CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Linear motion - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"c921d44a-c7fb-49c5-a583-3e75f4e8a103","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Linear_motion","wgTitle":"Linear motion","wgCurRevisionId":1263299876,"wgRevisionId":1263299876,"wgArticleId":16652317,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles with short description","Short description is different from Wikidata","Commons category link is on Wikidata","Linear motion","Classical mechanics"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Linear_motion","wgRelevantArticleId":16652317,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgRedirectedFrom":"Rectilinear_motion","wgNoticeProject": "wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":10000,"wgInternalRedirectTargetUrl":"/wiki/Linear_motion","wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q2035846","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false, "wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.tablesorter.styles":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["mediawiki.action.view.redirect","ext.cite.ux-enhancements","ext.scribunto.logs","site","mediawiki.page.ready","jquery.tablesorter","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher", "ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cjquery.tablesorter.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.8"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Linear motion - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Linear_motion"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Linear_motion&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Linear_motion"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Linear_motion rootpage-Linear_motion skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Linear+motion" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Linear+motion" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Linear+motion" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Linear+motion" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</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"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</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:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</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="Site"> <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="Contents" 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">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Background" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Background"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Background</span> </div> </a> <button aria-controls="toc-Background-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>Toggle Background subsection</span> </button> <ul id="toc-Background-sublist" class="vector-toc-list"> <li id="toc-Displacement" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Displacement"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Displacement</span> </div> </a> <ul id="toc-Displacement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Velocity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Velocity"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Velocity</span> </div> </a> <ul id="toc-Velocity-sublist" class="vector-toc-list"> <li id="toc-Average_velocity" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Average_velocity"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.1</span> <span>Average velocity</span> </div> </a> <ul id="toc-Average_velocity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Instantaneous_velocity" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Instantaneous_velocity"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.2</span> <span>Instantaneous velocity</span> </div> </a> <ul id="toc-Instantaneous_velocity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Acceleration" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Acceleration"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Acceleration</span> </div> </a> <ul id="toc-Acceleration-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Jerk" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Jerk"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Jerk</span> </div> </a> <ul id="toc-Jerk-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Jounce" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Jounce"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Jounce</span> </div> </a> <ul id="toc-Jounce-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Formulation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formulation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Formulation</span> </div> </a> <ul id="toc-Formulation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Comparison_to_circular_motion" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Comparison_to_circular_motion"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Comparison to circular motion</span> </div> </a> <ul id="toc-Comparison_to_circular_motion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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="Contents" 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="Toggle the table of contents" > <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">Toggle the table of contents</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">Linear motion</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="Go to an article in another language. Available in 31 languages" > <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-31" 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">31 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D8%B1%D9%83%D8%A9_%D8%AE%D8%B7%D9%8A%D8%A9" title="حركة خطية – Arabic" lang="ar" hreflang="ar" data-title="حركة خطية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B0%E0%A7%88%E0%A6%96%E0%A6%BF%E0%A6%95_%E0%A6%97%E0%A6%A4%E0%A6%BF" title="রৈখিক গতি – Bangla" lang="bn" hreflang="bn" data-title="রৈখিক গতি" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D1%80%D0%B0%D0%BC%D0%B0%D0%BB%D1%96%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B_%D1%80%D1%83%D1%85" title="Прамалінейны рух – Belarusian" lang="be" hreflang="be" data-title="Прамалінейны рух" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Jednoliko_kretanje_po_pravcu" title="Jednoliko kretanje po pravcu – Bosnian" lang="bs" hreflang="bs" data-title="Jednoliko kretanje po pravcu" data-language-autonym="Bosanski" data-language-local-name="Bosnian" 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/Moviment_rectilini" title="Moviment rectilini – Catalan" lang="ca" hreflang="ca" data-title="Moviment rectilini" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D3%B3%D1%80%C4%95_%D0%BA%D1%83%C3%A7%C4%83%D0%BC" title="Тӳрĕ куçăм – Chuvash" lang="cv" hreflang="cv" data-title="Тӳрĕ куçăм" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/P%C5%99%C3%ADmo%C4%8Dar%C3%BD_pohyb" title="Přímočarý pohyb – Czech" lang="cs" hreflang="cs" data-title="Přímočarý pohyb" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Movimiento_rectil%C3%ADneo" title="Movimiento rectilíneo – Spanish" lang="es" hreflang="es" data-title="Movimiento rectilíneo" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Higidura_zuzen" title="Higidura zuzen – Basque" lang="eu" hreflang="eu" data-title="Higidura zuzen" data-language-autonym="Euskara" data-language-local-name="Basque" 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%AD%D8%B1%DA%A9%D8%AA_%D8%AE%D8%B7%DB%8C" title="حرکت خطی – Persian" lang="fa" hreflang="fa" data-title="حرکت خطی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Mouvement_rectiligne" title="Mouvement rectiligne – French" lang="fr" hreflang="fr" data-title="Mouvement rectiligne" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B0%E0%A5%88%E0%A4%96%E0%A4%BF%E0%A4%95_%E0%A4%97%E0%A4%A4%E0%A4%BF" title="रैखिक गति – Hindi" lang="hi" hreflang="hi" data-title="रैखिक गति" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Translacija" title="Translacija – Croatian" lang="hr" hreflang="hr" data-title="Translacija" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Gerak_lurus" title="Gerak lurus – Indonesian" lang="id" hreflang="id" data-title="Gerak lurus" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Moto_rettilineo" title="Moto rettilineo – Italian" lang="it" hreflang="it" data-title="Moto rettilineo" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/To%27g%27ri_chiziqli_harakat" title="To'g'ri chiziqli harakat – Uzbek" lang="uz" hreflang="uz" data-title="To'g'ri chiziqli harakat" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B0%E0%A9%87%E0%A8%96%E0%A8%BF%E0%A8%95_%E0%A8%97%E0%A8%A4%E0%A9%80" title="ਰੇਖਿਕ ਗਤੀ – Punjabi" lang="pa" hreflang="pa" data-title="ਰੇਖਿਕ ਗਤੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Movimento_retil%C3%ADneo" title="Movimento retilíneo – Portuguese" lang="pt" hreflang="pt" data-title="Movimento retilíneo" data-language-autonym="Português" data-language-local-name="Portuguese" 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/Mi%C8%99care_rectilinie" title="Mișcare rectilinie – Romanian" lang="ro" hreflang="ro" data-title="Mișcare rectilinie" data-language-autonym="Română" data-language-local-name="Romanian" 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%9F%D1%80%D1%8F%D0%BC%D0%BE%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%BE%D0%B5_%D0%B4%D0%B2%D0%B8%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5" title="Прямолинейное движение – Russian" lang="ru" hreflang="ru" data-title="Прямолинейное движение" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://sc.wikipedia.org/wiki/Movimentu_in_caminu_deretu" title="Movimentu in caminu deretu – Sardinian" lang="sc" hreflang="sc" data-title="Movimentu in caminu deretu" data-language-autonym="Sardu" data-language-local-name="Sardinian" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/L%C3%ABvizja_drejtvizore_e_nj%C3%ABtrajtshme" title="Lëvizja drejtvizore e njëtrajtshme – Albanian" lang="sq" hreflang="sq" data-title="Lëvizja drejtvizore e njëtrajtshme" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Priamo%C4%8Diary_pohyb" title="Priamočiary pohyb – Slovak" lang="sk" hreflang="sk" data-title="Priamočiary