Angular Momentum – The Physics Hypertextbook

<!doctype html> <html lang="en" itemscope itemtype="https://schema.org/WebPage"> <head> <meta charset="utf-8"> <title>Angular Momentum – The Physics Hypertextbook</title> <link rel="canonical" href="https://physics.info/rotational-momentum/"> <link rel="prev" href="https://physics.info/rotational-statics/"> <link rel="next" href="https://physics.info/rotational-momentum/summary.shtml"> <link rel="stylesheet" href="https://omniscientwalnut.com/walnut.css"> <link rel="stylesheet" href="https://omniscientwalnut.com/walpaper.css" media="print"> <link rel="stylesheet" href="https://omniscientwalnut.com/physics.css"> <meta name="viewport" content="width=device-width, initial-scale=1, viewport-fit=cover">     <link rel="author" href="https://glennelert.us"> <meta name="author" content="Glenn Elert">  <script>if (window!= top) top.location.href=location.href</script>  <script src="https://ajax.googleapis.com/ajax/libs/jquery/3.6.0/jquery.min.js"></script>  <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "Organization", "name": "hypertextbook", "url": "https://hypertextbook.com", "logo": "https://omniscientwalnut.com/eglobe.png" } </script> <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "WebSite", "name": "The Physics Hypertextbook", "url": "https://physics.info" } </script> <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "Person", "name": "Glenn Elert", "description": "Author, illustrator, webmaster. Career science teacher. Citizen of the United States. Omniscient walnut.", "image": "https://glennelert.us/walnut.png", "url": "https://glennelert.us", "sameAs": [ "https://twitter.com/GlennElert", "https://www.youtube.com/GlennElert" ] } </script>  <meta name="apple-mobile-web-app-title" content="physics.info"> <meta name="application-name" content="physics.info"> <meta name="msapplication-config" content="https://physics.info/physics/browserconfig.xml"> <meta name="msapplication-TileColor" content="#001f3d"> <meta name="theme-color" content="#ffffff"> <link rel="manifest" href="https://physics.info/physics/site.webmanifest"> <link rel="apple-touch-icon" href="https://physics.info/physics/apple-touch-icon.png" sizes="180x180"> <link rel="apple-touch-icon" href="https://physics.info/physics/apple-touch-icon-152x152.png" sizes="152x152"> <link rel="apple-touch-icon" href="https://physics.info/physics/apple-touch-icon-120x120.png" sizes="120x120"> <link rel="apple-touch-icon" href="https://physics.info/physics/apple-touch-icon-76x76.png" sizes="76x76"> <link rel="apple-touch-icon" href="https://physics.info/physics/apple-touch-icon-60x60.png" sizes="60x60">  <link rel="shortcut icon" href="https://physics.info/favicon.ico" sizes="64x64"> <link rel="shortcut icon" href="https://physics.info/favicon-48x48.ico" sizes="48x48"> <link rel="icon" href="https://physics.info/favicon-32x32.png" sizes="32x32" type="image/png"> <link rel="icon" href="https://physics.info/favicon-16x16.png" sizes="16x16" type="image/png"> <link rel="mask-icon" href="https://physics.info/safari-pinned-tab.svg" color="#001f3d">  <script type="text/javascript" async=true> (function() { var host = window.location.hostname; var element = document.createElement('script'); var firstScript = document.getElementsByTagName('script')[0]; var url = 'https://cmp.inmobi.com' .concat('/choice/', '2cH8w1NPvzsTT', '/', host, '/choice.js?tag_version=V3'); var uspTries = 0; var uspTriesLimit = 3; element.async = true; element.type = 'text/javascript'; element.src = url; firstScript.parentNode.insertBefore(element, firstScript); function makeStub() { var TCF_LOCATOR_NAME = '__tcfapiLocator'; var queue = []; var win = window; var cmpFrame; function addFrame() { var doc = win.document; var otherCMP = !!(win.frames[TCF_LOCATOR_NAME]); if (!otherCMP) { if (doc.body) { var iframe = doc.createElement('iframe'); iframe.style.cssText = 'display:none'; iframe.name = TCF_LOCATOR_NAME; doc.body.appendChild(iframe); } else { setTimeout(addFrame, 5); } } return !otherCMP; } function tcfAPIHandler() { var gdprApplies; var args = arguments; if (!args.length) { return queue; } else if (args[0] === 'setGdprApplies') { if ( args.length > 3 && args[2] === 2 && typeof args[3] === 'boolean' ) { gdprApplies = args[3]; if (typeof args[2] === 'function') { args[2]('set', true); } } } else if (args[0] === 'ping') { var retr = { gdprApplies: gdprApplies, cmpLoaded: false, cmpStatus: 'stub' }; if (typeof args[2] === 'function') { args[2](retr); } } else { if(args[0] === 'init' && typeof args[3] === 'object') { args[3] = Object.assign(args[3], { tag_version: 'V3' }); } queue.push(args); } } function postMessageEventHandler(event) { var msgIsString = typeof event.data === 'string'; var json = {}; try { if (msgIsString) { json = JSON.parse(event.data); } else { json = event.data; } } catch (ignore) {} var payload = json.__tcfapiCall; if (payload) { window.__tcfapi( payload.command, payload.version, function(retValue, success) { var returnMsg = { __tcfapiReturn: { returnValue: retValue, success: success, callId: payload.callId } }; if (msgIsString) { returnMsg = JSON.stringify(returnMsg); } if (event && event.source && event.source.postMessage) { event.source.postMessage(returnMsg, '*'); } }, payload.parameter ); } } while (win) { try { if (win.frames[TCF_LOCATOR_NAME]) { cmpFrame = win; break; } } catch (ignore) {} if (win === window.top) { break; } win = win.parent; } if (!cmpFrame) { addFrame(); win.__tcfapi = tcfAPIHandler; win.addEventListener('message', postMessageEventHandler, false); } }; makeStub(); var uspStubFunction = function() { var arg = arguments; if (typeof window.__uspapi !== uspStubFunction) { setTimeout(function() { if (typeof window.__uspapi !== 'undefined') { window.__uspapi.apply(window.__uspapi, arg); } }, 500); } }; var checkIfUspIsReady = function() { uspTries++; if (window.