sup>−8</sup></td> </tr> <tr> <td colspan="5" style="padding-top:0;"></td> <td colspan="4" style="padding-top:0;"></td> </tr> <tr><th style="font-weight:normal;">M</th> <td><a href="/wiki/Lineaire_dichtheid" title="Lineaire dichtheid">lineaire dichtheid</a>: <i><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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span></i><br /><a href="/wiki/Kilogram" title="Kilogram">kg</a>·m<sup>−1</sup></td> <td><a href="/wiki/Massa_(natuurkunde)" title="Massa (natuurkunde)">massa</a>: <i>m</i><br /><a href="/wiki/Kilogram" title="Kilogram">kg</a></td> <td></td> <td></td> <th style="font-weight:normal;">ML<sup>2</sup></th> <td><a href="/wiki/Traagheidsmoment" title="Traagheidsmoment">massatraagheidsmoment</a>: <i>I</i><br />kg·m<sup>2</sup></td> <td></td> <td></td> </tr> <tr> <th style="font-weight:normal;font-size:80%;">Wat meten tijdsafgeleiden?</th> <th style="font-weight:normal;"></th> <th style="font-weight:normal;"></th> <th style="font-weight:normal;">'sterkheid' ('forceness')</th> <th></th> </tr> <tr> <th style="font-weight:normal;">MT<sup>−1</sup></th> <td><a href="/wiki/Viscositeit#Dynamische_viscositeit_(Pa·s)" title="Viscositeit">dynamische viscositeit</a>: <span style="font-family:'Times New Roman', 'Nimbus Roman No9 L', Times, serif; font-size:118%; white-space:nowrap;"><i>η</i></span><br />kg·m<sup>−1</sup>·s<sup>−1</sup>, <a href="/wiki/Newton_(eenheid)" title="Newton (eenheid)">N</a>·m<sup>−2</sup>·s, Pa·s</td> <td></td> <td><a class="mw-selflink selflink">impuls</a>: <b>p</b> (<i>momentum</i>),<br /><a href="/wiki/Stoot_(natuurkunde)" title="Stoot (natuurkunde)">stoot</a>: <b>J</b>, <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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32769037c408874e1890f77554c65f39c523ebe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.176ex;" alt="{\displaystyle \Delta }"></span><b>p</b> (<i>impulse</i>)<br />kg·m·s<sup>−1</sup>, <a href="/wiki/Newton_(eenheid)" title="Newton (eenheid)">N</a>·s</td> <td><a href="/wiki/Actie_(natuurkunde)" title="Actie (natuurkunde)">actie</a>: <b>𝒮</b><br /><a href="/w/index.php?title=Actergie_(natuurkunde)&action=edit&redlink=1" class="new" title="Actergie (natuurkunde) (de pagina bestaat niet)">actergie</a>: <span style="font-family:'Times New Roman', 'Nimbus Roman No9 L', Times, serif; font-size:118%; white-space:nowrap;"><i>ℵ</i></span><br />kg·m<sup>2</sup>·s<sup>−1</sup>, <a href="/wiki/Newton_(eenheid)" title="Newton (eenheid)">N</a>·m·s, <a href="/wiki/Joule" title="Joule">J</a>·s</td> <th style="font-weight:normal;">ML<sup>2</sup>T<sup>−1</sup></th> <td></td> <td><a href="/wiki/Impulsmoment" title="Impulsmoment">impulsmoment</a> (<i>momentum angularis</i>): <b>L</b><br />kg·m<sup>2</sup>·s<sup>−1</sup></td> <td><a href="/wiki/Actie_(natuurkunde)" title="Actie (natuurkunde)">actie</a>: <b>𝒮</b><br /><a href="/w/index.php?title=Actergie_(natuurkunde)&action=edit&redlink=1" class="new" title="Actergie (natuurkunde) (de pagina bestaat niet)">actergie</a>: <span style="font-family:'Times New Roman', 'Nimbus Roman No9 L', Times, serif; font-size:118%; white-space:nowrap;"><i>ℵ</i></span><br />kg·m<sup>2</sup>·s<sup>−1</sup>, <a href="/wiki/Newton_(eenheid)" title="Newton (eenheid)">N</a>·m·s, <a href="/wiki/Joule" title="Joule">J</a>·s</td> </tr> <tr> <th style="font-weight:normal;">MT<sup>−2</sup></th> <td><a href="/wiki/Druk_(grootheid)" title="Druk (grootheid)">druk</a>: <i>p</i><br /><a href="/wiki/Mechanische_spanning" title="Mechanische spanning">mechanische spanning</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 \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span><br /><a