pohyb" data-language-autonym="Slovenčina" data-language-local-name="Slovak" 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/Premo_gibanje" title="Premo gibanje – Slovenian" lang="sl" hreflang="sl" data-title="Premo gibanje" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AC%D9%88%D9%88%DA%B5%DB%95%DB%8C_%DA%95%D8%A7%D8%B3%D8%AA%DB%95%D9%88%DA%95%D8%A7%D8%B3%D8%AA" title="جووڵەی ڕاستەوڕاست – Central Kurdish" lang="ckb" hreflang="ckb" data-title="جووڵەی ڕاستەوڕاست" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Pravolinijsko_kretanje" title="Pravolinijsko kretanje – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Pravolinijsko kretanje" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Suoraviivainen_liike" title="Suoraviivainen liike – Finnish" lang="fi" hreflang="fi" data-title="Suoraviivainen liike" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Do%C4%9Frusal_hareket" title="Doğrusal hareket – Turkish" lang="tr" hreflang="tr" data-title="Doğrusal hareket" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D1%8F%D0%BC%D0%BE%D0%BB%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B8%D0%B9_%D1%80%D1%83%D1%85" title="Прямолінійний рух – Ukrainian" lang="uk" hreflang="uk" data-title="Прямолінійний рух" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Chuy%E1%BB%83n_%C4%91%E1%BB%99ng_th%E1%BA%B3ng" title="Chuyển động thẳng – Vietnamese" lang="vi" hreflang="vi" data-title="Chuyển động thẳng" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%9B%B4%E7%B7%9A%E9%81%8B%E5%8B%95" title="直線運動 – Chinese" lang="zh" hreflang="zh" data-title="直線運動" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q2035846#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Linear_motion" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Linear_motion" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Linear_motion"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Linear_motion&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Linear_motion&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Linear_motion"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Linear_motion&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Linear_motion&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Linear_motion" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Linear_motion" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Linear_motion&oldid=1263299876" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Linear_motion&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Linear_motion&id=1263299876&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FLinear_motion"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FLinear_motion"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Linear_motion&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Linear_motion&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</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"> In other projects </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:Linear_movement" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q2035846" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</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="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <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">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</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">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Rectilinear_motion&redirect=no" class="mw-redirect" title="Rectilinear motion">Rectilinear motion</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Type of motion in which the path of the moving object is a straight line</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For the class of linkages, see <a href="/wiki/Straight_line_mechanism" class="mw-redirect" title="Straight line mechanism">straight line mechanism</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1126788409">.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><style data-mw-deduplicate="TemplateStyles:r1246091330">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle" style="padding-left:0.9em;padding-right:0.9em;"><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold">F</mtext> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2ad0a6d6780c3abc5247abd82bd8a2249d56ff3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.318ex; height:5.509ex;" alt="{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}"></span><div class="sidebar-caption" style="font-size:90%;padding:0.6em 0;font-style:italic;"><a href="/wiki/Second_law_of_motion" class="mw-redirect" title="Second law of motion">Second law of motion</a></div></td></tr><tr><th class="sidebar-heading" style="font-weight: bold; display:block;margin-bottom:1.0em;"> <div class="hlist"> <ul><li><a href="/wiki/History_of_classical_mechanics" title="History of classical mechanics">History</a></li> <li><a href="/wiki/Timeline_of_classical_mechanics" title="Timeline of classical mechanics">Timeline</a></li> <li><a href="/wiki/List_of_textbooks_on_classical_mechanics_and_quantum_mechanics" title="List of textbooks on classical mechanics and quantum mechanics">Textbooks</a></li></ul> </div></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Branches</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Applied_mechanics" title="Applied mechanics">Applied</a></li> <li><a href="/wiki/Celestial_mechanics" title="Celestial mechanics">Celestial</a></li> <li><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum</a></li> <li><a href="/wiki/Analytical_dynamics" class="mw-redirect" title="Analytical dynamics">Dynamics</a></li> <li><a href="/wiki/Classical_field_theory" title="Classical field theory">Field theory</a></li> <li><a href="/wiki/Kinematics" title="Kinematics">Kinematics</a></li> <li><a href="/wiki/Kinetics_(physics)" title="Kinetics (physics)">Kinetics</a></li> <li><a href="/wiki/Statics" title="Statics">Statics</a></li> <li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical mechanics</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Fundamentals</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Acceleration" title="Acceleration">Acceleration</a></li> <li><a href="/wiki/Angular_momentum" title="Angular momentum">Angular momentum</a></li> <li><a href="/wiki/Couple_(mechanics)" title="Couple (mechanics)">Couple</a></li> <li><a href="/wiki/D%27Alembert%27s_principle" title="D'Alembert's principle">D'Alembert's principle</a></li> <li><a href="/wiki/Energy" title="Energy">Energy</a> <ul><li><a href="/wiki/Kinetic_energy#Newtonian_kinetic_energy" title="Kinetic energy">kinetic</a></li> <li><a href="/wiki/Potential_energy" title="Potential energy">potential</a></li></ul></li> <li><a href="/wiki/Force" title="Force">Force</a></li> <li><a href="/wiki/Frame_of_reference" title="Frame of reference">Frame of reference</a></li> <li><a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">Inertial frame of reference</a></li> <li><a href="/wiki/Impulse_(physics)" title="Impulse (physics)">Impulse</a></li> <li><span class="nowrap"><a href="/wiki/Inertia" title="Inertia">Inertia</a> / <a href="/wiki/Moment_of_inertia" title="Moment of inertia">Moment of inertia</a></span></li> <li><a href="/wiki/Mass" title="Mass">Mass</a></li> <li><br /><a href="/wiki/Mechanical_power_(physics)" class="mw-redirect" title="Mechanical power (physics)">Mechanical power</a></li> <li><a href="/wiki/Work_(physics)" title="Work (physics)">Mechanical work</a></li> <li><br /><a href="/wiki/Moment_(physics)" title="Moment (physics)">Moment</a></li> <li><a href="/wiki/Momentum" title="Momentum">Momentum</a></li> <li><a href="/wiki/Space" title="Space">Space</a></li> <li><a href="/wiki/Speed" title="Speed">Speed</a></li> <li><a href="/wiki/Time" title="Time">Time</a></li> <li><a href="/wiki/Torque" title="Torque">Torque</a></li> <li><a href="/wiki/Velocity" title="Velocity">Velocity</a></li> <li><a href="/wiki/Virtual_work" title="Virtual work">Virtual work</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Formulations</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"> <ul><li><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><b><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a></b></div></li> <li><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><b><a href="/wiki/Analytical_mechanics" title="Analytical mechanics">Analytical mechanics</a></b> <div class="plainlist"><ul><li><a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian mechanics</a></li><li><a href="/wiki/Hamiltonian_mechanics" title="Hamiltonian mechanics">Hamiltonian mechanics</a></li><li><a href="/wiki/Routhian_mechanics" title="Routhian mechanics">Routhian mechanics</a></li><li><a href="/wiki/Hamilton%E2%80%93Jacobi_equation" title="Hamilton–Jacobi equation">Hamilton–Jacobi equation</a></li><li><a href="/wiki/Appell%27s_equation_of_motion" title="Appell's equation of motion">Appell's equation of motion</a></li><li><a href="/wiki/Koopman%E2%80%93von_Neumann_classical_mechanics" title="Koopman–von Neumann classical mechanics">Koopman–von Neumann mechanics</a></li></ul></div></div></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Core topics</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Damping" title="Damping">Damping</a></li> <li><a href="/wiki/Displacement_(geometry)" title="Displacement (geometry)">Displacement</a></li> <li><a href="/wiki/Equations_of_motion" title="Equations of motion">Equations of motion</a></li> <li><a href="/wiki/Euler%27s_laws_of_motion" title="Euler's laws of motion"><span class="wrap">Euler's laws of motion</span></a></li> <li><a href="/wiki/Fictitious_force" title="Fictitious force">Fictitious force</a></li> <li><a href="/wiki/Friction" title="Friction">Friction</a></li> <li><a href="/wiki/Harmonic_oscillator" title="Harmonic oscillator">Harmonic oscillator</a></li></ul> </div> <ul><li><span class="nowrap"><a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">Inertial</a> / <a href="/wiki/Non-inertial_reference_frame" title="Non-inertial reference frame">Non-inertial reference frame</a></span></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Motion" title="Motion">Motion</a> (<a class="mw-selflink selflink">linear</a>)</li> <li><a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation"><span class="wrap">Newton's law of