__uspapi === uspStubFunction && uspTries < uspTriesLimit) { console.warn('USP is not accessible'); } else { clearInterval(uspInterval); } }; if (typeof window.__uspapi === 'undefined') { window.__uspapi = uspStubFunction; var uspInterval = setInterval(checkIfUspIsReady, 6000); } })(); </script>   <script type='text/javascript' src='https://platform-api.sharethis.com/js/sharethis.js#property=64432e98e412510019625a9d&product=sop' async='async'></script>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-K3X8V5NL6L"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-K3X8V5NL6L'); </script>  <script> (function() { var cx = '010156806650563000082:WMX1678554632'; var gcse = document.createElement('script'); gcse.type = 'text/javascript'; gcse.async = true; gcse.src = (document.location.protocol == 'https:' ? 'https:' : 'http:') + '//www.google.com/cse/cse.js?cx=' + cx; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(gcse, s); })(); </script>  <meta name="description" content="Objects in motion will continue moving. Objects in rotation will continue rotating. The measure of this latter tendency is called rotational momentum.">  <meta property="fb:app_id" content="650318438466819"> <meta property="og:type" content="article"> <meta property="og:site_name" content="The Physics Hypertextbook"> <meta property="og:url" content="https://physics.info/rotational-momentum/"> <meta property="og:title" content="Angular Momentum – The Physics Hypertextbook"> <meta property="og:description" content="Objects in motion will continue moving. Objects in rotation will continue rotating. The measure of this latter tendency is called rotational momentum."> <meta property="og:image" content="https://physics.info/rotational-momentum/og-image.jpg"> <meta property="article:author" content="https://glennelert.us">  <meta name="twitter:card" content="summary"> <meta name="twitter:site" content="@hypertextbook"> <meta name="twitter:creator" content="@glennelert"> <meta name="twitter:url" content="https://physics.info/rotational-momentum/"> <meta name="twitter:title" content="Angular Momentum – The Physics Hypertextbook"> <meta name="twitter:description" content="Objects in motion will continue moving. Objects in rotation will continue rotating. The measure of this latter tendency is called rotational momentum."> <meta name="twitter:image" content="https://physics.info/rotational-momentum/og-image.jpg">  <meta itemprop="name" content="Angular Momentum – The Physics Hypertextbook"> <meta itemprop="description" content="Objects in motion will continue moving. Objects in rotation will continue rotating. The measure of this latter tendency is called rotational momentum."> <meta itemprop="image" content="https://physics.info/rotational-momentum/og-image.jpg">  <meta name="citation_author" content="Glenn Elert"> <meta name="citation_author_email" content="elert@hypertextbook.com"> <meta name="citation_date" content="2023"> <meta name="citation_language" content="en"> <meta name="citation_publisher" content="hypertextbook"> <meta name="citation_title" content="Angular Momentum"> <meta name="citation_inbook_title" content="The Physics Hypertextbook"> </head> <body> <header> <nav><ul><li title="The Chaos Hypertextbook Mathematics in the age of the computer"><a href="https://hypertextbook.com/chaos/" target="_top">chaos</a></li><li title="E-World Articles, essays, ideas, opinions, unabridged"><a href="https://hypertextbook.com/eworld/" target="_top">eworld</a></li><li title="The Physics Factbook An encyclopedia of scientific essays"><a href="https://hypertextbook.com/facts/" target="_top">facts</a></li><li title="Get Bent Coast to coast by recumbent bicycle"><a href="https://hypertextbook.com/bent/" target="_top">get bent</a></li><li title="The Physics Hypertextbook A work in progress" class="selected"><a href="https://physics.info" target="_top">physics</a></li></ul></nav> <div class="title" title="The Physics Hypertextbook"><a href="https://physics.info" target="_top">The Physics<br>Hypertextbook</a></div><div class="subtitle" title="A work in progress"><a href="https://physics.info/about/" target="_top">Opus in profectus</a></div> <nav id="forehead"><ul><li>… <a href="https://physics.info/rotational-statics/" target="_top" id="topic-prev" title="The previous topic">rotational-statics</a></li><li class="selected"><a href="./" target="_top" title="The current topic">rotational-momentum</a></li><li><a href="https://physics.info/rotational-energy/" target="_top" id="topic-next" title="The next topic">rotational-energy</a> …</li></ul></nav> </header> <article id="section"> <header> <h1>Angular Momentum</h1> <nav> <ul> <li class="selected"><a href="./" target="_top" title="Discussion of this topic">discuss<span class="tight">ion</span></a></li> <li><a href="summary.shtml" target="_top" title="Summary of this topic">summary</a></li> <li><a href="practice.shtml" target="_top" title="Practice problems for this topic with solutions">practice</a></li> <li><a href="problems.shtml" target="_top" title="Problems for this topic">problems</a></li> <li><a href="resources.shtml" target="_top" title="Resources for this topic on other websites">resources</a></li> </ul> </nav> <div class="add add-yes"><div class="sharethis-inline-share-buttons"></div><span class="add-goo"><a href="#search"><img src="https://omniscientwalnut.com/search.svg" alt="search icon" title="Search this site"></a></span></div><div id="search" class="overlay"><div class="popup shadow"><a class="close" href="#" title="Close this window">[close]</a><div class="gcse-searchbox-only"></div></div></div> </header> <section id="discussion">  <h2>Discussion</h2> <h3>the idea</h3> <p>text</p> <table class="maths"> <tr> <td style="text-align:right;"><b>L</b> = </td> <td