href="/wiki/Energiedichtheid" title="Energiedichtheid">energiedichtheid</a>: U<br />kg·m<sup>−1</sup>·s<sup>−2</sup>, <a href="/wiki/Newton_(eenheid)" title="Newton (eenheid)">N</a>·m<sup>−2</sup>, <a href="/wiki/Joule" title="Joule">J</a>·m<sup>−3</sup>, Pa</td> <td><a href="/wiki/Oppervlaktespanning" title="Oppervlaktespanning">oppervlaktespanning</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 \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> of <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 \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span><br />kg·s<sup>−2</sup>, <a href="/wiki/Newton_(eenheid)" title="Newton (eenheid)">N</a>·m<sup>−1</sup>, <a href="/wiki/Joule" title="Joule">J</a>·m<sup>−2</sup></td> <td><a href="/wiki/Kracht" title="Kracht">kracht</a>: <b>F</b><br /><a href="/wiki/Gewicht" title="Gewicht">gewicht</a>: <b>F</b><sub>g</sub><br />·kg·m·s<sup>−2</sup>, <a href="/wiki/Newton_(eenheid)" title="Newton (eenheid)">N</a></td> <td><a href="/wiki/Energie" title="Energie">energie</a>: <i>E</i><br /><a href="/wiki/Arbeid_(natuurkunde)" title="Arbeid (natuurkunde)">arbeid</a>: <i>W</i><br /><a href="/wiki/Warmte" title="Warmte">warmte</a>: <i>Q</i><br />kg·m<sup>2</sup>·s<sup>−2</sup>, <a href="/wiki/Newtonmeter" title="Newtonmeter">Nm</a>, <a href="/wiki/Joule" title="Joule">J</a></td> <th style="font-weight:normal;">ML<sup>2</sup>T<sup>−2</sup></th> <td></td> <td><a href="/wiki/Krachtmoment" class="mw-redirect" title="Krachtmoment">krachtmoment</a> (<i>torque</i>): <b>M</b>, <b>τ</b><br />kg·m<sup>2</sup>·s<sup>−2</sup>, <a href="/wiki/Newtonmeter" title="Newtonmeter">Nm</a></td> <td><a href="/wiki/Energie" title="Energie">energie</a>: <i>E</i><br /><a href="/wiki/Arbeid_(natuurkunde)" title="Arbeid (natuurkunde)">arbeid</a>: <i>W</i><br /><a href="/wiki/Warmte" title="Warmte">warmte</a>: <i>Q</i><br />kg·m<sup>2</sup>·s<sup>−2</sup>, <a href="/wiki/Newtonmeter" title="Newtonmeter">Nm</a>, <a href="/wiki/Joule" title="Joule">J</a></td> </tr> <tr> <th style="font-weight:normal;">MT<sup>−3</sup></th> <td></td> <td></td> <td><i>yank</i> (Engels): <b>Y</b><br />kg·m·s<sup>−3</sup>, <a href="/wiki/Newton_(eenheid)" title="Newton (eenheid)">N</a>·s<sup>−1</sup></td> <td><a href="/wiki/Vermogen_(natuurkunde)" title="Vermogen (natuurkunde)">vermogen</a>: <i>P</i><br />kg·m<sup>2</sup>·s<sup>−3</sup>, <a href="/wiki/Watt_(eenheid)" title="Watt (eenheid)">W</a></td> <th style="font-weight:normal;">ML<sup>2</sup>T<sup>−3</sup></th> <td></td> <td><i>rotatum</i>: <b>P</b><br />kg·m<sup>2</sup>·s<sup>−3</sup>, N·m·s<sup>−1</sup></td> <td><a href="/wiki/Vermogen_(natuurkunde)" title="Vermogen (natuurkunde)">vermogen</a>: <i>P</i><br />kg·m<sup>2 </sup>·s<sup>−3</sup>, <a href="/wiki/Watt_(eenheid)" title="Watt (eenheid)">W</a></td> </tr> <tr> <th style="font-weight:normal;">MT<sup>−4</sup></th> <td></td> <td></td> <td><i>tug</i> (Engels): <b>T</b><br />kg·m·s<sup>−4</sup>, <a href="/wiki/Newton_(eenheid)" title="Newton (eenheid)">N</a>·s<sup>−2</sup></td> </tr> <tr><th style="font-weight:normal;">MT<sup>−5</sup></th> <td></td> <td></td> <td><i>snatch</i> (Engels): <b>S</b><br />kg·m·s<sup>−5</sup>, <a href="/wiki/Newton_(eenheid)" title="Newton (eenheid)">N</a>·s<sup>−3</sup></td> </tr> <tr><th style="font-weight:normal;">MT<sup>−6</sup></th> <td></td> <td></td> <td><i>shake</i> (Engels): <b>Sh</b><br />kg·m·s<sup>−6</sup>, <a href="/wiki/Newton_(eenheid)" title="Newton (eenheid)">N</a>·s<sup>−4</sup></td> </tr> </tbody></table> </div></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r67837862"> <div class="navigatie" role="navigation" aria-labelledby="Elementaire_begrippen_in_de_mechanica"> <div class="navigatie-afb-links noviewer"><div class="navigatie-bewerken show-autoconfirmed 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class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/OOjs_UI_icon_speechBubbles-ltr.svg/24px-OOjs_UI_icon_speechBubbles-ltr.