universal gravitation</span></a></li> <li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a></li> <li><a href="/wiki/Relative_velocity" title="Relative velocity">Relative velocity</a></li> <li><a href="/wiki/Rigid_body" title="Rigid body">Rigid body</a> <ul><li><a href="/wiki/Rigid_body_dynamics" title="Rigid body dynamics">dynamics</a></li> <li><a href="/wiki/Euler%27s_equations_(rigid_body_dynamics)" title="Euler's equations (rigid body dynamics)">Euler's equations</a></li></ul></li> <li><a href="/wiki/Simple_harmonic_motion" title="Simple harmonic motion">Simple harmonic motion</a></li> <li><a href="/wiki/Vibration" title="Vibration">Vibration</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)"><a href="/wiki/Rotation_around_a_fixed_axis" title="Rotation around a fixed axis">Rotation</a></div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Circular_motion" title="Circular motion">Circular motion</a></li> <li><a href="/wiki/Rotating_reference_frame" title="Rotating reference frame">Rotating reference frame</a></li> <li><a href="/wiki/Centripetal_force" title="Centripetal force">Centripetal force</a></li> <li><a href="/wiki/Centrifugal_force" title="Centrifugal force">Centrifugal force</a> <ul><li><a href="/wiki/Reactive_centrifugal_force" title="Reactive centrifugal force">reactive</a></li></ul></li> <li><a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis force</a></li> <li><a href="/wiki/Pendulum_(mechanics)" title="Pendulum (mechanics)">Pendulum</a></li> <li><a href="/wiki/Tangential_speed" title="Tangential speed">Tangential speed</a></li> <li><a href="/wiki/Rotational_frequency" title="Rotational frequency">Rotational frequency</a></li></ul> </div> <ul><li><a href="/wiki/Angular_acceleration" title="Angular acceleration">Angular acceleration</a> / <a href="/wiki/Angular_displacement" title="Angular displacement">displacement</a> / <a href="/wiki/Angular_frequency" title="Angular frequency">frequency</a> / <a href="/wiki/Angular_velocity" title="Angular velocity">velocity</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-bottom: 1px solid black;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"><div class="hlist"> <ul><li><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a></li> <li><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Jeremiah_Horrocks" title="Jeremiah Horrocks">Horrocks</a></li> <li><a href="/wiki/Edmond_Halley" title="Edmond Halley">Halley</a></li> <li><a href="/wiki/Pierre_Louis_Maupertuis" title="Pierre Louis Maupertuis">Maupertuis</a></li> <li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a></li> <li><a href="/wiki/Johann_Bernoulli" title="Johann Bernoulli">Johann Bernoulli</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/wiki/Jean_le_Rond_d%27Alembert" title="Jean le Rond d'Alembert">d'Alembert</a></li> <li><a href="/wiki/Alexis_Clairaut" title="Alexis Clairaut">Clairaut</a></li> <li><a href="/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange">Lagrange</a></li> <li><a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Laplace</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/William_Rowan_Hamilton" title="William Rowan Hamilton">Hamilton</a></li> <li><a href="/wiki/Carl_Gustav_Jacob_Jacobi" title="Carl Gustav Jacob Jacobi">Jacobi</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a></li> <li><a href="/wiki/Edward_Routh" title="Edward Routh">Routh</a></li> <li><a href="/wiki/Joseph_Liouville" title="Joseph Liouville">Liouville</a></li> <li><a href="/wiki/Paul_%C3%89mile_Appell" title="Paul Émile Appell">Appell</a></li> <li><a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs</a></li> <li><a href="/wiki/Bernard_Koopman" title="Bernard Koopman">Koopman</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-below hlist" style="background-color: transparent; border-color: #A2B8BF"> <ul><li><span class="nowrap"><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/14px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="14" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/21px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/28px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Classical_mechanics" title="Category:Classical mechanics">Category</a></span></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Classical_mechanics" title="Template:Classical mechanics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Classical_mechanics" title="Template talk:Classical mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Classical_mechanics" title="Special:EditPage/Template:Classical mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Linear motion</b>, also called <b>rectilinear motion</b>,<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> is one-dimensional <a href="/wiki/Motion_(physics)" class="mw-redirect" title="Motion (physics)">motion</a> along a <a href="/wiki/Line_(mathematics)" class="mw-redirect" title="Line (mathematics)">straight line</a>, and can therefore be described mathematically using only one spatial <a href="/wiki/Dimension" title="Dimension">dimension</a>. The linear motion can be of two types: <b>uniform linear motion</b>, with constant <a href="/wiki/Velocity" title="Velocity">velocity</a> (zero <a href="/wiki/Acceleration" title="Acceleration">acceleration</a>); and <b>non-uniform linear motion</b>, with variable velocity (non-zero acceleration). The motion of a <a href="/wiki/Point_particle" title="Point particle">particle</a> (a point-like object) along a line can be described by its position <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 x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>, which <a href="/wiki/Time-variant_system" title="Time-variant system">varies</a> with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> (time). An example of linear motion is an athlete running a <a href="/wiki/100-meter_dash" class="mw-redirect" title="100-meter dash">100-meter dash</a> along a straight track.<sup id="cite_ref-auto_2-0" class="reference"><a href="#cite_note-auto-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Linear motion is the most basic of all motion. According to <a href="/wiki/Newton%27s_first_law_of_motion" class="mw-redirect" title="Newton's first law of motion">Newton's first law of motion</a>, objects that do not experience any <a href="/wiki/Net_force" title="Net force">net force</a> will continue to move in a straight line with a constant velocity until they are subjected to a net force. Under everyday circumstances, external forces such as <a href="/wiki/Gravity" title="Gravity">gravity</a> and <a href="/wiki/Friction" title="Friction">friction</a> can cause an object to change the direction of its motion, so that its motion cannot be described as linear.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>One may compare linear motion to general motion. In general motion, a particle's position and velocity are described by <a href="/wiki/Vector_(geometric)" class="mw-redirect" title="Vector (geometric)">vectors</a>, which have a magnitude and direction. In linear motion, the directions of all the vectors describing the system are equal and constant which means the objects move along the same axis and do not change direction. The analysis of such systems may therefore be simplified by neglecting the direction components of the vectors involved and dealing only with the <a href="/wiki/Magnitude_(mathematics)" title="Magnitude (mathematics)">magnitude</a>.<sup id="cite_ref-auto_2-1" class="reference"><a href="#cite_note-auto-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Background">Background</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=1" title="Edit section: Background"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Displacement">Displacement</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=2" title="Edit section: Displacement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Displacement_(vector)" class="mw-redirect" title="Displacement (vector)">Displacement (vector)</a></div> <p>The motion in which all the particles of a body move through the same distance in the same time is called translatory motion. There are two types of translatory motions: rectilinear motion; <a href="/wiki/Curvilinear_motion" title="Curvilinear motion">curvilinear motion</a>. Since linear motion is a motion in a single dimension, the <a href="/wiki/Distance" title="Distance">distance</a> traveled by an object in particular direction is the same as <a href="/wiki/Displacement_(vector)" class="mw-redirect" title="Displacement (vector)">displacement</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/SI" class="mw-redirect" title="SI">SI</a> unit of displacement is the <a href="/wiki/Metre" title="Metre">metre</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-auto1_6-0" class="reference"><a href="#cite_note-auto1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> If <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 x_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8788bf85d532fa88d1fb25eff6ae382a601c308" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{1}}"></span> is the initial position of an object and <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 x_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7af1b928f06e4c7e3e8ebfd60704656719bd766" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{2}}"></span> is the final position, then mathematically the displacement is given by: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta x=x_{2}-x_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo>=</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x=x_{2}-x_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a73839bf6f41b9940a2e657f9cad8820f2adf61" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.972ex; height:2.509ex;" alt="{\displaystyle \Delta x=x_{2}-x_{1}}"></span> </p><p>The equivalent of displacement in <a href="/wiki/Rotational_motion" class="mw-redirect" title="Rotational motion">rotational motion</a> is the <a href="/wiki/Angular_displacement" title="Angular displacement">angular displacement</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 \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> measured in <a href="/wiki/Radian" title="Radian">radians</a>. The displacement of an object cannot be greater than the distance because it is also a distance but the shortest one. Consider a person travelling to work daily. Overall displacement when he returns home is zero, since the person ends up back where he started, but the distance travelled is clearly not zero. </p> <div class="mw-heading mw-heading3"><h3 id="Velocity">Velocity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=3" title="Edit section: Velocity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Velocity" title="Velocity">Velocity</a> and <a href="/wiki/Speed" title="Speed">Speed</a></div> <p>Velocity refers to a displacement in one direction with respect to an interval of time. It is defined as the rate of change of displacement over change in time.