style="text-align:left;"><b>r</b> × <b>p</b></td> </tr> <tr> <td style="text-align:right;"><b>L</b> = </td> <td style="text-align:left;"><b>r</b> × <i>m</i><b>v</b></td> </tr> <tr> <td style="text-align:right;"><b>L</b> = </td> <td style="text-align:left;"><i>m</i><b>r</b> × (<b>ω</b> × <b>r</b>)</td> </tr> <tr> <td style="text-align:right;"><b>L</b> = </td> <td style="text-align:left;"><i>m</i><b>ω</b>(<b>r</b> ⋅ <b>r</b>) − <i>mr</i>(<b>r</b> ⋅ <b>ω</b>)</td> </tr> <tr> <td style="text-align:right;"><b>L</b> = </td> <td style="text-align:left;"><i>mr</i><sup>2</sup><b>ω</b> − 0</td> </tr> <tr> <td style="text-align:right;"><b>L</b> = </td> <td style="text-align:left;"><i>mr</i><sup>2</sup><b>ω</b></td> </tr> <tr> <td style="text-align:right;"><b>L</b> = </td> <td style="text-align:left;"><i>I</i><b>ω</b></td> </tr> </table> <p>Moment of inertia again</p> <table class="maths"> <tr> <td><i>I</i> = ∑<i>r</i><sup>2</sup><i>m</i> = </td> <td class="split">⌠<br>⌡</td> <td><i>r</i><sup>2</sup> <i>dm</i> = ρ</td> <td class="split">⌠<br>⌡</td> <td><i>r</i><sup>2</sup> <i>dV</i></td> </tr> </table> <p>Conservation of angular momentum</p> <table class="maths"> <tr> <td rowspan="2">∑<b>τ</b> = </td> <td class="solidus"><i>d</i></td> <td rowspan="2"> <b>L</b> = 0</td> </tr> <tr> <td><i>dt</i></td> </tr> </table> <p>Thus</p> <p class="maths"><b>L</b> = constant</p> <script> function loadCSS(filename) { var file = document.createElement("link") file.setAttribute("rel", "stylesheet") file.setAttribute("type", "text/css") file.setAttribute("href", filename) if (typeof file !== "undefined") document.getElementsByTagName("head")[0].appendChild(file) } loadCSS("https://omniscientwalnut.com/rawhide.css") </script> <table class="vibrant compact rawhide"> <caption>Translational and rotational quantities compared</caption> <thead> <tr> <th>concept</th> <th colspan="2">translation</th> <th colspan="2">connection</th> <th colspan="2">rotation</th> </tr> </thead> <tbody> <tr> <td>momentum</td> <td class="maths"><b>p</b> = </td> <td class="maths"><i>m</i><b>v</b></td> <td class="maths"><b>L</b> = </td> <td class="maths"><b>r</b> × <b>p</b> = <i>m</i><b>r</b> × <b>v</b></td> <td class="maths"><b>L</b> = </td> <td class="maths"><i>I</i><b>ω</b></td> </tr> <tr> <td>impulse-momentum</td> <td class="maths">∫ <b>F</b> ⋅ <i>dt</i><br><b>F</b> = </td> <td class="maths"> = ∆<b>p</b><br><i>d</i><b>p</b>/<i>dt</i></td> <td></td> <td></td> <td class="maths">∫ <b>τ</b> ⋅ <i>dt</i><br><b>τ</b> = </td> <td class="maths"> = ∆<b>L</b> <br><i>d</i><b>L</b>/<i>dt</i></td> </tr> </tbody> </table> <h3>spaceports</h3><p>spaceports</p> <table class="vibrant"> <caption>Orbital spaceports</caption> <thead> <tr> <th>country</th> <th>status</th> <th style="text-align:left;">name</th> </tr> </thead> <tbody> <tr><td><a href="../rotational-momentum/map-au-woomera.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Australia">au</span></a></td><td>disused</td><td style="text-align:left;">Woomera Launch Site</td></tr> <tr><td><a href="../rotational-momentum/map-au-capeyork.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Australia">au</span></a></td><td>canceled</td><td style="text-align:left;">Cape York Spaceport</td></tr> <tr><td><a href="../rotational-momentum/map-au-christmasisland.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Australia">au</span></a></td><td>proposed</td><td style="text-align:left;">Christmas Island Spaceport</td></tr> <tr><td><a href="../rotational-momentum/map-br-alcantara.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Brasil">br</span></a></td><td>active</td><td style="text-align:left;"><a href="http://www.cla.aer.mil.br" target="_blank">Alcantara Launch Center</a> (Centro de Lançamento de Alcântara)</td></tr> <tr><td><a href="../rotational-momentum/map-cn-jiuquan.html" rel="nofollow" title="Google Maps" target="_blank"><span title="China">cn</span></a></td><td>active</td><td style="text-align:left;"><a href="http://www.spacechina.com" target="_blank">Jiuquan Satellite Launch Center</a> (酒泉卫星发射中心)</td></tr> <tr><td><a href="../rotational-momentum/map-cn-taiyuan.html" rel="nofollow" title="Google Maps" target="_blank"><span title="China">cn</span></a></td><td>active</td><td style="text-align:left;"><a href="http://www.spacechina.com" target="_blank">Taiyuan Satellite Launch Center</a> (太原卫星发射中心)</td></tr> <tr><td><a href="../rotational-momentum/map-cn-wenchang.html" rel="nofollow" title="Google Maps" target="_blank"><span title="China">cn</span></a></td><td>active</td><td style="text-align:left;"><a href="http://www.spacechina.com" target="_blank">Wenchang Satellite Launch Center</a> (文昌卫星发射中心)</td></tr> <tr><td><a href="../rotational-momentum/map-cn-xichang.html" rel="nofollow" title="Google Maps" target="_blank"><span title="China">cn</span></a></td><td>active</td><td style="text-align:left;"><a href="http://www.spacechina.com" target="_blank">Xichang Satellite Launch Center</a> (西昌卫星发射中心)</td></tr> <tr><td><a href="../rotational-momentum/map-fr-kourou.html" rel="nofollow" title="Google Maps" target="_blank"><span title="France">fr</span></a></td><td>active</td><td style="text-align:left;"><a href="https://www.cnes.fr" target="_blank">Guiana Space Center</a> (Centre Spatial Guyanais)</td></tr> <tr><td><a href="../rotational-momentum/map-fr-hammaguir.html" rel="nofollow" title="Google Maps" target="_blank"><span title="France">fr</span></a></td><td>disused</td><td style="text-align:left;">Hammaguir Launch Site</td></tr> <tr><td><a href="../rotational-momentum/map-it-sanmarco.