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mw-ui-icon-wikimedia-userAdd"></span> <span>创建账号</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E8%A7%92%E9%80%9F%E5%BA%A6" title="建议你登录，尽管并非必须。[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</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">序言</div> </a> </li> <li id="toc-质点的角速度" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#质点的角速度"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>质点的角速度</span> </div> </a> <button aria-controls="toc-质点的角速度-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>开关质点的角速度子章节</span> </button> <ul id="toc-质点的角速度-sublist" class="vector-toc-list"> <li id="toc-二維坐標系" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#二維坐標系"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>二維坐標系</span> </div> </a> <ul id="toc-二維坐標系-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-三維坐標系" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#三維坐標系"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>三維坐標系</span> </div> </a> <ul id="toc-三維坐標系-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-高维空间" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#高维空间"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>高维空间</span> </div> </a> <ul id="toc-高维空间-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-刚体角速度" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#刚体角速度"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>刚体角速度</span> </div> </a> <ul id="toc-刚体角速度-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參見" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參見"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>參見</span> </div> </a> <ul id="toc-參見-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參考" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參考"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>參考</span> </div> </a> <ul id="toc-參考-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部連接" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部連接"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>外部連接</span> </div> </a> <ul id="toc-外部連接-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="目录" 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="开关目录" > <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">开关目录</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">角速度</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="前往另一种语言写成的文章。69种语言可用" > <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-69" 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">69种语言</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/Hoeksnelheid" title="Hoeksnelheid – 南非荷兰语" lang="af" hreflang="af" data-title="Hoeksnelheid" data-language-autonym="Afrikaans" data-language-local-name="南非荷兰语" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B3%D8%B1%D8%B9%D8%A9_%D8%B2%D8%A7%D9%88%D9%8A%D8%A9" title="سرعة زاوية – 阿拉伯语" lang="ar" hreflang="ar" data-title="سرعة زاوية" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Velocid%C3%A1_angular" title="Velocidá angular – 阿斯图里亚斯语" lang="ast" hreflang="ast" data-title="Velocidá angular" data-language-autonym="Asturianu" data-language-local-name="阿斯图里亚斯语" 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/Bucaq_s%C3%BCr%C9%99ti" title="Bucaq sürəti – 阿塞拜疆语" lang="az" hreflang="az" data-title="Bucaq sürəti" data-language-autonym="Azərbaycanca" data-language-local-name="阿塞拜疆语" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%92%D1%83%D0%B3%D0%BB%D0%B0%D0%B2%D0%B0%D1%8F_%D1%81%D0%BA%D0%BE%D1%80%D0%B0%D1%81%D1%86%D1%8C" title="Вуглавая скорасць – 白俄罗斯语" lang="be" hreflang="be" data-title="Вуглавая скорасць" data-language-autonym="Беларуская" data-language-local-name="白俄罗斯语" 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%9A%D1%83%D1%82%D0%B0%D0%B2%D0%B0%D1%8F_%D1%85%D1%83%D1%82%D0%BA%D0%B0%D1%81%D1%8C%D1%86%D1%8C" title="Кутавая хуткасьць – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Кутавая хуткасьць" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%AA%D0%B3%D0%BB%D0%BE%D0%B2%D0%B0_%D1%81%D0%BA%D0%BE%D1%80%D0%BE%D1%81%D1%82" title="Ъглова скорост – 保加利亚语" lang="bg" hreflang="bg" data-title="Ъглова скорост" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8C%E0%A6%A3%E0%A6%BF%E0%A6%95_%E0%A6%AC%E0%A7%87%E0%A6%97" title="কৌণিক বেগ – 孟加拉语" lang="bn" hreflang="bn" data-title="কৌণিক বেগ" data-language-autonym="বাংলা" data-language-local-name="孟加拉语" 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/Ugaona_brzina" title="Ugaona brzina – 波斯尼亚语" lang="bs" hreflang="bs" data-title="Ugaona brzina" data-language-autonym="Bosanski" data-language-local-name="波斯尼亚语" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Velocitat_angular" title="Velocitat angular – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Velocitat angular" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" 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%AF%DB%86%D8%B4%DB%95_%D8%AE%DB%8E%D8%B1%D8%A7%DB%8C%DB%8C" title="گۆشە خێرایی – 中库尔德语" lang="ckb" hreflang="ckb" data-title="گۆشە خێرایی" data-language-autonym="کوردی" data-language-local-name="中库尔德语" 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/%C3%9Ahlov%C3%A1_rychlost" title="Úhlová rychlost – 捷克语" lang="cs" hreflang="cs" data-title="Úhlová rychlost" data-language-autonym="Čeština" data-language-local-name="捷克语" 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%9A%C4%95%D1%82%D0%B5%D1%81%D0%BB%D0%B5_%D1%85%C4%83%D0%B2%C4%83%D1%80%D1%82%D0%BB%C4%83%D1%85" title="Кĕтесле хăвăртлăх – 楚瓦什语" lang="cv" hreflang="cv" data-title="Кĕтесле хăвăртлăх" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什语" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Cyflymder_onglaidd" title="Cyflymder onglaidd – 威尔士语" lang="cy" hreflang="cy" data-title="Cyflymder onglaidd" data-language-autonym="Cymraeg" data-language-local-name="威尔士语" 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/Vinkelhastighed" title="Vinkelhastighed – 丹麦语" lang="da" hreflang="da" data-title="Vinkelhastighed" data-language-autonym="Dansk" data-language-local-name="丹麦语" 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/Winkelgeschwindigkeit" title="Winkelgeschwindigkeit – 德语" lang="de" hreflang="de" data-title="Winkelgeschwindigkeit" data-language-autonym="Deutsch" data-language-local-name="德语" 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%93%CF%89%CE%BD%CE%B9%CE%B1%CE%BA%CE%AE_%CF%84%CE%B1%CF%87%CF%8D%CF%84%CE%B7%CF%84%CE%B1" title="Γωνιακή ταχύτητα – 希腊语" lang="el" hreflang="el" data-title="Γωνιακή ταχύτητα" data-language-autonym="Ελληνικά" data-language-local-name="希腊语" 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/Angular_velocity" title="Angular velocity – 英语" lang="en" hreflang="en" data-title="Angular velocity" data-language-autonym="English" data-language-local-name="英语" 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/Angula_rapido" title="Angula rapido – 世界语" lang="eo" hreflang="eo" data-title="Angula rapido" data-language-autonym="Esperanto" data-language-local-name="世界语" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Velocidad_angular" title="Velocidad angular – 西班牙语" lang="es" hreflang="es" data-title="Velocidad angular" data-language-autonym="Español" data-language-local-name="西班牙语" 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/Nurkkiirus" title="Nurkkiirus – 爱沙尼亚语" lang="et" hreflang="et" data-title="Nurkkiirus" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" 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/Abiadura_angeluar" title="Abiadura angeluar – 巴斯克语" lang="eu" hreflang="eu" data-title="Abiadura angeluar" data-language-autonym="Euskara" data-language-local-name="巴斯克语" 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%B3%D8%B1%D8%B9%D8%AA_%D8%B2%D8%A7%D9%88%DB%8C%D9%87%E2%80%8C%D8%A7%DB%8C" title="سرعت زاویه‌ای – 波斯语" lang="fa" hreflang="fa" data-title="سرعت زاویه‌ای" data-language-autonym="فارسی" data-language-local-name="波斯语" 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/Kulmanopeus" title="Kulmanopeus – 芬兰语" lang="fi" hreflang="fi" data-title="Kulmanopeus" data-language-autonym="Suomi" data-language-local-name="芬兰语" 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/Vecteur_vitesse_angulaire" title="Vecteur vitesse angulaire – 法语" lang="fr" hreflang="fr" data-title="Vecteur vitesse angulaire" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Velocidade_angular" title="Velocidade angular – 加利西亚语" lang="gl" hreflang="gl" data-title="Velocidade