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/OOjs_UI_icon_speechBubbles-ltr.svg/32px-OOjs_UI_icon_speechBubbles-ltr.svg.png 2x" data-file-width="20" data-file-height="20" /></span></span> · <span typeof="mw:File"><a href="//nl.wikipedia.org/w/index.php?title=Sjabloon:Navigatie_mechanica&action=edit" title="Sjabloon bewerken"><img alt="Sjabloon bewerken" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr.svg/16px-OOjs_UI_icon_edit-ltr.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr.svg/24px-OOjs_UI_icon_edit-ltr.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr.svg/32px-OOjs_UI_icon_edit-ltr.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></span></div></div> <div id="Elementaire_begrippen_in_de_mechanica" class="navigatie-titel">Elementaire begrippen in de mechanica</div> <div class="navigatie-inhoud"> <style data-mw-deduplicate="TemplateStyles:r67785531">.mw-parser-output .navigatie-tabel{margin:0 auto 0 auto;text-align:left}.mw-parser-output .navigatie-tabel .links{text-align:right}.mw-parser-output .navigatie-tabel .rechts{padding-left:0.5em}@media screen and (max-width:640px){.mw-parser-output .navigatie-tabel tr{display:grid;grid-template-columns:1fr;width:100%;margin-bottom:0.5em}.mw-parser-output .navigatie-tabel tr:last-of-type{margin-bottom:0}.mw-parser-output .navigatie-tabel .links{text-align:unset}.mw-parser-output .navigatie-tabel .rechts{padding:unset}}</style><table class="navigatie-tabel vatop" cellpadding="0" cellspacing="0" style=""><tbody><tr><td class="links" style=""><span class="nowrap"><b>Lineaire grootheid:</b></span></td><td class="rechts"><a href="/wiki/Snelheid" title="Snelheid">(bewegings)snelheid</a> · <a href="/wiki/Versnelling_(natuurkunde)" title="Versnelling (natuurkunde)">versnelling</a> · <a href="/wiki/Ruk_(natuurkunde)" title="Ruk (natuurkunde)">ruk</a> | <a href="/wiki/Massa_(natuurkunde)" title="Massa (natuurkunde)">massa</a> | <a class="mw-selflink selflink">impuls</a> · <a href="/wiki/Stoot_(natuurkunde)" title="Stoot (natuurkunde)">stoot</a> · <a href="/wiki/Kracht_(hoofdbetekenis)" class="mw-redirect" title="Kracht (hoofdbetekenis)">kracht</a></td></tr><tr><td class="links"><b>Rotatiegrootheid:</b></td><td class="rechts"><a href="/wiki/Hoeksnelheid" title="Hoeksnelheid">hoeksnelheid</a> · <a href="/wiki/Hoekversnelling" title="Hoekversnelling">hoekversnelling</a> | <a href="/wiki/Traagheidsmoment" title="Traagheidsmoment">traagheidsmoment</a> | <a href="/wiki/Impulsmoment" title="Impulsmoment">impulsmoment</a> · <a href="/wiki/Moment_(mechanica)" title="Moment (mechanica)">krachtmoment</a></td></tr><tr><td class="links"><b>Overig:</b></td><td class="rechts"><a href="/wiki/Eenparige_beweging" title="Eenparige beweging">eenparige beweging</a> · <a href="/wiki/Eenparig_versnelde_beweging" title="Eenparig versnelde beweging">eenparig versnelde beweging</a> · <a href="/wiki/Beweging_(natuurkunde)" title="Beweging (natuurkunde)">verplaatsing</a> · <a href="/wiki/Rotatie_(natuurkunde)" title="Rotatie (natuurkunde)">rotatie</a> · <a href="/wiki/Koppel_(natuurkunde)" title="Koppel (natuurkunde)">koppel (natuurkunde)</a> · <a href="/wiki/Koppel_(aandrijftechniek)" title="Koppel (aandrijftechniek)">koppel (aandrijftechniek)</a> · <a href="/wiki/Moment_en_koppel" title="Moment en koppel">moment en koppel</a> · <a href="/wiki/Gewicht" title="Gewicht">gewicht</a></td></tr></tbody></table> </div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: 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