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Italy">it</span></a></td><td>disused</td><td style="text-align:left;">Luigi Broglio Space Centre</td></tr> <tr><td><a href="../rotational-momentum/map-in-sriharikota.html" rel="nofollow" title="Google Maps" target="_blank"><span title="India">in</span></a></td><td>active</td><td style="text-align:left;"><a href="https://www.shar.gov.in" target="_blank">Satish Dhawan Space Centre</a> (सतीश धवन अंतरिक्ष केंद्र)</td></tr> <tr><td><a href="../rotational-momentum/map-in-trivandrum.html" rel="nofollow" title="Google Maps" target="_blank"><span title="India">in</span></a></td><td>active</td><td style="text-align:left;">Vikram Sarabhai Space Center (विक्रम साराभाई अंतरिक्ष केंद्)</td></tr> <tr><td><a href="../rotational-momentum/map-ir-semnan.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Iran">ir</span></a></td><td>active</td><td style="text-align:left;"><a href="https://www.isa.ir" target="_blank">Imam Khomeini Space Center</a></td></tr> <tr><td><a href="../rotational-momentum/map-il-palmachim.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Israel">il</span></a></td><td>active</td><td style="text-align:left;">Palmachim Air Force Base (בָּסִיס חֵיל-הַאֲוִויר פַּלְמַחִים)</td></tr> <tr><td><a href="../rotational-momentum/map-jp-tanegashima.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Japan">jp</span></a></td><td>active</td><td style="text-align:left;"><a href="https://www.jaxa.jp" target="_blank">Tanegashima Space Center</a></td></tr> <tr><td><a href="../rotational-momentum/map-jp-uchinoura.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Japan">jp</span></a></td><td>active</td><td style="text-align:left;"><a href="https://www.jaxa.jp" target="_blank">Uchinoura Space Center</a> (内之浦宇宙空間観測所)</td></tr> <tr><td><a href="../rotational-momentum/map-kp-donghae.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Korea, North">kp</span></a></td><td>active</td><td style="text-align:left;">Tonghae Satellite Launching Ground (동해위성발사장)</td></tr> <tr><td><a href="../rotational-momentum/map-kp-sohae.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Korea, North">kp</span></a></td><td>active</td><td style="text-align:left;">Sŏhae Satellite Launching Station (서해위성발사장)</td></tr> <tr><td><a href="../rotational-momentum/map-kr-naro.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Korea, South">kr</span></a></td><td>active</td><td style="text-align:left;"><a href="http://www.kari.re.kr" target="_blank">Naro Space Center</a> (나로우주센터)</td></tr> <tr><td><a href="../rotational-momentum/map-mx-yucatan.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Mexico">mx</span></a></td><td>proposed</td><td style="text-align:left;"><a href="https://www.gob.mx/aem" target="_blank">Mexican Space Agency</a> (Agencia Espacial Mexicana)</td></tr> <tr><td><a href="../rotational-momentum/map-nz-mahia.html" rel="nofollow" title="Google Maps" target="_blank"><span title="New Zealand">nz</span></a></td><td>active</td><td style="text-align:left;"><a href="https://www.rocketlabusa.com" target="_blank">Mahia Launch Complex</a></td></tr> <tr><td><a href="../rotational-momentum/map-ru-baikonur.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Russia">ru</span></a></td><td>active</td><td style="text-align:left;"><a href="http://www.roscosmos.ru" target="_blank">Baikonur Cosmodrome</a> (Космодром Байконур)</td></tr> <tr><td><a href="../rotational-momentum/map-ru-vostochniy.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Russia">ru</span></a></td><td>active</td><td style="text-align:left;"><a href="http://www.roscosmos.ru" target="_blank">Vostochny Cosmodrome</a> (Космодром Восточный)</td></tr> <tr><td><a href="../rotational-momentum/map-ru-kapustinyar.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Russia">ru</span></a></td><td>active</td><td style="text-align:left;"><a href="http://www.roscosmos.ru" target="_blank">Kapustin Yar Cosmodrome</a> (Космодром Капустин Яр)</td></tr> <tr><td><a href="../rotational-momentum/map-ru-plesetsk.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Russia">ru</span></a></td><td>active</td><td style="text-align:left;"><a href="http://www.roscosmos.ru" target="_blank">Plesetsk Cosmodrome</a> (Космодром Плесецк)</td></tr> <tr><td><a href="../rotational-momentum/map-ru-yasniy.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Russia">ru</span></a></td><td>active</td><td style="text-align:left;"><a href="http://www.kosmotras.ru" target="_blank">Yasniy Launch Base</a> (Пусковая База Ясный)</td></tr> <tr><td><a href="../rotational-momentum/map-ru-svobodniy.html" rel="nofollow" title="Google Maps" target="_blank"><span title="Russia">ru</span></a></td><td>disused</td><td style="text-align:left;">Svobodniy Cosmodrome (Космодром Свободный)</td></tr> <tr><td><a href="../rotational-momentum/map-us-kennedy.html" rel="nofollow" title="Google Maps" target="_blank"><span title="United States">us</span></a></td><td>active</td><td style="text-align:left;"><a href="https://www.nasa.gov/centers/kennedy" target="_blank">Kennedy Space Center</a></td></tr> <tr><td><a href="../rotational-momentum/map-us-vandenberg.html" rel="nofollow" title="Google Maps" target="_blank"><span title="United States">us</span></a></td><td>active</td><td style="text-align:left;"><a href="https://www.vandenberg.spaceforce.mil" target="_blank">Vandenberg Air Force Base</a></td></tr> <tr><td><a href="../rotational-momentum/map-us-wallops.html" rel="nofollow" title="Google Maps" target="_blank"><span title="United States">us</span></a></td><td>active</td><td style="text-align:left;"><a href="https://www.nasa.gov/centers/wallops" target="_blank">Wallops Flight Facility</a></td></tr> <tr><td><a href="../rotational-momentum/map-us-kodiak.html" rel="nofollow" title="Google Maps" target="_blank"><span title="United States">us</span></a></td><td>active</td><td style="text-align:left;"><a href="https://akaerospace.com" target="_blank">Kodiak Launch Complex</a></td></tr> <tr><td><a href="../rotational-momentum/map-us-reagan.html" rel="nofollow" title="Google Maps" target="_blank"><span title="United States">us</span></a></td><td>active</td><td style="text-align:left;"><a href="https://www.ll.mit.edu/about/facilities/reagan-test-site" target="_blank">Ronald Reagan Ballistic Missile Defense Test Site</a></td></tr> <tr><td><a href="../rotational-momentum/map-us-sealaunch.html" rel="nofollow" title="Google Maps" target="_blank"><span title="United States">us</span></a></td><td>active</td><td style="text-align:left;"><a href="https://s7space.ru" target="_blank">Sea Launch</a></td></tr> </tbody> </table>  <h3>the earth</h3> <p>The earth is not the world's best clock.