angular" data-language-autonym="Galego" data-language-local-name="加利西亚语" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%94%D7%99%D7%A8%D7%95%D7%AA_%D7%96%D7%95%D7%95%D7%99%D7%AA%D7%99%D7%AA" title="מהירות זוויתית – 希伯来语" lang="he" hreflang="he" data-title="מהירות זוויתית" data-language-autonym="עברית" data-language-local-name="希伯来语" 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%95%E0%A5%8B%E0%A4%A3%E0%A5%80%E0%A4%AF_%E0%A4%B5%E0%A5%87%E0%A4%97" title="कोणीय वेग – 印地语" lang="hi" hreflang="hi" data-title="कोणीय वेग" data-language-autonym="हिन्दी" data-language-local-name="印地语" 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/Kutna_brzina" title="Kutna brzina – 克罗地亚语" lang="hr" hreflang="hr" data-title="Kutna brzina" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%B6%D5%AF%D5%B5%D5%B8%D6%82%D5%B6%D5%A1%D5%B5%D5%AB%D5%B6_%D5%A1%D6%80%D5%A1%D5%A3%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Անկյունային արագություն – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Անկյունային արագություն" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" 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/Kecepatan_sudut" title="Kecepatan sudut – 印度尼西亚语" lang="id" hreflang="id" data-title="Kecepatan sudut" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" 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/Hornhra%C3%B0i" title="Hornhraði – 冰岛语" lang="is" hreflang="is" data-title="Hornhraði" data-language-autonym="Íslenska" data-language-local-name="冰岛语" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Velocit%C3%A0_angolare" title="Velocità angolare – 意大利语" lang="it" hreflang="it" data-title="Velocità angolare" data-language-autonym="Italiano" data-language-local-name="意大利语" 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/%E8%A7%92%E9%80%9F%E5%BA%A6" title="角速度 – 日语" lang="ja" hreflang="ja" data-title="角速度" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%A3%E1%83%97%E1%83%AE%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A1%E1%83%98%E1%83%A9%E1%83%A5%E1%83%90%E1%83%A0%E1%83%94" title="კუთხური სიჩქარე – 格鲁吉亚语" lang="ka" hreflang="ka" data-title="კუთხური სიჩქარე" data-language-autonym="ქართული" data-language-local-name="格鲁吉亚语" 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%91%D2%B1%D1%80%D1%8B%D1%88%D1%82%D1%8B%D2%9B_%D0%B6%D1%8B%D0%BB%D0%B4%D0%B0%D0%BC%D0%B4%D1%8B%D2%9B" title="Бұрыштық жылдамдық – 哈萨克语" lang="kk" hreflang="kk" data-title="Бұрыштық жылдамдық" data-language-autonym="Қазақша" data-language-local-name="哈萨克语" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B0%81%EC%86%8D%EB%8F%84" title="각속도 – 韩语" lang="ko" hreflang="ko" data-title="각속도" data-language-autonym="한국어" data-language-local-name="韩语" 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/Velocitas_angularis" title="Velocitas angularis – 拉丁语" lang="la" hreflang="la" data-title="Velocitas angularis" data-language-autonym="Latina" data-language-local-name="拉丁语" 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/Kampinis_greitis" title="Kampinis greitis – 立陶宛语" lang="lt" hreflang="lt" data-title="Kampinis greitis" data-language-autonym="Lietuvių" data-language-local-name="立陶宛语" 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/Le%C5%86%C4%B7iskais_%C4%81trums" title="Leņķiskais ātrums – 拉脱维亚语" lang="lv" hreflang="lv" data-title="Leņķiskais ātrums" data-language-autonym="Latviešu" data-language-local-name="拉脱维亚语" 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%90%D0%B3%D0%BE%D0%BB%D0%BD%D0%B0_%D0%B1%D1%80%D0%B7%D0%B8%D0%BD%D0%B0" title="Аголна брзина – 马其顿语" lang="mk" hreflang="mk" data-title="Аголна брзина" data-language-autonym="Македонски" data-language-local-name="马其顿语" 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%95%E0%B5%8B%E0%B4%A3%E0%B5%80%E0%B4%AF_%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%B5%E0%B5%87%E0%B4%97%E0%B4%82" title="കോണീയ പ്രവേഗം – 马拉雅拉姆语" lang="ml" hreflang="ml" data-title="കോണീയ പ്രവേഗം" data-language-autonym="മലയാളം" data-language-local-name="马拉雅拉姆语" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%95%E0%A5%8B%E0%A4%A8%E0%A5%80%E0%A4%AF_%E0%A4%B5%E0%A5%87%E0%A4%97" title="कोनीय वेग – 马拉地语" lang="mr" hreflang="mr" data-title="कोनीय वेग" data-language-autonym="मराठी" data-language-local-name="马拉地语" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Halaju_sudut" title="Halaju sudut – 马来语" lang="ms" hreflang="ms" data-title="Halaju sudut" data-language-autonym="Bahasa Melayu" data-language-local-name="马来语" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hoeksnelheid" title="Hoeksnelheid – 荷兰语" lang="nl" hreflang="nl" data-title="Hoeksnelheid" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Vinkelfart" title="Vinkelfart – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Vinkelfart" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" 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/Vinkelhastighet" title="Vinkelhastighet – 书面挪威语" lang="nb" hreflang="nb" data-title="Vinkelhastighet" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pr%C4%99dko%C5%9B%C4%87_k%C4%85towa" title="Prędkość kątowa – 波兰语" lang="pl" hreflang="pl" data-title="Prędkość kątowa" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Velocidade_angular" title="Velocidade angular – 葡萄牙语" lang="pt" hreflang="pt" data-title="Velocidade angular" data-language-autonym="Português" data-language-local-name="葡萄牙语" 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/Vitez%C4%83_unghiular%C4%83" title="Viteză unghiulară – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Viteză unghiulară" data-language-autonym="Română" data-language-local-name="罗马尼亚语" 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%A3%D0%B3%D0%BB%D0%BE%D0%B2%D0%B0%D1%8F_%D1%81%D0%BA%D0%BE%D1%80%D0%BE%D1%81%D1%82%D1%8C" title="Угловая скорость – 俄语" lang="ru" hreflang="ru" data-title="Угловая скорость" data-language-autonym="Русский" data-language-local-name="俄语" 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/Kutna_brzina" title="Kutna brzina – 塞尔维亚-克罗地亚语" lang="sh" hreflang="sh" data-title="Kutna brzina" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞尔维亚-克罗地亚语" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Angular_velocity" title="Angular velocity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Angular velocity" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Uhlov%C3%A1_r%C3%BDchlos%C5%A5" title="Uhlová rýchlosť – 斯洛伐克语" lang="sk" hreflang="sk" data-title="Uhlová rýchlosť" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克语" 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/Kotna_hitrost" title="Kotna hitrost – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Kotna hitrost" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" 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/Spidhi_yepaGonyo" title="Spidhi yepaGonyo – 绍纳语" lang="sn" hreflang="sn" data-title="Spidhi yepaGonyo" data-language-autonym="ChiShona" data-language-local-name="绍纳语" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Shpejt%C3%ABsia_k%C3%ABndore" title="Shpejtësia këndore – 阿尔巴尼亚语" lang="sq" hreflang="sq" data-title="Shpejtësia këndore" data-language-autonym="Shqip" data-language-local-name="阿尔巴尼亚语" 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%A3%D0%B3%D0%B0%D0%BE%D0%BD%D0%B0_%D0%B1%D1%80%D0%B7%D0%B8%D0%BD%D0%B0" title="Угаона брзина – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Угаона брзина" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Vinkelhastighet" title="Vinkelhastighet – 瑞典语" lang="sv" hreflang="sv" data-title="Vinkelhastighet" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%95%E0%B1%8B%E0%B0%A3%E0%B1%80%E0%B0%AF_%E0%B0%B5%E0%B1%87%E0%B0%97%E0%B0%82" title="కోణీయ వేగం – 泰卢固语" lang="te" hreflang="te" data-title="కోణీయ వేగం" data-language-autonym="తెలుగు" data-language-local-name="泰卢固语" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/A%C3%A7%C4%B1sal_h%C4%B1z" title="Açısal hız – 土耳其语" lang="tr" hreflang="tr" data-title="Açısal hız" data-language-autonym="Türkçe" data-language-local-name="土耳其语" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9F%D0%BE%D1%87%D0%BC%D0%B0%D0%BA%D1%87%D0%B0_%D1%82%D0%B8%D0%B7%D0%BB%D0%B5%D0%BA" title="Почмакча тизлек – 鞑靼语" lang="tt" hreflang="tt" data-title="Почмакча тизлек" data-language-autonym="Татарча / tatarça" data-language-local-name="鞑靼语" 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%9A%D1%83%D1%82%D0%BE%D0%B2%D0%B0_%D1%88%D0%B2%D0%B8%D0%B4%D0%BA%D1%96%D1%81%D1%82%D1%8C" title="Кутова швидкість – 乌克兰语" lang="uk" hreflang="uk" data-title="Кутова