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Velocity is a vector quantity, representing a direction and a magnitude of movement. The magnitude of a velocity is called speed. The SI unit of speed is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{m}}\cdot {\text{s}}^{-1},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> <mo>⋅</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{m}}\cdot {\text{s}}^{-1},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f94e863aed1b458caa4f7c4c34d41354d69b5e56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.511ex; height:3.009ex;" alt="{\displaystyle {\text{m}}\cdot {\text{s}}^{-1},}"></span> that is <a href="/wiki/Metre_per_second" title="Metre per second">metre per second</a>.<sup id="cite_ref-auto1_6-1" class="reference"><a href="#cite_note-auto1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Average_velocity">Average velocity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=4" title="Edit section: Average velocity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Average_velocity" class="mw-redirect" title="Average velocity">average velocity</a> of a moving body is its total displacement divided by the total time needed to travel from the initial point to the final point. It is an estimated velocity for a distance to travel. Mathematically, it is given by:<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {v} _{\text{avg}}={\frac {\Delta \mathbf {x} }{\Delta t}}={\frac {\mathbf {x} _{2}-\mathbf {x} _{1}}{t_{2}-t_{1}}}}"> <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"> <mtext>avg</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} _{\text{avg}}={\frac {\Delta \mathbf {x} }{\Delta t}}={\frac {\mathbf {x} _{2}-\mathbf {x} _{1}}{t_{2}-t_{1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e93d446ec2596e7cd204eab72e38bc98f5d13dc6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:23.142ex; height:5.676ex;" alt="{\displaystyle \mathbf {v} _{\text{avg}}={\frac {\Delta \mathbf {x} }{\Delta t}}={\frac {\mathbf {x} _{2}-\mathbf {x} _{1}}{t_{2}-t_{1}}}}"></span> </p><p>where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb0768c0bd659f2f84fb5ef9f4b74f336123d915" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{1}}"></span> is the time at which the object was at position <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 {x} _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a02b3163e7a24d90f15c809c2dca63ba5cccca7c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.465ex; height:2.009ex;" alt="{\displaystyle \mathbf {x} _{1}}"></span> and</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/749fee708b41e7079eabd50d61c8bf3e965db16f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{2}}"></span> is the time at which the object was at position <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 {x} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1274d8a5c59d33efd3639a4137c7f91598038d1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.465ex; height:2.009ex;" alt="{\displaystyle \mathbf {x} _{2}}"></span></li></ul> <p>The magnitude of the average velocity <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 \left|\mathbf {v} _{\text{avg}}\right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>avg</mtext> </mrow> </msub> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|\mathbf {v} _{\text{avg}}\right|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bfa6631f10b4110d636a2e2e7b3df5bc2506e24f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.449ex; height:3.009ex;" alt="{\displaystyle \left|\mathbf {v} _{\text{avg}}\right|}"></span> is called an average speed. </p> <div class="mw-heading mw-heading4"><h4 id="Instantaneous_velocity">Instantaneous velocity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=5" title="Edit section: Instantaneous velocity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In contrast to an average velocity, referring to the overall motion in a finite time interval, the <a href="/wiki/Instantaneous_velocity" class="mw-redirect" title="Instantaneous velocity">instantaneous velocity</a> of an object describes the state of motion at a specific point in time. It is defined by letting the length of the time interval <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c28867ecd34e2caed12cf38feadf6a81a7ee542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.775ex; height:2.176ex;" alt="{\displaystyle \Delta t}"></span> tend to zero, that is, the velocity is the time derivative of the displacement as a function of time. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {v} =\lim _{\Delta t\to 0}{\frac {\Delta \mathbf {x} }{\Delta t}}={\frac {d\mathbf {x} }{dt}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} =\lim _{\Delta t\to 0}{\frac {\Delta \mathbf {x} }{\Delta t}}={\frac {d\mathbf {x} }{dt}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63eee5e2a93bfc6a273d543a62e7e00d566ad092" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:20.715ex; height:5.676ex;" alt="{\displaystyle \mathbf {v} =\lim _{\Delta t\to 0}{\frac {\Delta \mathbf {x} }{\Delta t}}={\frac {d\mathbf {x} }{dt}}.}"></span> </p><p>The magnitude of the instantaneous velocity <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"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </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/16a779e65de92152d395f5576ce1001c8e56d7f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.705ex; height:2.843ex;" alt="{\displaystyle |\mathbf {v} |}"></span> is called the instantaneous speed.The instantaneous velocity equation comes from finding the limit as t approaches 0 of the average velocity. The instantaneous velocity shows the position function with respect to time. From the instantaneous velocity the instantaneous speed can be derived by getting the magnitude of the instantaneous velocity. </p> <div class="mw-heading mw-heading3"><h3 id="Acceleration">Acceleration</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=6" title="Edit section: Acceleration"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Acceleration" title="Acceleration">Acceleration</a></div> <p>Acceleration is defined as the rate of change of velocity with respect to time. Acceleration is the second derivative of displacement i.e. acceleration can be found by differentiating position with respect to time twice or differentiating velocity with respect to time once.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The SI unit of acceleration is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {m\cdot s^{-2}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mo>⋅</mo> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {m\cdot s^{-2}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dfb24ef0fb8a75d7373cfc3961fb6504a4d56bca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.864ex; height:2.676ex;" alt="{\displaystyle \mathrm {m\cdot s^{-2}} }"></span> or <a href="/wiki/Metre_per_second_squared" title="Metre per second squared">metre per second squared</a>.<sup id="cite_ref-auto1_6-2" class="reference"><a href="#cite_note-auto1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>If <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 {a} _{\text{avg}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>avg</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {a} _{\text{avg}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87481d58f869cf3d9e060d44e4565aee78751a4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.044ex; height:2.343ex;" alt="{\displaystyle \mathbf {a} _{\text{avg}}}"></span> is the average acceleration and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \mathbf {v} =\mathbf {v} _{2}-\mathbf {v} _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \mathbf {v} =\mathbf {v} _{2}-\mathbf {v} _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81207385df6bbca848da9e618cd51050c1566c1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.216ex; height:2.509ex;" alt="{\displaystyle \Delta \mathbf {v} =\mathbf {v} _{2}-\mathbf {v} _{1}}"></span> is the change in velocity over the time interval <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c28867ecd34e2caed12cf38feadf6a81a7ee542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.775ex; height:2.176ex;" alt="{\displaystyle \Delta t}"></span> then mathematically, <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {a} _{\text{avg}}={\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {\mathbf {v} _{2}-\mathbf {v} _{1}}{t_{2}-t_{1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>avg</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {a} _{\text{avg}}={\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {\mathbf {v} _{2}-\mathbf {v} _{1}}{t_{2}-t_{1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fe6c2d559e8dbaede90b8cb137a700fe3731033" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:23.031ex; height:5.676ex;" alt="{\displaystyle \mathbf {a} _{\text{avg}}={\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {\mathbf {v} _{2}-\mathbf {v} _{1}}{t_{2}-t_{1}}}}"></span> </p><p>The instantaneous acceleration is the limit, as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c28867ecd34e2caed12cf38feadf6a81a7ee542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.775ex; height:2.176ex;" alt="{\displaystyle \Delta t}"></span> approaches zero, of the ratio <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \mathbf {v} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \mathbf {v} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ae2621f980eefffc0a3f3e806bfce57a5be867a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.347ex; height:2.176ex;" alt="{\displaystyle \Delta \mathbf {v} }"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c28867ecd34e2caed12cf38feadf6a81a7ee542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.775ex; height:2.176ex;" alt="{\displaystyle \Delta t}"></span>, i.e., <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {a} =\lim _{\Delta t\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mrow> <mrow> <mi>d</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {a} =\lim _{\Delta t\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dfa60403586b31b8fbddb9c9e235a6a31b91431" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:27.575ex; height:6.009ex;" alt="{\displaystyle \mathbf {a} =\lim _{\Delta t\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Jerk">Jerk</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=7" title="Edit section: Jerk"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Jerk_(physics)" title="Jerk (physics)">Jerk (physics)</a></div> <p>The rate of change of acceleration, the third derivative of displacement is known as jerk.