</p> <p class="inline"><a href="../time/lod-daily.svg" target="_blank"><embed src="../time/lod-daily.svg"><span class="donotprint">Magnify</span></a></p> <p class="inline"><a href="../time/lod-historical.svg" target="_blank"><embed src="../time/lod-historical.svg"><span class="donotprint">Magnify</span></a></p> <p>types of LOD change … horrible mess …</p> <ol> <li>a linear increase owing to tidal dissipation. Paraphrase, "The tidal friction between the oceans and the Earth's surface causes the Earth's rotation to slow by approximately 0.002 seconds every century. However, ignoring energy lost to heat generated by the tides, the angular momentum of the Earth-Moon system must remain constant. The Earth's angular momentum is decreasing, so the Moon's must increase. The only way it can do this is by moving into a higher orbit around the Earth. Thus, the distance to the farthest point of the lunar orbit is increasing by about 3.8 centimeters per year."</li> <li>Larger, irregular variations, on the scale of decades, owing to core-mantle interactions</li> <li>Solar flares are known to abruptly alter the Earth's rotation. For example, the great flares of 1959 and 1972 brought abrupt changes in the LOD. Both long-term and short-term changes in solar activity alter the Earth's rotation. The 11-year, 22-year and 56-year solar cycles are conspicuous in the LOD data. Long-term (secular) changes were noted at times of fluctuations in solar activity in the past, and the evidence indicates that these changes were very likely abrupt. Observations of the LOD, like so many other geophysical phenomena, reveal the solar-FEM linkage.</li> <li>Seasonal changes from the angular momentum exchange between crust and atmosphere.</li> </ol> <p>The rate of rotation of the Earth is high in summer and low in winter (northern hemisphere).</p> <ul> <li>exchange of angular momentum between the solid Earth and the atmosphere</li> <li>yearly melting of snow and ice in northern Spring</li> <li>and distribution of groundwater?</li> </ul> <p>At time scales of hours to days, tidally driven? ocean currents and variations in the ocean height dominate</p>  </section> <footer> <div class="add add-yes"><div class="sharethis-inline-share-buttons"></div><span class="add-goo"><a href="#search"><img src="https://omniscientwalnut.com/search.svg" alt="search icon" title="Search this site"></a></span></div> <nav> <ul> <li class="selected"><a href="./" target="_top" title="Discussion of this topic">discuss<span class="tight">ion</span></a></li> <li><a href="summary.shtml" target="_top" title="Summary of this topic">summary</a></li> <li><a href="practice.shtml" target="_top" title="Practice problems for this topic with solutions">practice</a></li> <li><a href="problems.shtml" target="_top" title="Problems for this topic">problems</a></li> <li><a href="resources.shtml" target="_top" title="Resources for this topic on other websites">resources</a></li> </ul> </nav> <h1>Angular Momentum</h1> </footer> </article> <footer> <nav><ul><li>… <a href="https://physics.info/rotational-statics/" target="_top" title="The previous topic">rotational-statics</a></li><li class="selected"><a href="./" title="The current topic">rotational-momentum</a></li><li><a href="https://physics.info/rotational-energy/" target="_top" title="The next topic">rotational-energy</a> …</li></ul></nav> <div class="signature"><span><a href="https://hypertextbook.com" target="_top"><img src="https://omniscientwalnut.com/eglobe.svg" title="hypertextbook.com" alt="eglobe logo"></a></span><span><a href="https://physics.info" target="_top" title="Opus in profectus">The Physics Hypertextbook</a><br><a href="https://glennelert.us" target="_blank" title="Say my name. You know who I am.">©1998–2024 Glenn Elert<br>Author, Illustrator, Webmaster</a></span></div><p title="No condition is permanent">No condition is permanent.</p>  <nav> <ol> <li style="-webkit-column-break-before:avoid; break-before:avoid;" id="mechanics">Mechanics <ol> <li>Kinematics <ol> <li><a href="https://physics.info/motion/" target="_top">Motion</a></li> <li><a href="https://physics.info/displacement/" target="_top">Distance and Displacement</a></li> <li><a href="https://physics.info/velocity/" target="_top">Speed and Velocity</a></li> <li><a href="https://physics.info/acceleration/" target="_top">Acceleration</a></li> <li><a href="https://physics.info/motion-equations/" target="_top">Equations of Motion</a></li> <li><a href="https://physics.info/falling/" target="_top">Free Fall</a></li> <li><a href="https://physics.info/motion-graphs/" target="_top">Graphs of Motion</a></li> <li><a href="https://physics.info/kinematics-calculus/" target="_top">Kinematics and Calculus</a></li> <li><a href="https://physics.info/kinematics-2d/" target="_top">Kinematics in Two Dimensions</a></li> <li><a href="https://physics.info/projectiles/" target="_top">Projectiles</a></li> <li><a href="https://physics.info/parametric/" target="_top">Parametric Equations</a></li> </ol></li> <li>Dynamics I: Force <ol> <li><a href="https://physics.info/newton-first/" target="_top">Forces</a></li> <li><a href="https://physics.info/newton-second/" target="_top">Force and Mass</a></li> <li><a href="https://physics.info/newton-third/" target="_top">Action-Reaction</a></li> <li><a