швидкість" data-language-autonym="Українська" data-language-local-name="乌克兰语" 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/%D8%B2%D8%A7%D9%88%DB%8C%D8%A7%D8%A6%DB%8C_%D8%B3%D9%85%D8%AA%D8%A7%D8%B1" title="زاویائی سمتار – 乌尔都语" lang="ur" hreflang="ur" data-title="زاویائی سمتار" data-language-autonym="اردو" data-language-local-name="乌尔都语" 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/Burchak_tezligi" title="Burchak tezligi – 乌兹别克语" lang="uz" hreflang="uz" data-title="Burchak tezligi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="乌兹别克语" 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/V%E1%BA%ADn_t%E1%BB%91c_g%C3%B3c" title="Vận tốc góc – 越南语" lang="vi" hreflang="vi" data-title="Vận tốc góc" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%A7%92%E9%80%9F%E5%BA%A6" title="角速度 – 吴语" lang="wuu" hreflang="wuu" data-title="角速度" data-language-autonym="吴语" data-language-local-name="吴语" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Kak-sok-t%C5%8D%CD%98" title="Kak-sok-tō͘ – 闽南语" lang="nan" hreflang="nan" data-title="Kak-sok-tō͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="闽南语" 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打印/导出 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="electron-print_pdf" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=%E8%A7%92%E9%80%9F%E5%BA%A6&action=show-download-screen"><span>下载为PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="本页面的可打印版本[p]" accesskey="p"><span>打印页面</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 在其他项目中 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Angular_velocity" hreflang="en"><span>维基共享资源</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q161635" title="链接到连接的数据仓库项目[g]" accesskey="g"><span>维基数据项目</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="外观"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">外观</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">隐藏</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">维基百科，自由的百科全书</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Angularvelocity.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Angularvelocity.svg/220px-Angularvelocity.svg.png" decoding="async" width="220" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Angularvelocity.svg/330px-Angularvelocity.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Angularvelocity.svg/440px-Angularvelocity.svg.png 2x" data-file-width="272" data-file-height="235" /></a><figcaption>角速度是用來描述<a href="/wiki/%E8%BD%89%E5%8B%95" class="mw-redirect" title="轉動">轉動</a>的速度以及該轉動發生當時的轉動軸方向。角速度向量的方向會在轉動軸方向上，在本例中（逆時針轉動）轉動向量是指向讀者的。</figcaption></figure> <p><b>角速度</b>（<b>Angular velocity</b>）是在<a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%A6" title="物理学">物理学</a>中定义为<a href="/wiki/%E8%A7%92%E4%BD%8D%E7%A7%BB" class="mw-redirect" title="角位移">角位移</a>的变化率，描述物体轉動時，在单位时间内转过多少角度以及转动方向的<a href="/wiki/%E5%90%91%E9%87%8F" title="向量">向量</a>，（更准确地说，是<a href="/wiki/%E8%B4%97%E5%90%91%E9%87%8F" class="mw-redirect" title="贗向量">贗向量</a>），通常用希腊字母<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Omega }"></span>或<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span>来表示。 </p><p>在<a href="/wiki/%E5%9B%BD%E9%99%85%E5%8D%95%E4%BD%8D%E5%88%B6" title="国际单位制">国际单位制</a>中，单位是<a href="/wiki/%E5%BC%A7%E5%BA%A6" title="弧度">弧度</a>每秒（rad/s）。在日常生活，通常量度單位時間內的轉動週數，即是<a href="/wiki/%E6%AF%8F%E5%88%86%E9%90%98%E8%BD%89%E9%80%9F" title="每分鐘轉速">每分鐘轉速</a>（rpm），電腦<a href="/wiki/%E7%A1%AC%E7%9B%98" title="硬盘">機械硬碟</a>和汽車引擎轉數就是以rpm來量度，物理學則以rev/min表示每分鐘轉動週數。 </p><p>角速度的方向垂直于转动平面，可通过<a href="/wiki/%E5%8F%B3%E6%89%8B%E5%AE%9A%E5%89%87" title="右手定則">右手定则</a>来确定，物體以逆時針方向轉動其角速度為正值，物體以順時針方向轉動其角速度為負值。 </p><p>角速度量值的大小稱作<b><a href="/wiki/%E8%A7%92%E9%A0%BB%E7%8E%87" class="mw-redirect" title="角頻率">角速率</a></b>，通常也是用ω來表示。<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="质点的角速度"><span id=".E8.B4.A8.E7.82.B9.E7.9A.84.E8.A7.92.E9.80.9F.E5.BA.A6"></span>质点的角速度</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%A7%92%E9%80%9F%E5%BA%A6&action=edit&section=1" title="编辑章节：质点的角速度"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="二維坐標系"><span id=".E4.BA.8C.E7.B6.AD.E5.9D.90.E6.A8.99.E7.B3.BB"></span>二維坐標系</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%A7%92%E9%80%9F%E5%BA%A6&action=edit&section=2" title="编辑章节：二維坐標系"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:AngularVelocity01.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/AngularVelocity01.png/256px-AngularVelocity01.png" decoding="async" width="256" height="256" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/AngularVelocity01.png/384px-AngularVelocity01.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/AngularVelocity01.png/512px-AngularVelocity01.png 2x" data-file-width="1790" data-file-height="1788" /></a><figcaption>位於<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/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>點的<a href="/wiki/%E8%B4%A8%E7%82%B9" class="mw-redirect" title="质点">质点</a>相對於<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/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>點的<b>角速度</b>是由其<a href="/wiki/%E9%80%9F%E5%BA%A6" title="速度">速度</a><a href="/wiki/%E5%90%91%E9%87%8F" title="向量">向量</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 \mathbf {V} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">V</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {V} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0048514530d0c0fb8a7beb795110815a818784d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.019ex; height:2.176ex;" alt="{\displaystyle \mathbf {V} }"></span>" <a href="/wiki/%E5%9E%82%E7%9B%B4" title="垂直">垂直</a>於<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 OP}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle OP}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdb46a90bdafeabc0a654bb9ad4067d5ce34e832" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.519ex; height:2.176ex;" alt="{\displaystyle OP}"></span><a href="/wiki/%E8%BF%9E%E7%BA%BF" title="连线">連線</a>的<a href="/wiki/%E5%88%86%E9%87%8F" class="mw-redirect" title="分量">分量</a>來決定 。</figcaption></figure> <p>一個质点在<a href="/w/index.php?title=%E4%BA%8C%E7%B6%AD%E5%B9%B3%E9%9D%A2&action=edit&redlink=1" class="new" title="二維平面（页面不存在）">二維平面</a>上的角速度是最基本的。如右圖所示，假使從<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span>點向（<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/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>）质点畫一條直線，則該<a href="/wiki/%E7%B2%92%E5%AD%90" title="粒子">粒子</a>的速度向量（<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 \mathbf {v} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35c1866e359fbfd2e0f606c725ba5cc37a5195d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.411ex; height:1.676ex;" alt="{\displaystyle \mathbf {v} }"></span>）可分成在沿著徑向上分量（<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 {v} _{\parallel }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∥</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {v} _{\parallel }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d62d38f5273c082e42311a8c4c948860edd65c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.282ex; height:2.509ex;" alt="{\displaystyle \mathrm {v} _{\parallel }}"></span>， - 徑向分量）以及<a href="/wiki/%E5%9E%82%E7%9B%B4" title="垂直">垂直</a>於<a href="/w/index.php?title=%E5%BE%91%E5%90%91&action=edit&redlink=1" class="new" title="徑向（页面不存在）">徑向</a>的分量（<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 {v} _{\perp }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {v} _{\perp }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/549845dba6d998e4c16b659a7de1a26ee3ebedeb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.738ex; height:2.009ex;" alt="{\displaystyle \mathrm {v} _{\perp }}"></span> - 切線方向分量）。 </p><p>由於粒子在徑向上的<a href="/wiki/%E9%81%8B%E5%8B%95" class="mw-redirect" title="運動">運動</a>並不會造成相對於<a href="/wiki/%E5%8E%9F%E9%BB%9E" title="原點">原點</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 O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span>）的轉動，在求取該粒子的角速度時，可以忽略<a href="/wiki/%E6%B0%B4%E5%B9%B3" class="mw-disambig" title="水平">水平</a>（徑向）分量。因此，轉動完全是由<a href="/wiki/%E5%88%87%E7%B7%9A" class="mw-redirect" title="切線">切線</a>方向的運動所造成的（如同质点在繞著等速率圓周運動），即角速度是完全由垂直（切線方向）的分量所決定的。 <a href="/wiki/%E8%B4%A8%E7%82%B9" class="mw-redirect" title="质点">质点</a><a href="/wiki/%E8%A7%92%E5%BA%A6" class="mw-redirect" title="角度">角度</a><a href="/wiki/%E4%BD%8D%E7%BD%AE" class="mw-disambig" title="位置">位置</a>的<a href="/w/index.php?title=%E6%94%B9%E8%AE%8A%E7%8E%87&action=edit&redlink=1" class="new" title="改變率（页面不存在）">改變率</a>與其<a href="/w/index.php?title=%E5%88%87%E7%B7%9A%E6%96%B9%E5%90%91&action=edit&redlink=1" class="new" title="切線方向（页面不存在）">切線方向</a><a href="/wiki/%E9%80%9F%E5%BA%A6" title="速度">速度</a>的關係式如下： </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 \mathrm {v} _{\perp }=r\,{\frac {d\phi }{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> </mrow> </msub> <mo>=</mo> <mi>r</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>ϕ</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {v} _{\perp }=r\,{\frac {d\phi }{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/995e9a6e6de92899c2a8d10aa22664aff6a636ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.71ex; height:5.509ex;" alt="{\displaystyle \mathrm {v} _{\perp }=r\,{\frac {d\phi }{dt}}}"></span></dd></dl> <p>定義角速度為<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega ={\frac {d\varphi }{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>φ</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega ={\frac {d\varphi }{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b11b14fafa4c27496f46feb3e0e2564c2805754" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.116ex; height:5.509ex;" alt="{\displaystyle \omega ={\frac {d\varphi }{dt}}}"></span>(其中<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 \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span>是<a href="/wiki/%E5%BC%A7%E5%BA%A6" title="弧度">弧度</a>，即弧长除以半径)，而<a href="/wiki/%E9%80%9F%E5%BA%A6" title="速度">速度</a>的<a href="/w/index.php?title=%E5%9E%82%E7%9B%B4%E5%88%86%E9%87%8F&action=edit&redlink=1" class="new" title="垂直分量（页面不存在）">垂直分量</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 \mathrm {v} _{\perp }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {v} _{\perp }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/549845dba6d998e4c16b659a7de1a26ee3ebedeb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.738ex; height:2.009ex;" alt="{\displaystyle \mathrm {v} _{\perp }}"></span>等於<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 {\mathbf {v} } |\,\sin(\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mspace width="thinmathspace" /> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\mathrm {\mathbf {v} } |\,\sin(\theta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8521603e23ecaf6f2ca6d19c5482aab62bc67c09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.234ex; height:2.843ex;" alt="{\displaystyle |\mathrm {\mathbf {v} } |\,\sin(\theta )}"></span>；其中θ是<a href="/wiki/%E5%90%91%E9%87%8F" title="向量">向量</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 \mathbf {r} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eca0f46511c4c986c48b254073732c0bd98ae0c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.102ex; height:1.676ex;" alt="{\displaystyle \mathbf {r} }"></span>與<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 \mathbf {v} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35c1866e359fbfd2e0f606c725ba5cc37a5195d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.411ex; height:1.676ex;" alt="{\displaystyle \mathbf {v} }"></span>的<a href="/wiki/%E5%A4%BE%E8%A7%92" class="mw-redirect" title="夾角">夾角</a>，則導出： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega ={\frac {|\mathrm {\mathbf {v} } |\sin(\theta )}{|\mathrm {\mathbf {r} } |}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega ={\frac {|\mathrm {\mathbf {v} } |\sin(\theta )}{|\mathrm {\mathbf {r} } |}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b1380eefadbeec01f6c2dc9f189996fc1b9f25f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:14.228ex; height:6.509ex;" alt="{\displaystyle \omega ={\frac {|\mathrm {\mathbf {v} } |\sin(\theta )}{|\mathrm {\mathbf {r} } |}}}"></span></dd></dl> <p>在二維坐標系中，角速度是一个只有大小没有方向的<a href="/wiki/%E8%B4%97%E7%B4%94%E9%87%8F" title="贗純量">贗純量</a>，而非純量。純量與贗純量不同的地方在於，當<i>x</i> 軸與<i>y</i> 軸對調時，純量不會因此而改變正負符號，然而贗純量卻會因此而改變。角度及角速度則是贗純量。以一般的定義，從<i>x</i> 軸转向<i>y</i> 軸的方向為轉動的正方向。倘若座標軸對調，而物體轉動不變，則角度的正負符號將會改變，因此角速度的正負號也跟著改變。 </p><p><b>注意：</b>角速度的正負號及數值量取決於原點位置及座標軸方向的選定。 </p> <div class="mw-heading mw-heading3"><h3 id="三維坐標系"><span id=".E4.B8.89.E7.B6.AD.E5.9D.90.E6.A8.99.E7.B3.BB"></span>三維坐標系</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%A7%92%E9%80%9F%E5%BA%A6&action=edit&section=3" title="编辑章节：三維坐標系"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在三維坐標系中，角速度變得比較複雜。在此狀況下，角速度通常被當作向量來看待；甚至更精確一點要當作偽向量。它不只具有數值，而且同時具有方向的特性。數值指的是單位時間內的角度變化率，而方向則是用來描述轉動軸的。概念上，可以利用<a href="/wiki/%E5%8F%B3%E6%89%8B%E5%AE%9A%E5%89%87" title="右手定則">右手定則</a>來標示角速度偽向量的正方向。原則如下： </p> <dl><dd><i>假設將右手（除了大拇指以外）的手指順著轉動的方向朝內彎曲，則大拇指所指的方向即是<b>角速度向量</b>的方向。</i></dd></dl> <p>正如同在二維座標系的例子中，一個质点的移動速度相對於原點可以分成一個沿著徑向以及另一個垂直徑向的分量。舉例而言，原點與质点的速度垂直分量的組合可以定義一個<i>轉動平面</i>，质点在此平面上的行為就如同在二維坐標系中的狀況下，其轉動軸則是一條通過原點且垂直此平面的線，這個軸訂定了角速度偽向量的方向，而角速度的數值則是如同在二維座標系狀況下求得的偽純量的值。當定義一個指向角速度偽向量方向單位向量<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 {\hat {n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d125dccc556f5c8b0bf98a4f3847590b3f353bd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:2.176ex;" alt="{\displaystyle {\hat {n}}}"></span>時，可以用類似二維坐標系的方式來表示角速度： </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 {\boldsymbol {\omega }}={\frac {|\mathrm {\mathbf {v} } |\sin(\theta )}{|\mathrm {\mathbf {r} } |}}\,{\hat {n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\omega }}={\frac {|\mathrm {\mathbf {v} } |\sin(\theta )}{|\mathrm {\mathbf {r} } |}}\,{\hat {n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1372a4bbd73c4391f881c865ff31f0b7796769ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:16.232ex; height:6.509ex;" alt="{\displaystyle {\boldsymbol {\omega }}={\frac {|\mathrm {\mathbf {v} } |\sin(\theta )}{|\mathrm {\mathbf {r} } |}}\,{\hat {n}}}"></span></dd></dl> <p>再加上<a href="/wiki/%E5%A4%96%E7%A9%8D" class="mw-redirect mw-disambig" title="外積">外積</a>的定義，則可以寫成： </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 {\boldsymbol {\omega }}={\frac {\mathbf {r} \times \mathbf {v} }{|\mathrm {\mathbf {r} } |^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\omega }}={\frac {\mathbf {r} \times \mathbf {v} }{|\mathrm {\mathbf {r} } |^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41383b2e9978676efe8f6da419a9be4eb45d8dbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:10.957ex; height:6.009ex;" alt="{\displaystyle {\boldsymbol {\omega }}={\frac {\mathbf {r} \times \mathbf {v} }{|\mathrm {\mathbf {r} } |^{2}}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="高维空间"><span id=".E9.AB.98.E7.BB.B4.E7.A9.BA.E9.97.B4"></span>高维空间</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%A7%92%E9%80%9F%E5%BA%A6&action=edit&section=4" title="编辑章节：高维空间"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>一般而言，在高維空間的角速度是一個二階<a href="/wiki/%E6%96%9C%E5%AF%B9%E7%A7%B0" class="mw-redirect" title="斜对称">斜對稱</a>的角位移張量對時間的微分。此張量具有<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 {n(n-1)}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n(n-1)}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d7e4c7b0026c4729031e5aa8110d5bb700d0162" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.438ex; height:5.676ex;" alt="{\displaystyle {\frac {n(n-1)}{2}}}"></span>個獨立分量，其中"<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 {n(n-1)}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n(n-1)}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d7e4c7b0026c4729031e5aa8110d5bb700d0162" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.438ex; height:5.676ex;" alt="{\displaystyle {\frac {n(n-1)}{2}}}"></span>"這個數字指的是在<b>n</b>-維<a href="/wiki/%E5%86%85%E7%A7%AF%E7%A9%BA%E9%97%B4" title="内积空间">內積空間</a>中轉動<a href="/wiki/%E6%9D%8E%E7%BE%A4" title="李群">李群</a>之<a href="/wiki/%E6%9D%8E%E4%BB%A3%E6%95%B8" title="李代數">李代數</a>的維度。<sup id="cite_ref-baez_2-0" class="reference"><a href="#cite_note-baez-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="刚体角速度"><span id=".E5.88.9A.E4.BD.93.E8.A7.92.E9.80.9F.E5.BA.A6"></span>刚体角速度</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%A7%92%E9%80%9F%E5%BA%A6&action=edit&section=5" title="编辑章节：刚体角速度"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r85099211">.mw-parser-output .hatnote{font-size:small}.mw-parser-output div.hatnote{padding-left:2em;margin-bottom:0.8em;margin-top:0.8em}.mw-parser-output .hatnote-notice-img::after{content:"\202f \202f \202f \202f "}.mw-parser-output .hatnote-notice-img-small::after{content:"\202f \202f "}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}body.skin-minerva .mw-parser-output .hatnote-notice-img,body.skin-minerva .mw-parser-output .hatnote-notice-img-small{display:none}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E5%88%9A%E4%BD%93%E5%8A%A8%E5%8A%9B%E5%AD%A6" title="刚体动力学">刚体动力学</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:AngularVelocity02.