<sup id="cite_ref-auto2_11-0" class="reference"><a href="#cite_note-auto2-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The SI unit of jerk is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {m\cdot s^{-3}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mo>⋅</mo> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {m\cdot s^{-3}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d27fe303b9b8e4893c120ae831f851371a94cf2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.864ex; height:2.676ex;" alt="{\displaystyle \mathrm {m\cdot s^{-3}} }"></span>. In the UK jerk is also referred to as jolt. </p> <div class="mw-heading mw-heading3"><h3 id="Jounce">Jounce</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=8" title="Edit section: Jounce"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Jounce" class="mw-redirect" title="Jounce">Jounce</a></div> <p>The rate of change of jerk, the fourth derivative of displacement is known as jounce.<sup id="cite_ref-auto2_11-1" class="reference"><a href="#cite_note-auto2-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The SI unit of jounce is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {m\cdot s^{-4}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mo>⋅</mo> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {m\cdot s^{-4}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4f9a349b6632f886b8f7320af01f993e7f17890" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.864ex; height:2.676ex;" alt="{\displaystyle \mathrm {m\cdot s^{-4}} }"></span> which can be pronounced as <i>metres per quartic second</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Formulation">Formulation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=9" title="Edit section: Formulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Equations_of_motion" title="Equations of motion">Equations of motion</a></div> <p>In case of constant acceleration, the four <a href="/wiki/Physical_quantities" class="mw-redirect" title="Physical quantities">physical quantities</a> acceleration, velocity, time and displacement can be related by using the <a href="/wiki/Equations_of_motion" title="Equations of motion">equations of motion</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </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} _{\text{f}}=\mathbf {v} _{\text{i}}+\mathbf {a} t}"> <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"> <mtext>f</mtext> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} _{\text{f}}=\mathbf {v} _{\text{i}}+\mathbf {a} t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c51f2cb4f09000e4159ec694cefaff838adbb50a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.434ex; height:2.343ex;" alt="{\displaystyle \mathbf {v} _{\text{f}}=\mathbf {v} _{\text{i}}+\mathbf {a} t}"></span></dd></dl> <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 {d} =\mathbf {v} _{\text{i}}t+{\frac {1}{2}}\mathbf {a} t^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">d</mi> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> </msub> <mi>t</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {d} =\mathbf {v} _{\text{i}}t+{\frac {1}{2}}\mathbf {a} t^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49e40eb6c5ea11cbad95b9c3394dbffc2806743b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.556ex; height:5.176ex;" alt="{\displaystyle \mathbf {d} =\mathbf {v} _{\text{i}}t+{\frac {1}{2}}\mathbf {a} t^{2}}"></span></dd></dl> <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} _{\text{f}}^{2}=\mathbf {v} _{\text{i}}^{2}+2\mathbf {ad} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> <mi mathvariant="bold">d</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} _{\text{f}}^{2}=\mathbf {v} _{\text{i}}^{2}+2\mathbf {ad} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6df5ce4ae669c8320e32a1d3fff45dbde4f0f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.817ex; height:3.176ex;" alt="{\displaystyle \mathbf {v} _{\text{f}}^{2}=\mathbf {v} _{\text{i}}^{2}+2\mathbf {ad} }"></span></dd></dl> <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 {d} ={\frac {t}{2}}\left(\mathbf {v} _{\text{f}}+\mathbf {v} _{\text{i}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">d</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>t</mi> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {d} ={\frac {t}{2}}\left(\mathbf {v} _{\text{f}}+\mathbf {v} _{\text{i}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/003ac791f1f1b7c96b99fd113a1630c1ad6585be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.975ex; height:5.176ex;" alt="{\displaystyle \mathbf {d} ={\frac {t}{2}}\left(\mathbf {v} _{\text{f}}+\mathbf {v} _{\text{i}}\right)}"></span></dd></dl> <p>Here, </p> <ul><li><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} _{\text{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"> <mtext>i</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} _{\text{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68979aafacdb16a1bc146ed5051a809304a7d379" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.101ex; height:2.009ex;" alt="{\displaystyle \mathbf {v} _{\text{i}}}"></span> is the initial velocity</li> <li><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} _{\text{f}}}"> <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"> <mtext>f</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {v} _{\text{f}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/906af2d66ede429b258a88e9ab7ff9e74a49c135" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.255ex; height:2.009ex;" alt="{\displaystyle \mathbf {v} _{\text{f}}}"></span> is the final velocity</li> <li><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 {a} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {a} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a957216653a9ee0d0133dcefd13fb75e36b8b9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:1.676ex;" alt="{\displaystyle \mathbf {a} }"></span> is acceleration</li> <li><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 {d} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">d</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {d} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ec3b626fc045b6ff579316e29978fccfed884c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.485ex; height:2.176ex;" alt="{\displaystyle \mathbf {d} }"></span> is displacement</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> is time</li></ul> <p>These relationships can be demonstrated graphically. The <a href="/wiki/Slope" title="Slope">gradient</a> of a line on a displacement time graph represents the velocity. The gradient of the velocity time graph gives the acceleration while the area under the velocity time graph gives the displacement. The area under a graph of acceleration versus time is equal to the change in velocity. </p> <div class="mw-heading mw-heading2"><h2 id="Comparison_to_circular_motion">Comparison to circular motion</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=10" title="Edit section: Comparison to circular motion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/List_of_equations_in_classical_mechanics#Equations_of_motion_(constant_acceleration)" title="List of equations in classical mechanics">List of equations in classical mechanics § Equations of motion (constant acceleration)</a></div> <p>The following table refers to rotation of a <a href="/wiki/Rigid_body" title="Rigid body">rigid body</a> about a fixed axis: <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 {s} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">s</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {s} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/644ae690160e658898a141e568a7fb0ee6040004" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.056ex; height:1.676ex;" alt="{\displaystyle \mathbf {s} }"></span> is <a href="/wiki/Arc_length" title="Arc length">arc length</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> is the distance from the axis to any point, and <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 {a} _{\mathbf {t} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">t</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {a} _{\mathbf {t} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61abbc43778599c98cbd89e3b94c2128880c34d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.267ex; height:2.009ex;" alt="{\displaystyle \mathbf {a} _{\mathbf {t} }}"></span> is the <a href="/wiki/Acceleration#Tangential_and_centripetal_acceleration" title="Acceleration">tangential acceleration</a>, which is the component of the acceleration that is <i>parallel</i> to the motion. In contrast, the <a href="/wiki/Centripetal_force" title="Centripetal force">centripetal</a> acceleration, <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 {a} _{\mathbf {c} }=v^{2}/r=\omega ^{2}r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">c</mi> </mrow> </mrow> </msub> <mo>=</mo> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>r</mi> <mo>=</mo> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {a} _{\mathbf {c} }=v^{2}/r=\omega ^{2}r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/082db914e1132b64e633f2ca4357e3ce0980b99c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.51ex; height:3.176ex;" alt="{\displaystyle \mathbf {a} _{\mathbf {c} }=v^{2}/r=\omega ^{2}r}"></span>, is <i>perpendicular</i> to the motion. The component of the force parallel to the motion, or equivalently, <i>perpendicular</i> to the line connecting the <a href="https://en.wiktionary.org/wiki/lever_arm" class="extiw" title="wikt:lever arm">point of application</a> to the axis is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{\perp }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} _{\perp }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b8917a46f355dc6c70a85775921819c34e05fd1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.194ex; height:2.509ex;" alt="{\displaystyle \mathbf {F} _{\perp }}"></span>. The sum is over <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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span> from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span> to <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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> particles and/or points of application. </p> <table class="wikitable unsortable" style="text-align:center; font-size:90%;"> <caption>Analogy between Linear Motion and Rotational motion<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </caption> <tbody><tr> <th class="unsortable">Linear motion </th> <th class="unsortable">Rotational motion </th> <th class="unsortable">Defining equation </th></tr> <tr> <td>Displacement = <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 {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32adf004df5eb0a8c7fd8c0b6b7405183c5a5ef2" 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 {x} }"></span> </td> <td>Angular displacement = <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 \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> </td> <td><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 \theta =\mathbf {s} /\mathbf {r} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =\mathbf {s} /\mathbf {r} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/200b9310bb96143924888d2e48616a22d2afba94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.509ex; height:2.843ex;" alt="{\displaystyle \theta =\mathbf {s} /\mathbf {r} }"></span> </td></tr> <tr> <td>Velocity = <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> </td> <td>Angular velocity = <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> </td> <td><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 =\mathbf {v} /\mathbf {r} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega =\mathbf {v} /\mathbf {r} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43a253c157daecf5c69ad8e3fd8f9d1beafbf47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.22ex; height:2.843ex;" alt="{\displaystyle \omega =\mathbf {v} /\mathbf {r} }"></span> </td></tr> <tr> <td>Acceleration = <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 {a} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {a} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a957216653a9ee0d0133dcefd13fb75e36b8b9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:1.676ex;" alt="{\displaystyle \mathbf {a} }"></span> </td> <td>Angular acceleration = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha =\mathbf {a_{\mathbf {t} }} /\mathbf {r} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold">a</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">t</mi> </mrow> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha =\mathbf {a_{\mathbf {t} }} /\mathbf {r} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f4d4128092fe67e1ffd6378bfc2444089b1258c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.117ex; height:2.843ex;" alt="{\displaystyle \alpha =\mathbf {a_{\mathbf {t} }} /\mathbf {r} }"></span> </td></tr> <tr> <td>Mass = <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 {m} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {m} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58d48fbdcdf404353d3d53cdc2b5968c35fa5125" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.226ex; height:1.676ex;" alt="{\displaystyle \mathbf {m} }"></span> </td> <td>Moment of Inertia = <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 {I} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">I</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {I} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a458c8aeb096ce732abf346ae8edf3e4f53a126" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.014ex; height:2.176ex;" alt="{\displaystyle \mathbf {I} }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \mathbf {I} =\sum _{j}\mathbf {m} _{j}\mathbf {r} _{j}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">I</mi> </mrow> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \mathbf {I} =\sum _{j}\mathbf {m} _{j}\mathbf {r} _{j}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c64d1811c201d9000c70904792df59f24bf0b8e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:13.155ex; height:3.509ex;" alt="{\textstyle \mathbf {I} =\sum _{j}\mathbf {m} _{j}\mathbf {r} _{j}^{2}}"></span> </td></tr> <tr> <td>Force = <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 {F} =\mathbf {m} \mathbf {a} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">a</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} =\mathbf {m} \mathbf {a} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de587b9edc99c753b01ebdbc0b1dd56cf2c5772b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.307ex; height:2.176ex;" alt="{\displaystyle \mathbf {F} =\mathbf {m} \mathbf {a} }"></span> </td> <td>Torque = <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 \tau =\mathbf {I} \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">I</mi> </mrow> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau =\mathbf {I} \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0566eda35e095332d368e7bef2b846f5cab6d40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.802ex; height:2.176ex;" alt="{\displaystyle \tau =\mathbf {I} \alpha }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \tau =\sum _{j}\mathbf {r} _{j}\mathbf {F} _{\perp j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>τ</mi> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⊥</mo> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \tau =\sum _{j}\mathbf {r} _{j}\mathbf {F} _{\perp j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc71ae26628f987c7b9b8180c45f6686a97e93d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:13.934ex; height:3.343ex;" alt="{\textstyle \tau =\sum _{j}\mathbf {r} _{j}\mathbf {F} _{\perp j}}"></span> </td></tr> <tr> <td>Momentum= <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 {p} =\mathbf {m} \mathbf {v} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {p} =\mathbf {m} \mathbf {v} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72f889fca0b2ff61d9c9aa6a6675b83b906c9cb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.221ex; height:2.009ex;" alt="{\displaystyle \mathbf {p} =\mathbf {m} \mathbf {v} }"></span> </td> <td>Angular momentum= <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 {L} =\mathbf {I} \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">L</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">I</mi> </mrow> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {L} =\mathbf {I} \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/779c88db3e41f4d3e9ae515aacbf004e3984e110" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.166ex; height:2.176ex;" alt="{\displaystyle \mathbf {L} =\mathbf {I} \omega }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \mathbf {L} =\sum _{j}\mathbf {r} _{j}\mathbf {p} _{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">L</mi> </mrow> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \mathbf {L} =\sum _{j}\mathbf {r} _{j}\mathbf {p} _{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e018defadc4558678265a0bb00f1e1ac3e4eb8ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:12.864ex; height:3.343ex;" alt="{\textstyle \mathbf {L} =\sum _{j}\mathbf {r} _{j}\mathbf {p} _{j}}"></span> </td></tr> <tr> <td>Kinetic energy = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\frac {1}{2}}\mathbf {m} \mathbf {v} ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {1}{2}}\mathbf {m} \mathbf {v} ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee9795d4a91725a2cbbd2b789a10b7a440626b5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:6.35ex; height:3.509ex;" alt="{\textstyle {\frac {1}{2}}\mathbf {m} \mathbf {v} ^{2}}"></span> </td> <td>Kinetic energy = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\frac {1}{2}}\mathbf {I} \omega ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">I</mi> </mrow> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {1}{2}}\mathbf {I} \omega ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f7ec17b9b6897c7ce0ec4ac05abf8d08814e46e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:5.172ex; height:3.509ex;" alt="{\textstyle {\frac {1}{2}}\mathbf {I} \omega ^{2}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\frac {1}{2}}\sum _{j}\mathbf {m} _{j}\mathbf {v} _{j}^{2}={\frac {1}{2}}\sum _{j}\mathbf {m} _{j}\mathbf {r} _{j}^{2}\omega ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {1}{2}}\sum _{j}\mathbf {m} _{j}\mathbf {v} _{j}^{2}={\frac {1}{2}}\sum _{j}\mathbf {m} _{j}\mathbf {r} _{j}^{2}\omega ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b307859d7c1b7b6c0ef332ba3c1678da4c6a31b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:28.084ex; height:3.676ex;" alt="{\textstyle {\frac {1}{2}}\sum _{j}\mathbf {m} _{j}\mathbf {v} _{j}^{2}={\frac {1}{2}}\sum _{j}\mathbf {m} _{j}\mathbf {r} _{j}^{2}\omega ^{2}}"></span> </td></tr> </tbody></table> <p>The following table shows the analogy in derived SI units: </p> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Classical_mechanics_SI_units" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Classical_mechanics_SI_units" title="Template:Classical mechanics SI units"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Classical_mechanics_SI_units" title="Template talk:Classical mechanics SI units"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Classical_mechanics_SI_units" title="Special:EditPage/Template:Classical mechanics SI units"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Classical_mechanics_SI_units" style="font-size:114%;margin:0 