href="https://physics.info/weight/" target="_top">Weight</a></li> <li><a href="https://physics.info/dynamics/" target="_top">Dynamics</a></li> <li><a href="https://physics.info/statics/" target="_top">Statics</a></li> <li><a href="https://physics.info/friction/" target="_top">Friction</a></li> <li><a href="https://physics.info/force-2d/" target="_top">Forces in Two Dimensions</a></li> <li><a href="https://physics.info/centripetal/" target="_top">Centripetal Force</a></li> <li><a href="https://physics.info/frames/" target="_top">Frames of Reference</a></li> </ol></li> <li>Energy <ol> <li><a href="https://physics.info/work/" target="_top">Work</a></li> <li><a href="https://physics.info/energy/" target="_top">Energy</a></li> <li><a href="https://physics.info/energy-kinetic/" target="_top">Kinetic Energy</a></li> <li><a href="https://physics.info/energy-potential/" target="_top">Potential Energy</a></li> <li><a href="https://physics.info/energy-conservation/" target="_top">Conservation of Energy</a></li> <li><a href="https://physics.info/power/" target="_top">Power</a></li> <li><a href="https://physics.info/machines/" target="_top">Simple Machines</a></li> </ol></li> <li>Dynamics II: Momentum <ol> <li><a href="https://physics.info/momentum/" target="_top">Impulse and Momentum</a></li> <li><a href="https://physics.info/momentum-conservation/" target="_top">Conservation of Momentum</a></li> <li><a href="https://physics.info/momentum-energy/" target="_top">Momentum and Energy</a></li> <li><a href="https://physics.info/momentum-2d/" target="_top">Momentum in Two Dimensions</a></li> </ol></li> <li>Rotational Motion <ol> <li><a href="https://physics.info/rotational-kinematics/" target="_top">Rotational Kinematics</a></li> <li><a href="https://physics.info/rotational-inertia/" target="_top">Rotational Inertia</a></li> <li><a href="https://physics.info/rotational-dynamics/" target="_top">Rotational Dynamics</a></li> <li><a href="https://physics.info/rotational-statics/" target="_top">Rotational Statics</a></li> <li><a href="https://physics.info/rotational-momentum/" target="_top">Angular Momentum</a></li> <li><a href="https://physics.info/rotational-energy/" target="_top">Rotational Energy</a></li> <li><a href="https://physics.info/rolling/" target="_top">Rolling</a></li> <li><a href="https://physics.info/rotational-2d/" target="_top">Rotation in Two Dimensions</a></li> <li><a href="https://physics.info/coriolis/" target="_top">Coriolis Force</a></li> </ol></li> <li>Planetary Motion <ol> <li><a href="https://physics.info/geocentrism/" target="_top">Geocentrism</a></li> <li><a href="https://physics.info/heliocentrism/" target="_top">Heliocentrism</a></li> <li><a href="https://physics.info/gravitation/" target="_top">Universal Gravitation</a></li> <li><a href="https://physics.info/orbital-mechanics-1/" target="_top">Orbital Mechanics I</a></li> <li><a href="https://physics.info/gravitation-energy/" target="_top">Gravitational Potential Energy</a></li> <li><a href="https://physics.info/orbital-mechanics-2/" target="_top">Orbital Mechanics II</a></li> <li><a href="https://physics.info/gravitation-extended/" target="_top">Gravity of Extended Bodies</a></li> </ol></li> <li>Periodic Motion <ol> <li><a href="https://physics.info/springs/" target="_top">Springs</a></li> <li><a href="https://physics.info/sho/" target="_top">Simple Harmonic Oscillator</a></li> <li><a href="https://physics.info/pendulum/" target="_top">Pendulums</a></li> <li><a href="https://physics.info/resonance/" target="_top">Resonance</a></li> <li><a href="https://physics.info/elasticity/" target="_top">Elasticity</a></li> </ol></li> <li>Fluids <ol> <li><a href="https://physics.info/density/" target="_top">Density</a></li> <li><a href="https://physics.info/pressure/" target="_top">Pressure</a></li> <li><a href="https://physics.info/buoyancy/" target="_top">Buoyancy</a></li> <li><a href="https://physics.info/flow/" target="_top">Fluid Flow</a></li> <li><a href="https://physics.info/viscosity/" target="_top">Viscosity</a></li> <li><a href="https://physics.info/drag/" target="_top">Aerodynamic Drag</a></li> <li><a href="https://physics.info/turbulence/" target="_top">Flow Regimes</a></li> </ol></li> </ol></li> <li style="-webkit-column-break-before:always; break-before:column;" id="thermal">Thermal Physics <ol> <li>Heat & Temperature <ol> <li><a href="https://physics.info/temperature/" target="_top">Temperature</a></li> <li><a href="https://physics.info/expansion/" target="_top">Thermal Expansion</a></li> <li><a href="https://physics.info/atoms/" target="_top">The Atomic Nature of Matter</a></li> <li><a href="https://physics.info/gas-laws/" target="_top">Gas Laws</a></li> <li><a href="https://physics.info/kmt/" target="_top">Kinetic-Molecular Theory</a></li> <li><a href="https://physics.info/phases/" target="_top">Phases</a></li> </ol></li> <li>Calorimetry <ol> <li><a href="https://physics.info/heat-sensible/" target="_top">Sensible Heat</a></li> <li><a href="https://physics.info/heat-latent/" target="_top">Latent Heat</a></li> <li><a href="https://physics.info/energy-chemical/" target="_top">Chemical Potential Energy</a></li> </ol></li> <li>Heat Transfer <ol> <li><a href="https://physics.info/conduction/" target="_top">Conduction</a></li> <li><a href="https://physics.info/convection/" target="_top">Convection</a></li> <li><a href="https://physics.info/radiation/" target="_top">Radiation</a></li> </ol></li> <li>Thermodynamics <ol> <li><a href="https://physics.info/thermo-first/" target="_top">Heat and Work</a></li> <li><a href="https://physics.info/pressure-volume/" target="_top">Pressure-Volume Diagrams</a></li> <li><a href="https://physics.info/engines/" target="_top">Engines</a></li> <li><a href="https://physics.info/refrigerators/" target="_top">Refrigerators</a></li> <li><a