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/AngularVelocity02.png/256px-AngularVelocity02.png" decoding="async" width="256" height="157" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/AngularVelocity02.png/384px-AngularVelocity02.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/AngularVelocity02.png/512px-AngularVelocity02.png 2x" data-file-width="1280" data-file-height="784" /></a><figcaption><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 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/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>點在剛體（以藍色表示）上的位置，<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 \mathbf {R} _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {R} _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f89b7e6f1eb0602ce2df26f016b4a4a9d55f86f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.803ex; height:2.509ex;" alt="{\displaystyle \mathbf {R} _{i}}"></span>是以<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 O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span></i> 為中心在實驗室座標系上的位置；而<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 \mathbf {r} _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed603561819ebd007acd75a0931d3ba401ad677a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.902ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{i}}"></span>是以<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>O</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/470d46b4d626e35d82cd0d9f9aadc65ac47ab568" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.458ex; height:2.509ex;" alt="{\displaystyle O'}"></span>為中心在剛體座標系上的位置。此剛體座標系的原點則是在實驗室座標系中的向量位置<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 \mathbf {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5de85fcc2a00d8ba14aae84aeef812d7fef4b3d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.003ex; height:2.176ex;" alt="{\displaystyle \mathbf {R} }"></span></b>上。</figcaption></figure> <p>為了處理<a href="/wiki/%E5%89%9B%E9%AB%94" class="mw-redirect" title="剛體">剛體</a>運動的問題，最好採用固定在剛體上的座標系統，然後再學習此座標系統與實驗室座標系統之間的座標轉換。如右圖所示，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span>為實驗室座標系統的原點，而<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>O</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/470d46b4d626e35d82cd0d9f9aadc65ac47ab568" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.458ex; height:2.509ex;" alt="{\displaystyle O'}"></span>是剛體座標系統的原點，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span>與<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>O</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/470d46b4d626e35d82cd0d9f9aadc65ac47ab568" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.458ex; height:2.509ex;" alt="{\displaystyle O'}"></span>之間的向量<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 \mathbf {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5de85fcc2a00d8ba14aae84aeef812d7fef4b3d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.003ex; height:2.176ex;" alt="{\displaystyle \mathbf {R} }"></span>。質點（<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/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span>）在剛體上<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/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>點的位置上，此質點在實驗室座標中的向量位置是<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 \mathbf {R} _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {R} _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f89b7e6f1eb0602ce2df26f016b4a4a9d55f86f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.803ex; height:2.509ex;" alt="{\displaystyle \mathbf {R} _{i}}"></span>，而在剛體座標中的向量位置為<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 \mathbf {r} _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed603561819ebd007acd75a0931d3ba401ad677a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.902ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{i}}"></span>。我們可以看到此質點的位置可以寫成： </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 \mathbf {R} _{i}=\mathbf {R} +\mathbf {r} _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">R</mi> </mrow> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {R} _{i}=\mathbf {R} +\mathbf {r} _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6002070fa6d4ad65b2b6623f4f57918222bf11ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.647ex; height:2.509ex;" alt="{\displaystyle \mathbf {R} _{i}=\mathbf {R} +\mathbf {r} _{i}}"></span></dd></dl> <p>刚体最重要的特征为任意两点之间距离不随时间变化。这意味着矢量<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 \mathbf {r} _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed603561819ebd007acd75a0931d3ba401ad677a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.902ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{i}}"></span>的长度是不变的。根据欧拉刚体的有限旋转定理，我们可以用<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 {\mathcal {R}}\mathbf {r} _{io}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>o</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {R}}\mathbf {r} _{io}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d38bb10cad262bea46af36030009125705be2524" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.67ex; height:2.509ex;" alt="{\displaystyle {\mathcal {R}}\mathbf {r} _{io}}"></span>来代替<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 \mathbf {r} _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed603561819ebd007acd75a0931d3ba401ad677a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.902ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{i}}"></span>，其中<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 {\mathcal {R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74532dc308c806964b832df0d0d73352195c2f2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.971ex; height:2.176ex;" alt="{\displaystyle {\mathcal {R}}}"></span>代表旋转矩阵，而<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 \mathbf {r} _{io}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>o</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{io}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/419572dc2a878b11126313a6e131daab844ed8be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.699ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{io}}"></span>是初始时刻的质点的位置。这个替代显得非常有意义，随时间变化的只有<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 {\mathcal {R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74532dc308c806964b832df0d0d73352195c2f2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.971ex; height:2.176ex;" alt="{\displaystyle {\mathcal {R}}}"></span>，而不是相对矢量<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 \mathbf {r} _{io}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>o</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{io}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/419572dc2a878b11126313a6e131daab844ed8be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.699ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{io}}"></span>。