4em"><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a> <a href="/wiki/International_System_of_Units" title="International System of Units">SI units</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0;"><table class="wikitable" style="text-align:center;line-height:0.9;border-collapse:collapse;margin:auto;border:none;background:none;"> <tbody><tr> <td colspan="4" style="border:none;backgound:none; font-weight:bold;">Linear/translational quantities</td> <td rowspan="12" style="border:none;backgound:none;"></td> <td colspan="4" style="border:none;backgound:none; font-weight:bold;">Angular/rotational quantities</td> </tr> <tr> <th style="font-weight:normal;font-size:80%;">Dimensions</th> <th style="font-weight:normal;">1</th> <th style="font-weight:normal;">L</th> <th style="font-weight:normal;">L<sup>2</sup></th> <th style="font-weight:normal;font-size:80%;">Dimensions</th> <th style="font-weight:normal;">1</th> <th style="font-weight:normal;"><span class="texhtml"><i>θ</i></span></th> <th style="font-weight:normal;"><span class="texhtml"><i>θ</i></span><sup>2</sup></th> </tr> <tr> <th style="font-weight:normal;">T</th> <td><a href="/wiki/Time" title="Time">time</a>: <span class="texhtml"><i>t</i></span><br /><a href="/wiki/Second" title="Second">s</a></td> <td><a href="/wiki/Absement" title="Absement">absement</a>: <span class="texhtml"><b>A</b></span><br /><a href="/wiki/Meter_second" class="mw-redirect" title="Meter second">m s</a></td> <td></td> <th style="font-weight:normal;">T</th> <td><a href="/wiki/Time" title="Time">time</a>: <span class="texhtml"><i>t</i></span><br /><a href="/wiki/Second" title="Second">s</a></td> <td></td> <td></td> </tr> <tr> <th style="font-weight:normal;">1</th> <td></td> <td><a href="/wiki/Distance" title="Distance">distance</a>: <span class="texhtml"><i>d</i></span>, <span class="nowrap"><a href="/wiki/Position_(vector)" class="mw-redirect" title="Position (vector)">position</a>: <span class="texhtml"><b>r</b></span>, <span class="texhtml"><b>s</b></span>, <span class="texhtml"><b>x</b></span></span>, <a href="/wiki/Displacement_(vector)" class="mw-redirect" title="Displacement (vector)">displacement</a><br /><a href="/wiki/Metre" title="Metre">m</a></td> <td><a href="/wiki/Area" title="Area">area</a>: <span class="texhtml"><i>A</i></span><br /><a href="/wiki/Square_metre" title="Square metre">m<sup>2</sup></a></td> <th style="font-weight:normal;">1</th> <td></td> <td><a href="/wiki/Angle" title="Angle">angle</a>: <span class="texhtml"><i>θ</i></span>, <a href="/wiki/Angular_displacement" title="Angular displacement">angular displacement</a>: <span class="texhtml"><i><b>θ</b></i></span><br /><a href="/wiki/Radian" title="Radian">rad</a></td> <td><span class="nowrap"><a href="/wiki/Solid_angle" title="Solid angle">solid angle</a>: <span class="texhtml">Ω</span><br /><a href="/wiki/Steradian" title="Steradian">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/Frequency" title="Frequency">frequency</a>: <span class="texhtml"><i>f</i></span></span><br /><a href="/wiki/Inverse_second" title="Inverse second">s<sup>−1</sup></a>, <a href="/wiki/Hertz" title="Hertz">Hz</a></td> <td><a href="/wiki/Speed" title="Speed">speed</a>: <span class="texhtml"><i>v</i></span>, <a href="/wiki/Velocity" title="Velocity">velocity</a>: <span class="texhtml"><b>v</b></span><br /><a href="/wiki/Metre_per_second" title="Metre per second">m s<sup>−1</sup></a></td> <td><a href="/wiki/Kinematic_viscosity" class="mw-redirect" title="Kinematic viscosity">kinematic viscosity</a>: <span class="texhtml"><i>ν</i></span>,<br /><a href="/wiki/Specific_angular_momentum" title="Specific angular momentum">specific angular momentum</a>: <span class="texhtml"><b>h</b></span><br />m<sup>2</sup> s<sup>−1</sup></td> <th style="font-weight:normal;">T<sup>−1</sup></th> <td><span class="nowrap"><a href="/wiki/Frequency" title="Frequency">frequency</a>: <span class="texhtml"><i>f</i></span></span>, <span class="nowrap"><a href="/wiki/Rotational_speed" class="mw-redirect" title="Rotational speed">rotational speed</a>: <span class="texhtml"><i>n</i></span></span>, <span class="nowrap"><a href="/wiki/Rotational_velocity" class="mw-redirect" title="Rotational velocity">rotational velocity</a>: <span class="texhtml"><i><b>n</b></i></span></span><br /><a href="/wiki/Inverse_second" title="Inverse second">s<sup>−1</sup></a>, <a href="/wiki/Hertz" title="Hertz">Hz</a></td> <td><a href="/wiki/Angular_speed" class="mw-redirect" title="Angular speed">angular speed</a>: <span class="texhtml"><i>ω</i></span>, <a href="/wiki/Angular_velocity" title="Angular velocity">angular velocity</a>: <span class="texhtml"><i><b>ω</b></i></span><br /><a href="/wiki/Radian_per_second" title="Radian per second">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/Acceleration" title="Acceleration">acceleration</a>: <span class="texhtml"><b>a</b></span><br /><a href="/wiki/Metre_per_second_squared" title="Metre per second squared">m s<sup>−2</sup></a></td> <td></td> <th style="font-weight:normal;">T<sup>−2</sup></th> <td><span class="nowrap"><a href="/wiki/Rotational_acceleration" class="mw-redirect" title="Rotational acceleration">rotational acceleration</a></span><br /><a href="/wiki/Inverse_square_second" class="mw-redirect" title="Inverse square second">s<sup>−2</sup></a></td> <td><a href="/wiki/Angular_acceleration" title="Angular acceleration">angular acceleration</a>: <span class="texhtml"><i><b>α</b></i></span><br /><a href="/wiki/Radian_per_second_squared" class="mw-redirect" title="Radian per second squared">rad<span style="letter-spacing:0.1em"> </span>s<sup>−2</sup></a></td> <td></td> </tr> <tr> <th style="font-weight:normal;">T<sup>−3</sup></th> <td></td> <td><a href="/wiki/Jerk_(physics)" title="Jerk (physics)">jerk</a>: <span class="texhtml"><b>j</b></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/Jerk_(physics)#Jerk_in_rotation" title="Jerk (physics)">angular jerk</a>: <span class="texhtml"><b>ζ</b></span><br />rad<span style="letter-spacing:0.1em"> </span>s<sup>−3</sup></td> <td></td> </tr> <tr style="border-top: 3px double #a2a9b1;"> <th style="font-weight:normal;">M</th> <td><a href="/wiki/Mass" title="Mass">mass</a>: <span class="texhtml"><i>m</i></span><br /><a href="/wiki/Kilogram" title="Kilogram">kg</a></td> <td><a href="/wiki/Moment_(physics)" title="Moment (physics)">weighted position</a>: <span class="texhtml"><i>M</i> ⟨<i>x</i>⟩ = ∑ <i>m</i> <i>x</i></span> </td> <td><a href="/wiki/Moment_of_inertia" title="Moment of inertia">moment of inertia</a>: <span class="texhtml"><i>I</i></span><br /><a href="/wiki/Kilogram_square_metre" class="mw-redirect" title="Kilogram square metre">kg<span style="letter-spacing:0.1em"> </span>m<sup>2</sup></a></td> <th style="font-weight:normal;">ML</th> <td></td> <td></td> <td></td> </tr> <tr> <th style="font-weight:normal;">MT<sup>−1</sup></th> <td><a href="/wiki/Mass_flow_rate" title="Mass flow rate">Mass flow rate</a>: <span class="texhtml"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>m</mi> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad59b9876301e8fb75b9ddbf08de594b87251d3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:2.176ex;" alt="{\displaystyle {\dot {m}}}"></span></span><br /><a href="/wiki/Kilogram_per_second" class="mw-redirect" title="Kilogram per second">kg<span style="letter-spacing:0.1em"> </span>s<sup>−1</sup></a></td> <td><a href="/wiki/Momentum" title="Momentum">momentum</a>: <span class="texhtml"><b>p</b></span>, <a href="/wiki/Impulse_(physics)" title="Impulse (physics)">impulse</a>: <span class="texhtml"><b>J</b></span><br /><a href="/wiki/Kilogram_metre_per_second" class="mw-redirect" title="Kilogram metre per second">kg<span style="letter-spacing:0.1em"> </span>m s<sup>−1</sup></a>, <a href="/wiki/Newton_second" class="mw-redirect" title="Newton second">N s</a></td> <td><a href="/wiki/Action_(physics)" title="Action (physics)">action</a>: <span class="texhtml">𝒮</span>, <a href="/wiki/Absement#Applications" title="Absement">actergy</a>: <span class="texhtml">ℵ</span><br /><a href="/wiki/Kilogram_square_metre_per_second" class="mw-redirect" title="Kilogram square metre per second">kg<span style="letter-spacing:0.1em"> </span>m<sup>2</sup> s<sup>−1</sup></a>, <a href="/wiki/Joule-second" title="Joule-second">J s</a></td> <th style="font-weight:normal;">MLT<sup>−1</sup></th> <td></td> <td><a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a>: <span class="texhtml"><b>L</b></span>, <a href="/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities" title="List of equations in classical mechanics">angular impulse</a>: <span class="texhtml">Δ<b>L</b></span><br /><a href="/wiki/Kilogram_square_metre_per_second" class="mw-redirect" title="Kilogram square metre per second">kg<span style="letter-spacing:0.1em"> </span>m rad s<sup>−1</sup></a></td> <td></td> </tr> <tr> <th style="font-weight:normal;">MT<sup>−2</sup></th> <td></td> <td><a href="/wiki/Force" title="Force">force</a>: <span class="texhtml"><b>F</b></span>, <a href="/wiki/Weight" title="Weight">weight</a>: <span class="texhtml"><b>F</b><sub>g</sub></span><br /><span style="margin-right:0.1em;">kg </span> m s<sup>−2</sup>, <a href="/wiki/Newton_(unit)" title="Newton (unit)">N</a></td> <td><a href="/wiki/Energy" title="Energy">energy</a>: <span class="texhtml"><i>E</i></span>, <a href="/wiki/Work_(physics)" title="Work (physics)">work</a>: <span class="texhtml"><i>W</i></span>, <a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian</a>: <span class="texhtml"><i>L</i></span><br /><span style="margin-right:0.1em;">kg</span> m<sup>2</sup> s<sup>−2</sup>, <a href="/wiki/Joule" title="Joule">J</a></td> <th style="font-weight:normal;">MLT<sup>−2</sup></th> <td></td> <td><a href="/wiki/Torque" title="Torque">torque</a>: <span class="texhtml"><i><b>τ</b></i></span>, <a href="/wiki/Torque#Terminology" title="Torque">moment</a>: <span class="texhtml"><b>M</b></span><br /><span style="margin-right:0.1em;">kg</span> m rad s<sup>−2</sup>, <a href="/wiki/Newton-metre" title="Newton-metre">N m</a></td> <td></td> </tr> <tr> <th style="font-weight:normal;">MT<sup>−3</sup></th> <td></td> <td><a href="/wiki/Yank_(physics)" class="mw-redirect" title="Yank (physics)">yank</a>: <span class="texhtml"><b>Y</b></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/Power_(physics)" title="Power (physics)">power</a>: <span class="texhtml"><i>P</i></span><br /><span style="margin-right:0.1em;">kg</span> m<sup>2</sup> s<sup>−3</sup>, <a href="/wiki/Watt" title="Watt">W</a></td> <th style="font-weight:normal;">MLT<sup>−3</sup></th> <td></td> <td><a href="/wiki/Rotatum" class="mw-redirect" title="Rotatum">rotatum</a>: <span class="texhtml"><b>P</b></span><br /><span style="margin-right:0.1em;">kg</span> m rad s<sup>−3</sup>, N m s<sup>−1</sup></td> <td></td> </tr> </tbody></table></div></td></tr></tbody></table></div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=11" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Angular_motion" class="mw-redirect" title="Angular motion">Angular motion</a></li> <li><a href="/wiki/Centripetal_force" title="Centripetal force">Centripetal force</a></li> <li><a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">Inertial frame of reference</a></li> <li><a href="/wiki/Linear_actuator" title="Linear actuator">Linear actuator</a></li> <li><a href="/wiki/Linear_bearing" class="mw-redirect" title="Linear bearing">Linear bearing</a></li> <li><a href="/wiki/Linear_motor" title="Linear motor">Linear motor</a></li> <li><a href="/wiki/Motion_graphs_and_derivatives" title="Motion graphs and derivatives">Motion graphs and derivatives</a></li> <li><a href="/wiki/Reciprocating_motion" title="Reciprocating motion">Reciprocating motion</a></li> <li><a href="/wiki/Rectilinear_propagation" title="Rectilinear propagation">Rectilinear propagation</a></li> <li><a href="/wiki/Equations_of_motion#Equations_of_uniformly_accelerated_linear_motion" title="Equations of motion">Uniformly accelerated linear motion</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=12" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><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">Resnick, Robert and Halliday, David (1966), <i>Physics</i>, Section 3-4</span> </li> <li id="cite_note-auto-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-auto_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-auto_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.humankinetics.com/excerpts/excerpts/basic-mechanical-principles">"Basic principles for understanding sport mechanics"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Basic+principles+for+understanding+sport+mechanics&rft_id=http%3A%2F%2Fwww.humankinetics.com%2Fexcerpts%2Fexcerpts%2Fbasic-mechanical-principles&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://industrialbearingresource.com/info-center/category/definitions.html">"Motion Control Resource Info Center"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">19 January</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Motion+Control+Resource+Info+Center&rft_id=http%3A%2F%2Findustrialbearingresource.com%2Finfo-center%2Fcategory%2Fdefinitions.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.physicsclassroom.com/class/1dkin/u1l1c.cfm">"Distance and Displacement"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Distance+and+Displacement&rft_id=http%3A%2F%2Fwww.physicsclassroom.com%2Fclass%2F1dkin%2Fu1l1c.cfm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.chemie.fu-berlin.de/chemistry/general/si_en.html">"SI Units"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=SI+Units&rft_id=http%3A%2F%2Fwww.chemie.fu-berlin.de%2Fchemistry%2Fgeneral%2Fsi_en.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-auto1-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-auto1_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-auto1_6-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-auto1_6-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.iau.org/science/publications/proceedings_rules/units/">"SI Units"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=SI+Units&rft_id=http%3A%2F%2Fwww.iau.org%2Fscience%2Fpublications%2Fproceedings_rules%2Funits%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFElert2021" class="citation journal cs1">Elert, Glenn (2021). <a rel="nofollow" class="external text" href="http://physics.info/velocity">"Speed & Velocity"</a>. <i>The Physics Hypertextbook</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Physics+Hypertextbook&rft.atitle=Speed+%26+Velocity&rft.date=2021&rft.aulast=Elert&rft.aufirst=Glenn&rft_id=http%3A%2F%2Fphysics.info%2Fvelocity&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.worsleyschool.net/science/files/average/velocity.html">"Average speed and average velocity"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Average+speed+and+average+velocity&rft_id=http%3A%2F%2Fwww.worsleyschool.net%2Fscience%2Ffiles%2Faverage%2Fvelocity.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/vel2.html">"Average Velocity, Straight Line"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Average+Velocity%2C+Straight+Line&rft_id=http%3A%2F%2Fhyperphysics.phy-astr.gsu.edu%2Fhbase%2Fvel2.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110808181845/http://library.thinkquest.org/10796/ch3/ch3.htm">"Acceleration"</a>. Archived from <a rel="nofollow" class="external text" href="http://library.thinkquest.org/10796/ch3/ch3.htm">the original</a> on 2011-08-08.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Acceleration&rft_id=http%3A%2F%2Flibrary.thinkquest.org%2F10796%2Fch3%2Fch3.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-auto2-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-auto2_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-auto2_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://math.ucr.edu/home/baez/physics/General/jerk.html">"What is the term used for the third derivative of position?"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=What+is+the+term+used+for+the+third+derivative+of+position%3F&rft_id=http%3A%2F%2Fmath.ucr.edu%2Fhome%2Fbaez%2Fphysics%2FGeneral%2Fjerk.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.quintic.com/education/Case%20Study%2013%20-%20Equations%20of%20Motion.pdf">"Equations of motion"</a> <span class="cs1-format">(PDF)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Equations+of+motion&rft_id=http%3A%2F%2Fwww.quintic.com%2Feducation%2FCase%2520Study%252013%2520-%2520Equations%2520of%2520Motion.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#motcon">"Description of Motion in One Dimension"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Description+of+Motion+in+One+Dimension&rft_id=http%3A%2F%2Fhyperphysics.phy-astr.gsu.edu%2Fhbase%2Fmot.html%23motcon&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://wearcam.org/absement/Derivatives_of_displacement.htm">"What is derivatives of displacement?"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=What+is+derivatives+of+displacement%3F&rft_id=http%3A%2F%2Fwearcam.org%2Fabsement%2FDerivatives_of_displacement.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.physics.purdue.edu/webapps/index.php/course_document/index/phys214/1225/58/6957.pdf">"Linear Motion vs Rotational motion"</a> <span class="cs1-format">(PDF)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Linear+Motion+vs+Rotational+motion&rft_id=http%3A%2F%2Fwww.physics.purdue.edu%2Fwebapps%2Findex.php%2Fcourse_document%2Findex%2Fphys214%2F1225%2F58%2F6957.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+motion" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=13" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Resnick, Robert and Halliday, David (1966), <i>Physics</i>, Chapter 3 (Vol I and II, Combined edition), Wiley International Edition, Library of Congress Catalog Card No. 66-11527</li> <li>Tipler P.A., Mosca G., "Physics for Scientists and Engineers", Chapter 2 (5th edition), W. H. Freeman and company: New York and Basing stoke, 2003.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_motion&action=edit&section=14" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Linear_movement" class="extiw" title="commons:Category:Linear movement">Linear movement</a> at Wikimedia Commons </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Linear_motion&oldid=1263299876">https://en.wikipedia.org/w/index.php?title=Linear_motion&oldid=1263299876</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Linear_motion" title="Category:Linear motion">Linear motion</a></li><li><a href="/wiki/Category:Classical_mechanics" title="Category:Classical mechanics">Classical mechanics</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Commons_category_link_is_on_Wikidata" title="Category:Commons category link is on Wikidata">Commons category link is on Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 15 December 2024, at 21:45<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Linear_motion&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-59ccf9db48-ng7lz","wgBackendResponseTime":149,"wgPageParseReport":{"limitreport":{"cputime":"0.435","walltime":"0.701","ppvisitednodes":{"value":3771,"limit":1000000},"postexpandincludesize":{"value":82114,"limit":2097152},"templateargumentsize":{"value":7213,"limit":2097152},"expansiondepth":{"value":13,"limit":100},"expensivefunctioncount":{"value":11,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":101442,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 445.366 1 -total"," 29.67% 132.118 1 Template:Reflist"," 24.73% 110.159 1 Template:Classical_mechanics"," 24.24% 107.978 1 Template:Sidebar_with_collapsible_lists"," 21.14% 94.154 13 Template:Cite_web"," 15.17% 67.544 1 Template:Short_description"," 15.15% 67.484 1 Template:Classical_mechanics_derived_SI_units"," 13.91% 61.956 1 Template:Navbox"," 8.92% 39.737 2 Template:Pagetype"," 7.73% 34.434 47 Template:Math"]},"scribunto":{"limitreport-timeusage":{"value":"0.202","limit":"10.000"},"limitreport-memusage":{"value":6720170,"limit":52428800},"limitreport-logs":"table#1 {\n [\"size\"] = \"tiny\",\n}\n"},"cachereport":{"origin":"mw-web.codfw.main-59ccf9db48-qp62w","timestamp":"20250104215643","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Linear motion","url":"https:\/\/en.wikipedia.org\/wiki\/Linear_motion","sameAs":"http:\/\/www.wikidata.org\/entity\/Q2035846","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q2035846","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2008-03-29T03:44:20Z","dateModified":"2024-12-15T21:45:27Z","headline":"motion along a dimension of length (straight line in space)"}</script> </body> </html>