href="https://physics.info/thermo-second/" target="_top">Energy and Entropy</a></li> <li><a href="https://physics.info/thermo-third/" target="_top">Absolute Zero</a></li> </ol></li> </ol></li> <li style="-webkit-column-break-before:avoid; break-before:avoid;" id="waves">Waves & Optics <ol> <li>Wave Phenomena <ol> <li><a href="https://physics.info/waves/" target="_top">The Nature of Waves</a></li> <li><a href="https://physics.info/waves-periodic/" target="_top">Periodic Waves</a></li> <li><a href="https://physics.info/interference/" target="_top">Interference and Superposition</a></li> <li><a href="https://physics.info/interface/" target="_top">Interfaces and Barriers</a></li> </ol></li> <li>Sound <ol> <li><a href="https://physics.info/sound/" target="_top">The Nature of Sound</a></li> <li><a href="https://physics.info/intensity/" target="_top">Intensity</a></li> <li><a href="https://physics.info/doppler-sound/" target="_top">Doppler Effect (Sound)</a></li> <li><a href="https://physics.info/shock/" target="_top">Shock Waves</a></li> <li><a href="https://physics.info/interference-sound/" target="_top">Diffraction and Interference (Sound)</a></li> <li><a href="https://physics.info/waves-standing/" target="_top">Standing Waves</a></li> <li><a href="https://physics.info/beats/" target="_top">Beats</a></li> <li><a href="https://physics.info/music/" target="_top">Music and Noise</a></li> </ol></li> <li>Physical Optics <ol> <li><a href="https://physics.info/light/" target="_top">The Nature of Light</a></li> <li><a href="https://physics.info/polarization/" target="_top">Polarization</a></li> <li><a href="https://physics.info/doppler-light/" target="_top">Doppler Effect (Light)</a></li> <li><a href="https://physics.info/cerenkov/" target="_top">Cerenkov Radiation</a></li> <li><a href="https://physics.info/interference-light/" target="_top">Diffraction and Interference (Light)</a></li> <li><a href="https://physics.info/thin-films/" target="_top">Thin Film Interference</a></li> <li><a href="https://physics.info/color/" target="_top">Color</a></li> </ol></li> <li>Geometric Optics <ol> <li><a href="https://physics.info/reflection/" target="_top">Reflection</a></li> <li><a href="https://physics.info/refraction/" target="_top">Refraction</a></li> <li><a href="https://physics.info/mirrors/" target="_top">Spherical Mirrors</a></li> <li><a href="https://physics.info/lenses/" target="_top">Spherical Lenses</a></li> <li><a href="https://physics.info/aberration/" target="_top">Aberration</a></li> </ol></li> </ol></li> <li style="-webkit-column-break-before:always; break-before:column;" id="electricity">Electricity & Magnetism <ol> <li>Electrostatics <ol> <li><a href="https://physics.info/charge/" target="_top">Electric Charge</a></li> <li><a href="https://physics.info/coulomb/" target="_top">Coulomb's Law</a></li> <li><a href="https://physics.info/electric-field/" target="_top">Electric Field</a></li> <li><a href="https://physics.info/electric-potential/" target="_top">Electric Potential</a></li> <li><a href="https://physics.info/law-gauss/" target="_top">Gauss's Law</a></li> <li><a href="https://physics.info/conductors/" target="_top">Conductors</a></li> </ol></li> <li>Electrostatic Applications <ol> <li><a href="https://physics.info/capacitors/" target="_top">Capacitors</a></li> <li><a href="https://physics.info/dielectrics/" target="_top">Dielectrics</a></li> <li><a href="https://physics.info/batteries/" target="_top">Batteries</a></li> </ol></li> <li>Electric Current <ol> <li><a href="https://physics.info/electric-current/" target="_top">Electric Current</a></li> <li><a href="https://physics.info/electric-resistance/" target="_top">Electric Resistance</a></li> <li><a href="https://physics.info/electric-power/" target="_top">Electric Power</a></li> </ol></li> <li>DC Circuits <ol> <li><a href="https://physics.info/circuits-r/" target="_top">Resistors in Circuits</a></li> <li><a href="https://physics.info/circuits-v/" target="_top">Batteries in Circuits</a></li> <li><a href="https://physics.info/circuits-c/" target="_top">Capacitors in Circuits</a></li> <li><a href="https://physics.info/kirchhoff/" target="_top">Kirchhoff's Rules</a></li> </ol></li> <li>Magnetostatics <ol> <li><a href="https://physics.info/magnetism/" target="_top">Magnetism</a></li> <li><a href="https://physics.info/electromagnetism/" target="_top">Electromagnetism</a></li> <li><a href="https://physics.info/law-ampere/" target="_top">Ampère's Law</a></li> <li><a href="https://physics.info/lorentz/" target="_top">Electromagnetic Force</a></li> </ol></li> <li>Magnetodynamics <ol> <li><a href="https://physics.info/induction/" target="_top">Electromagnetic Induction</a></li> <li><a href="https://physics.info/law-faraday/" target="_top">Faraday's Law</a></li> <li><a href="https://physics.info/lenz/" target="_top">Lenz' Law</a></li> <li><a href="https://physics.info/inductance/" target="_top">Inductance</a></li> </ol></li> <li>AC Circuits <ol> <li><a href="https://physics.info/circuits-rc/" target="_top">RC Circuits</a></li> <li><a href="https://physics.info/circuits-rl/" target="_top">RL Circuits</a></li> <li><a href="https://physics.info/circuits-rlc/" target="_top">LC Circuits</a></li> <li><a href="https://physics.info/current-alternating/" target="_top">Alternating Current</a></li> <li><a href="https://physics.info/impedance/" target="_top">Impedance</a></li> </ol></li> <li>Electromagnetic Waves <ol> <li><a href="https://physics.info/maxwell/" target="_top">Maxwell's Equations</a></li> <li><a href="https://physics.info/em-waves/" target="_top">Electromagnetic Waves</a></li> <li><a href="https://physics.info/em-spectrum/" target="_top">Electromagnetic Spectrum</a></li> </ol></li> </ol></li> <li style="-webkit-column-break-before:always; break-before:column;" id="modern">Modern