對於刚体就<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>O</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/470d46b4d626e35d82cd0d9f9aadc65ac47ab568" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.458ex; height:2.509ex;" alt="{\displaystyle O'}"></span>旋转，质点的位置可以写为： </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 \mathbf {R} _{i}=\mathbf {R} +{\mathcal {R}}\mathbf {r} _{io}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">R</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>o</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {R} _{i}=\mathbf {R} +{\mathcal {R}}\mathbf {r} _{io}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e76fd46d3c2f96a1752f583607b2805912b6824" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.415ex; height:2.509ex;" alt="{\displaystyle \mathbf {R} _{i}=\mathbf {R} +{\mathcal {R}}\mathbf {r} _{io}}"></span></dd></dl> <p>就质点的速度对时间微分，可以得到質點的速度： </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 \mathbf {V} _{i}=\mathbf {V} +{\frac {d{\mathcal {R}}}{dt}}\mathbf {r} _{io}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">V</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>o</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {V} _{i}=\mathbf {V} +{\frac {d{\mathcal {R}}}{dt}}\mathbf {r} _{io}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83503b51071d1ba39e50cc008eb2268688325852" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:17.499ex; height:5.509ex;" alt="{\displaystyle \mathbf {V} _{i}=\mathbf {V} +{\frac {d{\mathcal {R}}}{dt}}\mathbf {r} _{io}}"></span></dd></dl> <p>其中<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 \mathbf {V} _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {V} _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6961baf3efe47cd95e04a2e32f917e33fe787ef3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.819ex; height:2.509ex;" alt="{\displaystyle \mathbf {V} _{i}}"></span>是质点在實驗室座標中的速度，而<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 \mathbf {V} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">V</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {V} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0048514530d0c0fb8a7beb795110815a818784d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.019ex; height:2.176ex;" alt="{\displaystyle \mathbf {V} }"></span></b>是<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>O</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/470d46b4d626e35d82cd0d9f9aadc65ac47ab568" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.458ex; height:2.509ex;" alt="{\displaystyle O'}"></span>点（剛體座標的原點）的在實驗室座標中的速度，故质点的速度可以写成： </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 \mathbf {V} _{i}=\mathbf {V} +{\boldsymbol {\Omega }}\mathbf {r} _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">V</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Ω</mi> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {V} _{i}=\mathbf {V} +{\boldsymbol {\Omega }}\mathbf {r} _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b1327a1518152b6388c7ec125f12dd9ec075018" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.611ex; height:2.509ex;" alt="{\displaystyle \mathbf {V} _{i}=\mathbf {V} +{\boldsymbol {\Omega }}\mathbf {r} _{i}}"></span></dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Omega }"></span>是角速度<a href="/wiki/%E5%BC%A0%E9%87%8F" class="mw-redirect" title="张量">张量</a>，如果我们取角速度张量的对偶，我们即可得到角速度的伪矢量。 </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 {\boldsymbol {\omega }}=[\omega _{x},\omega _{y},\omega _{z}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> <mo>=</mo> <mo stretchy="false">[</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\omega }}=[\omega _{x},\omega _{y},\omega _{z}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8f418d52c41570663e22f7b19a8d3a427b69cab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.69ex; height:3.009ex;" alt="{\displaystyle {\boldsymbol {\omega }}=[\omega _{x},\omega _{y},\omega _{z}]}"></span></dd></dl> <p>而矩陣的乘法可以用外積來取代，導出： </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 \mathbf {V} _{i}=\mathbf {V} +{\boldsymbol {\omega }}\times \mathbf {r} _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">V</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {V} _{i}=\mathbf {V} +{\boldsymbol {\omega }}\times \mathbf {r} _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c2646d1b052981bf942e306064293e86f6dd90d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.188ex; height:2.509ex;" alt="{\displaystyle \mathbf {V} _{i}=\mathbf {V} +{\boldsymbol {\omega }}\times \mathbf {r} _{i}}"></span></dd></dl> <p>由此可見，剛體中質點的速度可分解成兩項—剛體中某固定參考點的速度再加上一項包含該質點相對於此參考點的角速度的外積。相較於<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>O</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/470d46b4d626e35d82cd0d9f9aadc65ac47ab568" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.458ex; height:2.509ex;" alt="{\displaystyle O'}"></span>點對於<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span>點的角速度，這個角速度是“自旋”角速度。 </p><p>很<b>重要</b>的是，每個在剛體中的質點具有相同的自轉角速度，此自轉角速度與剛體上或是實驗室座標系統的原點的選擇無關。換句話說，這是一個剛體特質所具有的真實物理量，與座標系統的選擇無關。然而剛體上的參考點相對於實驗室座標原點的角速度則和座標系統的選擇有關，為了方便起見，通常選擇該剛體的<a href="/wiki/%E8%B3%AA%E5%BF%83" title="質心">質心</a>當作剛體座標系統的原點，這將大大地簡化以數學形式在剛體<a href="/wiki/%E8%A7%92%E5%8B%95%E9%87%8F" class="mw-redirect" title="角動量">角動量</a>上的表達。 </p> <div class="mw-heading mw-heading2"><h2 id="參見"><span id=".E5.8F.83.E8.A6.8B"></span>參見</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%A7%92%E9%80%9F%E5%BA%A6&action=edit&section=6" title="编辑章节：參見"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E8%A7%92%E9%A0%BB%E7%8E%87" class="mw-redirect" title="角頻率">角頻率</a></li> <li><a href="/wiki/%E8%A7%92%E5%8B%95%E9%87%8F" class="mw-redirect" title="角動量">角動量</a></li> <li><a href="/w/index.php?title=%E9%9D%A2%E7%A9%8D%E9%80%9F%E5%BA%A6&action=edit&redlink=1" class="new" title="面積速度（页面不存在）">面積速度</a></li> <li><a href="/wiki/%E7%AD%89%E8%B7%9D%E5%90%8C%E6%A7%8B" class="mw-redirect" title="等距同構">等距同構</a></li> <li><a href="/wiki/%E6%9D%8E%E4%BB%A3%E6%95%B8" title="李代數">李代數</a></li> <li><a href="/wiki/%E6%AD%A3%E4%BA%A4%E7%BE%A4" title="正交群">正交群</a></li> <li><a href="/wiki/%E8%BD%AC%E5%8A%A8%E7%BE%A4" title="转动群">轉動群</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="參考"><span id=".E5.8F.83.E8.80.83"></span>參考</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%A7%92%E9%80%9F%E5%BA%A6&action=edit&section=7" title="编辑章节：參考"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Halliday、Resnick、Walker 原著。《物理（上）第七版》，第10-5頁。全華圖書股份有限公司出版。</span> </li> <li id="cite_note-baez-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-baez_2-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://math.ucr.edu/home/baez/classical/galilei2.pdf">Rotations and Angular Momentum</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20210423113315/http://math.ucr.edu/home/baez/classical/galilei2.pdf">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>） on the Classical Mechanics page of <a rel="nofollow" class="external text" href="http://math.ucr.edu/home/baez/README.html">the website of John Baez</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20201125190752/http://math.ucr.edu/home/baez/README.html">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）, especially Questions 1 and 2.</span> </li> </ol></div> <style data-mw-deduplicate="TemplateStyles:r80540462">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .refbegin-100{font-size:100%}</style><div class="refbegin" style=""> <ul><li><span class="citation wikicite" id="endnote_Symon1971"><sup></sup></span> <cite class="citation book">Symon, Keith. Mechanics. Addison-Wesley, Reading, MA. 1971. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9780201073928" class="internal mw-magiclink-isbn">ISBN 978-0-201-07392-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%A7%92%E9%80%9F%E5%BA%A6&rft.aufirst=Keith&rft.aulast=Symon&rft.btitle=Mechanics&rft.date=1971&rft.genre=book&rft.pub=Addison-Wesley%2C+Reading%2C+MA&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><span class="citation wikicite" id="endnote_LL"><sup></sup></span> <cite class="citation book"><a href="/wiki/%E5%88%97%E5%A4%AB%C2%B7%E6%9C%97%E9%81%93" title="列夫·朗道">Landau, L.D.</a>; <a href="/wiki/%E5%8F%B6%E5%A4%AB%E6%A0%B9%E5%B0%BC%C2%B7%E5%88%A9%E5%A4%AB%E5%B8%8C%E8%8C%A8" title="叶夫根尼·利夫希茨">Lifshitz, E.M.</a> Mechanics. Butterworth-Heinemann. 1997. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-750-62896-0" title="Special:网络书源/0-750-62896-0"><span title="国际标准书号">ISBN</span> 0-750-62896-0</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%A7%92%E9%80%9F%E5%BA%A6&rft.aufirst=L.D.&rft.aulast=Landau&rft.btitle=Mechanics&rft.date=1997&rft.genre=book&rft.isbn=0-750-62896-0&rft.pub=Butterworth-Heinemann&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> <span style="display:none;font-size:100%" class="error citation-comment">引文使用过时参数<code style="color:inherit; border:inherit; padding:inherit;">coauthors</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#deprecated_params" title="Help:引文格式1错误">帮助</a>)</span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="外部連接"><span id=".E5.A4.96.E9.83.A8.E9.80.A3.E6.8E.A5"></span>外部連接</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%A7%92%E9%80%9F%E5%BA%A6&action=edit&section=8" title="编辑章节：外部連接"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r82655521">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box side-box-right plainlinks sistersitebox" style="font-size:small;"><style data-mw-deduplicate="TemplateStyles:r82655520">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/40px-Wiktionary-logo.svg.png" decoding="async" width="40" height="38" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/60px-Wiktionary-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/80px-Wiktionary-logo.svg.png 2x" data-file-width="370" data-file-height="350" /></span></span></div> <div class="side-box-text plainlist">查看<a href="/wiki/%E7%BB%B4%E5%9F%BA%E8%AF%8D%E5%85%B8" title="维基词典">维基词典</a>中的词条「<b><a href="https://zh.wiktionary.org/wiki/Special:Search/%E8%A7%92%E9%80%9F%E5%BA%A6" class="extiw" title="wikt:Special:Search/角速度">角速度</a></b>」。</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r82655521"><div class="side-box side-box-right plainlinks sistersitebox" style="font-size:small;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r82655520"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist"><a href="/wiki/%E7%BB%B4%E5%9F%BA%E5%85%B1%E4%BA%AB%E8%B5%84%E6%BA%90" title="维基共享资源">维基共享资源</a>上的相关多媒体资源：<a href="https://commons.wikimedia.org/wiki/Category:Angular_velocity" class="extiw" title="commons:Category:Angular velocity"><span style="font-weight:bold;">角速度</span></a></div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://books.google.com/books?id=QBc5AAAAMAAJ&pg=PA88">A college text-book of physics</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20201202074045/https://books.google.com/books?id=QBc5AAAAMAAJ&pg=PA88">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>） By Arthur Lalanne Kimball (<i>Angular Velocity of a particle</i>)</li> <li><cite class="citation web">Pickering, Steve. <a rel="nofollow" class="external text" href="http://www.sixtysymbols.com/videos/angularvelocity.htm">ω Speed of Rotation [Angular Velocity]</a>. Sixty Symbols. <a href="/wiki/Brady_Haran" class="mw-redirect" title="Brady Haran">Brady Haran</a> for the <a href="/wiki/University_of_Nottingham" class="mw-redirect" title="University of Nottingham">University of Nottingham</a>. 2009 <span class="reference-accessdate"> [<span class="nowrap">2017-02-13</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20200808030328/http://www.sixtysymbols.com/videos/angularvelocity.htm">存档</a>于2020-08-08）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%A7%92%E9%80%9F%E5%BA%A6&rft.atitle=%CF%89+Speed+of+Rotation+%5BAngular+Velocity%5D&rft.aufirst=Steve&rft.aulast=Pickering&rft.date=2009&rft.genre=unknown&rft.jtitle=Sixty+Symbols&rft_id=http%3A%2F%2Fwww.sixtysymbols.com%2Fvideos%2Fangularvelocity.htm&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div class="navbox-styles"><style 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<tbody><tr> <th colspan="4">线性（平动）的量</th> <td rowspan="12" style="border:none;backgound:none;"></td> <th colspan="4">角度（转动）的量</th> </tr> <tr> <th style="font-weight:normal;font-size:80%;">量纲</th> <th style="font-weight:normal;">—</th> <th style="font-weight:normal;">L</th> <th style="font-weight:normal;">L<sup>2</sup></th> <th style="font-weight:normal;font-size:80%;">量纲</th> <th style="font-weight:normal;">—</th> <th style="font-weight:normal;">—</th> <th style="font-weight:normal;">—</th> </tr> <tr> <th style="font-weight:normal;">T</th> <td><a href="/wiki/%E6%97%B6%E9%97%B4" title="时间">时间</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">t</span></span><br /><a href="/wiki/%E7%A7%92" title="秒">s</a></td> <td><a href="/wiki/%E4%BD%8D%E7%A7%BB%E7%A7%AF%E5%88%86" title="位移积分">位移积分</a>: <span class="serif"><span class="texhtml"><b>A</b></span></span><br /><span class="ilh-all" data-orig-title="m s" data-lang-code="en" data-lang-name="英语" data-foreign-title="meter second"><span class="ilh-page"><a href="/w/index.php?title=M_s&action=edit&redlink=1" class="new" title="M s（页面不存在）">m s</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/meter_second" class="extiw" title="en:meter second"><span lang="en" dir="auto">meter second</span></a></span>）</span></span></td> <td></td> <th style="font-weight:normal;">T</th> <td><a href="/wiki/%E6%97%B6%E9%97%B4" title="时间">时间</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">t</span></span><br /><a href="/wiki/%E7%A7%92" title="秒">s</a></td> <td></td> <td></td> </tr> <tr> <th style="font-weight:normal;">—</th> <td></td> <td><a href="/wiki/%E8%B7%9D%E7%A6%BB" title="距离">距离</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">d</span></span>, <span class="nowrap"><a href="/wiki/%E4%BD%8D%E7%BD%AE%E5%90%91%E9%87%8F" title="位置向量">位矢</a>: <span class="serif"><span class="texhtml"><b>r</b></span></span>, <span class="serif"><span class="texhtml"><b>s</b></span></span>, <span class="serif"><span class="texhtml"><b>x</b></span></span></span>, <a href="/wiki/%E4%BD%8D%E7%A7%BB" title="位移">位移</a><br /><a href="/wiki/%E7%B1%B3_(%E5%8D%95%E4%BD%8D)" title="米 (单位)">m</a></td> <td><a href="/wiki/%E9%9D%A2%E7%A7%AF" title="面积">面积</a>: <span class="serif"><span class="texhtml"><i>A</i></span></span><br /><a href="/wiki/%E5%B9%B3%E6%96%B9%E7%B1%B3" title="平方米">m<sup>2</sup></a></td> <th style="font-weight:normal;">—</th> <td></td> <td><a href="/wiki/%E8%A7%92" title="角">角度</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">θ</span></span>, <a href="/wiki/%E8%A7%92%E7%A7%BB" title="角移">角移</a>: <span class="serif"><span class="texhtml"><b>θ</b></span></span><br /><a href="/wiki/%E5%BC%A7%E5%BA%A6" title="弧度">rad</a></td> <td><span class="nowrap"><a href="/wiki/%E7%AB%8B%E9%AB%94%E8%A7%92" title="立體角">立體角</a>: <span class="serif"><span class="texhtml">Ω</span></span><br /><a href="/wiki/%E7%90%83%E9%9D%A2%E5%BA%A6" title="球面度">rad<sup>2</sup>, sr</a></span></td> </tr> <tr> <th style="font-weight:normal;">T<sup>−1</sup></th> <td><span class="nowrap"><a href="/wiki/%E9%A0%BB%E7%8E%87_(%E7%89%A9%E7%90%86%E5%AD%B8)" title="頻率 (物理學)">頻率</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">f</span></span></span><br /><span class="ilh-all" data-orig-title="每秒" data-lang-code="en" data-lang-name="英语" data-foreign-title="inverse second"><span class="ilh-page"><a href="/w/index.php?title=%E6%AF%8F%E7%A7%92&action=edit&redlink=1" class="new" title="每秒（页面不存在）">s<sup>−1</sup></a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/inverse_second" class="extiw" title="en:inverse second"><span lang="en" dir="auto">inverse second</span></a></span>）</span></span>, <a href="/wiki/%E8%B5%AB%E5%85%B9" title="赫兹">Hz</a></td> <td><a href="/wiki/%E9%80%9F%E7%8E%87" title="速率">速率</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">v</span></span>, <a href="/wiki/%E9%80%9F%E5%BA%A6" title="速度">速度</a>: <span class="serif"><span class="texhtml"><b>v</b></span></span><br /><a href="/wiki/%E7%B1%B3%E6%AF%8F%E7%A7%92" title="米每秒">m s<sup>−1</sup></a></td> <td><a href="/wiki/%E9%BB%8F%E5%BA%A6" title="黏度">面積速率</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">ν</span></span><br /><a href="https://en.wikipedia.org/wiki/metre_squared_per_second" class="extiw" title="en:metre squared per second">m<sup>2</sup> s<sup>−1</sup></a></td> <th style="font-weight:normal;">T<sup>−1</sup></th> <td><span class="nowrap"><a href="/wiki/%E9%A0%BB%E7%8E%87_(%E7%89%A9%E7%90%86%E5%AD%B8)" title="頻率 (物理學)">頻率</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">f</span></span></span><br /><span class="ilh-all" data-orig-title="每秒" data-lang-code="en" data-lang-name="英语" data-foreign-title="inverse second"><span class="ilh-page"><a href="/w/index.php?title=%E6%AF%8F%E7%A7%92&action=edit&redlink=1" class="new" title="每秒（页面不存在）">s<sup>−1</sup></a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/inverse_second" class="extiw" title="en:inverse second"><span lang="en" dir="auto">inverse second</span></a></span>）</span></span>, <a href="/wiki/%E8%B5%AB%E5%85%B9" title="赫兹">Hz</a></td> <td><a class="mw-selflink selflink">角速率</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">ω</span></span>, <a class="mw-selflink selflink">角速度</a>: <span class="serif"><span class="texhtml"><b>ω</b></span></span><br /><a href="/wiki/%E5%BC%A7%E5%BA%A6%E6%AF%8F%E7%A7%92" title="弧度每秒">rad<span style="letter-spacing:0.1em"> </span>s<sup>−1</sup></a></td> <td></td> </tr> <tr> <th style="font-weight:normal;">T<sup>−2</sup></th> <td></td> <td><a href="/wiki/%E5%8A%A0%E9%80%9F%E5%BA%A6" title="加速度">加速度</a>: <span class="serif"><span class="texhtml"><b>a</b></span></span><br /><a href="/wiki/%E7%B1%B3%E6%AF%8F%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A7%92" title="米每二次方秒">m s<sup>−2</sup></a></td> <td></td> <th style="font-weight:normal;">T<sup>−2</sup></th> <td></td> <td><a href="/wiki/%E8%A7%92%E5%8A%A0%E9%80%9F%E5%BA%A6" title="角加速度">角加速度</a>: <span class="serif"><span class="texhtml"><b>α</b></span></span><br />rad<span