Physics <ol> <li>Relativity <ol> <li><a href="https://physics.info/space-time/" target="_top">Space-Time</a></li> <li><a href="https://physics.info/mass-energy/" target="_top">Mass-Energy</a></li> <li><a href="https://physics.info/general-relativity/" target="_top">General Relativity</a></li> </ol></li> <li>Quanta <ol> <li><a href="https://physics.info/planck/" target="_top">Blackbody Radiation</a></li> <li><a href="https://physics.info/photoelectric/" target="_top">Photoelectric Effect</a></li> <li><a href="https://physics.info/x-ray/" target="_top">X-rays</a></li> <li><a href="https://physics.info/antimatter/" target="_top">Antimatter</a></li> </ol></li> <li>Wave Mechanics <ol> <li><a href="https://physics.info/debroglie/" target="_top">Matter Waves</a></li> <li><a href="https://physics.info/atomic-models/" target="_top">Atomic Models</a></li> <li><a href="https://physics.info/semiconductors/" target="_top">Semiconductors</a></li> <li><a href="https://physics.info/condensed-matter/" target="_top">Condensed Matter</a></li> </ol></li> <li>Nuclear Physics <ol> <li><a href="https://physics.info/isotopes/" target="_top">Isotopes</a></li> <li><a href="https://physics.info/decay/" target="_top">Radioactive Decay</a></li> <li><a href="https://physics.info/half-life/" target="_top">Half Life</a></li> <li><a href="https://physics.info/binding/" target="_top">Binding Energy</a></li> <li><a href="https://physics.info/fission/" target="_top">Fission</a></li> <li><a href="https://physics.info/fusion/" target="_top">Fusion</a></li> <li><a href="https://physics.info/nucleosynthesis/" target="_top">Nucleosynthesis</a></li> <li><a href="https://physics.info/weapons/" target="_top">Nuclear Weapons</a></li> <li><a href="https://physics.info/radiobiology/" target="_top">Radiobiology</a></li> </ol></li> <li>Particle Physics <ol> <li><a href="https://physics.info/standard/" target="_top">The Standard Model</a></li> <li><a href="https://physics.info/qed/" target="_top">Quantum Electrodynamics</a></li> <li><a href="https://physics.info/qcd/" target="_top">Quantum Chromodynamics</a></li> <li><a href="https://physics.info/qfd/" target="_top">Quantum Flavordynamics</a></li> <li><a href="https://physics.info/beyond/" target="_top">Beyond the Standard Model</a></li> </ol></li> </ol></li> <li style="-webkit-column-break-before:avoid; break-before:avoid;" id="foundations">Foundations <ol> <li>Units <ol> <li><a href="https://physics.info/system-international/" target="_top">International System of Units</a></li> <li><a href="https://physics.info/system-gaussian/" target="_top">Gaussian System of Units</a></li> <li><a href="https://physics.info/system-english/" target="_top">British-American System of Units</a></li> <li><a href="https://physics.info/system-miscellaneous/" target="_top">Miscellaneous Units</a></li> <li><a href="https://physics.info/time/" target="_top">Time</a></li> <li><a href="https://physics.info/unit-conversion/" target="_top">Unit Conversion</a></li> </ol></li> <li>Measurement <ol> <li><a href="https://physics.info/significant-digits/" target="_top">Significant Digits</a></li> <li><a href="https://physics.info/orders-magnitude/" target="_top">Order of Magnitude</a></li> </ol></li> <li>Graphs <ol> <li><a href="https://physics.info/graphs/" target="_top">Graphical Representation of Data</a></li> <li><a href="https://physics.info/linear-regression/" target="_top">Linear Regression</a></li> <li><a href="https://physics.info/curve-fitting/" target="_top">Curve Fitting</a></li> <li><a href="https://physics.info/calculus/" target="_top">Calculus</a></li> </ol></li> <li>Vectors <ol> <li><a href="https://physics.info/trigonometry/" target="_top">Trigonometry</a></li> <li><a href="https://physics.info/vector-addition/" target="_top">Vector Addition and Subtraction</a></li> <li><a href="https://physics.info/vector-components/" target="_top">Vector Resolution and Components</a></li> <li><a href="https://physics.info/vector-multiplication/" target="_top">Vector Multiplication</a></li> </ol></li> <li>Reference <ol> <li><a href="https://physics.info/symbols/" target="_top">Special Symbols</a></li> <li><a href="https://physics.info/equations/" target="_top">Frequently Used Equations</a></li> <li><a href="https://physics.info/constants/" target="_top">Physical Constants</a></li> <li><a href="https://physics.info/astronomical/" target="_top">Astronomical Data</a></li> <li><a href="https://physics.info/periodic-table/" target="_top">Periodic Table of the Elements</a></li> <li><a href="https://physics.info/people/" target="_top">People in Physics</a></li> </ol></li> </ol></li> <li style="-webkit-column-break-before:avoid; break-before:avoid;" id="back">Back matter <ol> <li>Preface <ol> <li><a href="https://physics.info/about/" target="_top">About this book</a></li> </ol></li> <li>Contact the author <ol> <li><a href="https://glennelert.us" rel="me" target="_blank">glennelert.us</a></li> <li><a href="https://www.behance.net/elert" rel="me" target="_blank">Behance</a></li> <li><a href="https://www.instagram.com/elert" rel="me" target="_blank">Instagram</a></li> <li><a href="https://www.twitter.com/glennelert" rel="me" target="_blank">Twitter</a></li> <li><a href="https://www.youtube.com/GlennElert" rel="me" target="_blank">YouTube</a></li> </ol></li> <li>Affiliated websites <ol> <li><a href="https://hypertextbook.com" rel="me" title="Hypertextbook" target="_blank">hypertextbook.com</a></li> <li><a href="http://midwoodscience.org" rel="me" title="Midwood High School Science Research Program" target="_blank">midwoodscience.org</a></li> </ol></li> </ol></li> </ol> </nav>  <script> $('html,body').delay(1000).animate({scrollTop: $('#forehead').offset().top },500); </script> </footer> </body> </html>

CINXE.COM

Angular Momentum – The Physics Hypertextbook