style="letter-spacing:0.1em"> </span>s<sup>−2</sup></td> <td></td> </tr> <tr> <th style="font-weight:normal;">T<sup>−3</sup></th> <td></td> <td><a href="/wiki/%E5%8A%A0%E5%8A%A0%E9%80%9F%E5%BA%A6" title="加加速度">加加速度</a>: <span class="serif"><span class="texhtml"><b>j</b></span></span><br />m s<sup>−3</sup></td> <td></td> <th style="font-weight:normal;">T<sup>−3</sup></th> <td></td> <td><a href="/wiki/%E5%8A%A0%E5%8A%A0%E9%80%9F%E5%BA%A6" title="加加速度">角加加速度</a>: <span class="serif"><span class="texhtml"><b>ζ</b></span></span><br />rad<span style="letter-spacing:0.1em"> </span>s<sup>−3</sup></td> <td></td> </tr> <tr> <td colspan="4" 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/%E8%B4%A8%E9%87%8F" title="质量">质量</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">m</span></span><br /><a href="/wiki/%E5%8D%83%E5%85%8B" title="千克">kg</a></td> <td></td> <td></td> <th style="font-weight:normal;">ML<sup>2</sup></th> <td><a href="/wiki/%E8%BD%89%E5%8B%95%E6%85%A3%E9%87%8F" title="轉動慣量">轉動慣量</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">I</span></span><br />kg<span style="letter-spacing:0.1em"> </span>m<sup>2</sup></td> <td></td> <td></td> </tr> <tr> <th style="font-weight:normal;">MT<sup>−1</sup></th> <td></td> <td><a href="/wiki/%E5%8A%A8%E9%87%8F" title="动量">动量</a>: <span class="serif"><span class="texhtml"><b>p</b></span></span>, <a href="/wiki/%E5%86%B2%E9%87%8F" title="冲量">冲量</a>: <span class="serif"><span class="texhtml"><b>J</b></span></span><br />kg<span style="letter-spacing:0.1em"> </span>m s<sup>−1</sup>, <span class="ilh-all" data-orig-title="N s" data-lang-code="en" data-lang-name="英语" data-foreign-title="newton second"><span class="ilh-page"><a href="/w/index.php?title=N_s&action=edit&redlink=1" class="new" title="N s（页面不存在）">N s</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/newton_second" class="extiw" title="en:newton second"><span lang="en" dir="auto">newton second</span></a></span>）</span></span></td> <td><a href="/wiki/%E4%BD%9C%E7%94%A8%E9%87%8F" title="作用量">作用量</a>: <span class="serif"><span class="texhtml">𝒮</span></span>, <a href="/wiki/Actergy" class="mw-redirect" title="Actergy">actergy</a>: <span class="serif"><span class="texhtml">ℵ</span></span><br />kg<span style="letter-spacing:0.1em"> </span>m<sup>2</sup> s<sup>−1</sup>, <span class="ilh-all" data-orig-title="J s" data-lang-code="en" data-lang-name="英语" data-foreign-title="joule-second"><span class="ilh-page"><a href="/w/index.php?title=J_s&action=edit&redlink=1" class="new" title="J s（页面不存在）">J s</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/joule-second" class="extiw" title="en:joule-second"><span lang="en" dir="auto">joule-second</span></a></span>）</span></span></td> <th style="font-weight:normal;">ML<sup>2</sup>T<sup>−1</sup></th> <td></td> <td><a href="/wiki/%E8%A7%92%E5%8A%A8%E9%87%8F" title="角动量">角动量</a>: <span class="serif"><span class="texhtml"><b>L</b></span></span>, <a href="/wiki/%E7%B6%93%E5%85%B8%E5%8A%9B%E5%AD%B8%E6%96%B9%E7%A8%8B%E5%88%97%E8%A1%A8#導出的動力學物理量" title="經典力學方程列表">角衝量</a>: <span class="serif"><span class="texhtml"><b>ι</b></span></span><br />kg<span style="letter-spacing:0.1em"> </span>m<sup>2</sup> s<sup>−1</sup></td> <td><a href="/wiki/%E4%BD%9C%E7%94%A8%E9%87%8F" title="作用量">作用量</a>: <span class="serif"><span class="texhtml">𝒮</span></span>, <a href="/wiki/Actergy" class="mw-redirect" title="Actergy">actergy</a>: <span class="serif"><span class="texhtml">ℵ</span></span><br />kg<span style="letter-spacing:0.1em"> </span>m<sup>2</sup> s<sup>−1</sup>, <span class="ilh-all" data-orig-title="J s" data-lang-code="en" data-lang-name="英语" data-foreign-title="joule-second"><span class="ilh-page"><a href="/w/index.php?title=J_s&action=edit&redlink=1" class="new" title="J s（页面不存在）">J s</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/joule-second" class="extiw" title="en:joule-second"><span lang="en" dir="auto">joule-second</span></a></span>）</span></span></td> </tr> <tr> <th style="font-weight:normal;">MT<sup>−2</sup></th> <td></td> <td><a href="/wiki/%E5%8A%9B" title="力">力</a>: <span class="serif"><span class="texhtml"><b>F</b></span></span>, <a href="/wiki/%E9%87%8D%E9%87%8F" title="重量">重量</a>: <span class="serif"><span class="texhtml"><b>F</b><sub>g</sub></span></span><br /><span style="margin-right:0.1em;">kg </span> m s<sup>−2</sup>, <a href="/wiki/%E7%89%9B%E9%A0%93_(%E5%96%AE%E4%BD%8D)" title="牛頓 (單位)">N</a></td> <td><a href="/wiki/%E8%83%BD%E9%87%8F" title="能量">能量</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">E</span></span>, <a href="/wiki/%E5%8A%9F" title="功">功</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">W</span></span><br /><span style="margin-right:0.1em;">kg</span> m<sup>2</sup> s<sup>−2</sup>, <a href="/wiki/%E7%84%A6%E8%80%B3" title="焦耳">J</a></td> <th style="font-weight:normal;">ML<sup>2</sup>T<sup>−2</sup></th> <td></td> <td><a href="/wiki/%E5%8A%9B%E7%9F%A9" title="力矩">力矩</a>: <span class="serif"><span class="texhtml"><b>τ</b></span></span>, <span class="ilh-all" data-orig-title="Moment (physics)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Moment (physics)"><span class="ilh-page"><a href="/w/index.php?title=Moment_(physics)&action=edit&redlink=1" class="new" title="Moment (physics)（页面不存在）">moment</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Moment_(physics)" class="extiw" title="en:Moment (physics)"><span lang="en" dir="auto">Moment (physics)</span></a></span>）</span></span>: <span class="serif"><span class="texhtml"><b>M</b></span></span><br /><span style="margin-right:0.1em;">kg</span> m<sup>2</sup> s<sup>−2</sup>, <a href="/wiki/%E7%89%9B%E9%A0%93%E7%B1%B3" title="牛頓米">N m</a></td> <td><a href="/wiki/%E8%83%BD%E9%87%8F" title="能量">能量</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">E</span></span>, <a href="/wiki/%E5%8A%9F" title="功">功</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">W</span></span><br /><span style="margin-right:0.1em;">kg</span> m<sup>2</sup> s<sup>−2</sup>, <a href="/wiki/%E7%84%A6%E8%80%B3" title="焦耳">J</a></td> </tr> <tr> <th style="font-weight:normal;">MT<sup>−3</sup></th> <td></td> <td><a href="/wiki/%E5%8A%A0%E5%8A%9B" title="加力">加力</a>: <span class="serif"><span class="texhtml"><b>Y</b></span></span><br /><span style="margin-right:0.1em;">kg</span> m s<sup>−3</sup>, N s<sup>−1</sup></td> <td><a href="/wiki/%E5%8A%9F%E7%8E%87" title="功率">功率</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">P</span></span><br /><span style="margin-right:0.1em;">kg</span> m<sup>2</sup> s<sup>−3</sup>, <a href="/wiki/%E7%93%A6%E7%89%B9" title="瓦特">W</a></td> <th style="font-weight:normal;">ML<sup>2</sup>T<sup>−3</sup></th> <td></td> <td><span class="ilh-all" data-orig-title="rotatum" data-lang-code="en" data-lang-name="英语" data-foreign-title="rotatum"><span class="ilh-page"><a href="/w/index.php?title=Rotatum&action=edit&redlink=1" class="new" title="Rotatum（页面不存在）">rotatum</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/rotatum" class="extiw" title="en:rotatum"><span lang="en" dir="auto">rotatum</span></a></span>）</span></span>: <span class="serif"><span class="texhtml"><b>P</b></span></span><br /><span style="margin-right:0.1em;">kg</span> m<sup>2</sup> s<sup>−3</sup>, N m s<sup>−1</sup></td> <td><a href="/wiki/%E5%8A%9F%E7%8E%87" title="功率">功率</a>: <span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;">P</span></span><br /><span style="margin-right:0.1em;">kg</span> m<sup>2</sup> s<sup>−3</sup>, <a href="/wiki/%E7%93%A6%E7%89%B9" title="瓦特">W</a></td> </tr> </tbody></table></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">检索自“<a dir="ltr" href="https://zh.wikipedia.org/w/index.php?title=角速度&oldid=84618630">https://zh.wikipedia.org/w/index.php?title=角速度&oldid=84618630</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:%E9%A1%B5%E9%9D%A2%E5%88%86%E7%B1%BB" title="Special:页面分类">分类</a>：<ul><li><a href="/wiki/Category:%E8%A7%92" title="Category:角">角</a></li><li><a href="/wiki/Category:%E8%BF%90%E5%8A%A8%E5%AD%A6%E6%80%A7%E8%B4%A8" title="Category:运动学性质">运动学性质</a></li><li><a href="/wiki/Category:%E6%97%8B%E8%BD%89%E5%B0%8D%E7%A8%B1" title="Category:旋轉對稱">旋轉對稱</a></li><li><a href="/wiki/Category:%E6%97%B6%E9%97%B4%E9%80%9F%E7%8E%87" title="Category:时间速率">时间速率</a></li><li><a href="/wiki/Category:%E5%BC%A0%E9%87%8F" title="Category:张量">张量</a></li><li><a href="/wiki/Category:%E9%80%9F%E5%BA%A6" title="Category:速度">速度</a></li></ul></div><div id="mw-hidden-catlinks" 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