{"id":5698,"date":"2019-11-25T18:20:38","date_gmt":"2019-11-25T12:50:38","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=5698"},"modified":"2022-11-04T12:06:29","modified_gmt":"2022-11-04T06:36:29","slug":"rotational-motion-formulas-list","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/rotational-motion-formulas-list\/","title":{"rendered":"Rotational Motion Formulas list"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2019\/11\/Rotational-Motion-Formulas-list-1024x576.png\" alt=\"Rotational Motion Formulas\" class=\"wp-image-5808\" srcset=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2019\/11\/Rotational-Motion-Formulas-list-1024x576.png 1024w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2019\/11\/Rotational-Motion-Formulas-list-300x169.png 300w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2019\/11\/Rotational-Motion-Formulas-list-768x432.png 768w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2019\/11\/Rotational-Motion-Formulas-list.png 1080w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>This Rotational motion formulas list has a list of frequently used rotational motion equations. These equations involve trigonometry and vector products.<br><a rel=\"noreferrer noopener\" aria-label=\"Rotational motion (opens in a new tab)\" href=\"https:\/\/physicscatalyst.com\/mech\/rotational-motion.php\" >Rotational motion<\/a> is the motion of a body around a fixed axis (see <a href=\"https:\/\/physicscatalyst.com\/article\/types-of-motion\/\">types of motion<\/a>). Variables of motion in case of rotational motion are <br>1. angular displacement \\(\\theta\\)<br>2. <a rel=\"noreferrer noopener\" aria-label=\"angular velocity (opens in a new tab)\" href=\"https:\/\/physicscatalyst.com\/mech\/angular-velocity.php\" >angular velocity<\/a> \\(\\omega\\)<br>3. <a rel=\"noreferrer noopener\" aria-label=\"angular acceleration (opens in a new tab)\" href=\"https:\/\/physicscatalyst.com\/mech\/angular-acceleration.php\" >angular acceleration<\/a> \\(\\alpha\\)<br>Also see <a href=\"https:\/\/physicscatalyst.com\/article\/translational-motion\/\">translational motion<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Rotational motion equations formula list<\/h3>\n\n\n\n<p>If a body is executing <a href=\"https:\/\/physicscatalyst.com\/mech\/rotation-with-constant-angular-acceleration.php\"  rel=\"noreferrer noopener\" aria-label=\"rotation with constant acceleration (opens in a new tab)\">rotation with constant acceleration<\/a>, the equations of motion can be written as \\[\\omega =\\omega _0+\\alpha t\\] \\[\\theta =\\omega _0t+\\frac{1}{2}\\alpha t^2\\] \\[\\omega ^2-\\omega _{0}^{2}=2\\alpha t\\] <strong>Units and notations used<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(\\theta\\) : angular displacement its unit is \\(radian\\)<\/li><li>\\(\\omega_0\\): initial angular velocity its unit is \\(rad \\,\\, s^{-1}\\)<\/li><li> \\(\\omega\\) : final angular velocity its unit is \\(rad \\,\\, s^{-1}\\) <\/li><li> \\(\\alpha\\) : angular acceleration its unit is \\(rad \\,\\, s^{-2}\\) <\/li><\/ul>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Formulas for torque, angular momentum, power and work done<\/h3>\n\n\n\n<p><strong>Torque<\/strong> \\begin{align*}\\text{Torque} =&amp;\\text{force }\\times \\\\ &amp;\\text{its perpendicular distance from axis of rotation}\\end{align*} or, \\[\\tau =Fd\\] Torque  \\[\\tau =rF\\sin \\theta \\] or, \\[\\vec{\\tau} =\\vec{r}\\times \\vec{F}\\]<br>Learn more about  <a rel=\"noreferrer noopener\" href=\"https:\/\/physicscatalyst.com\/mech\/torque.php\" >Torque<\/a> <\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p><strong>Power of Torque<\/strong> \\[\\text{Power of a torque} = \\text{torque} \\times \\text{angular velocity}\\] or,  \\[P=\\tau \\omega\\]  \\[\\text{Work done by torque = torque} \\times  \\text{ angular displacement}\\] or, \\[W=\\tau \\theta\\] <\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p><strong>Angular Momentum<\/strong> \\begin{align*}\\text{Angular momentum} =&amp;\\text{ Linear momentum } \\times \\\\ &amp;\\text{its perpendicular distance from the axis of rotation}\\end{align*} \\[L=pd\\] \\[\\text{Angular momentum } l=rp\\sin \\theta\\] or,  \\[\\vec{L}=\\vec{r}\\times \\vec{p}\\] For a particle of mass \\(m\\) moving with uniform speed \\(v\\) along a circle of radius \\(r\\),  \\[L=mvr\\] \\[\\text{torque = rate of change of angular momentum}\\] or,  \\[\\tau =\\frac{dL}{dt}\\] <\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p><strong>Unit used: <\/strong><br> torque &#8211; \\(Nm\\) <br> Work done &#8211; \\(Joule\\)<br> Power &#8211; \\(Watt\\)<br> angular velocity &#8211; \\(\\text{rad}.\\text{s^{-1}}\\)<br> <a rel=\"noreferrer noopener\" aria-label=\"angular momentum (opens in a new tab)\" href=\"https:\/\/physicscatalyst.com\/mech\/angular-momentum.php\" >angular momentum<\/a> &#8211; \\(Kgm^2s^{-1}\\)<br>learn more about <a rel=\"noreferrer noopener\" aria-label=\"work done in rotational motion (opens in a new tab)\" href=\"https:\/\/physicscatalyst.com\/mech\/work-done-in-rotational-motion.php\" >work done in rotational motion<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Moment of Inertia formula list<\/h3>\n\n\n\n<p><a rel=\"noreferrer noopener\" aria-label=\"Moment of inertia (opens in a new tab)\" href=\"https:\/\/physicscatalyst.com\/mech\/moment-of-inertia.php\" >Moment of inertia<\/a> of a body about any given axis of rotation,  \\[I=m_1r_1^2+m_2r_2^2+m_3r_3^2+&#8230;&#8230;..m_nr_n^2=\\sum_{i=1}^n{m_ir_i^2}\\]     Radius of gyration \\(K\\) is given by \\[K=\\sqrt{\\frac{I}{M}}\\]     <a rel=\"noreferrer noopener\" aria-label=\"Theorem of perpendicular axis (opens in a new tab)\" href=\"https:\/\/physicscatalyst.com\/mech\/perpendicular-axis-theorem.php\" >Theorem of perpendicular axis<\/a>     \\[I_z=I_x+I_y\\]     <a rel=\"noreferrer noopener\" aria-label=\"Theorem of parallel axis (opens in a new tab)\" href=\"https:\/\/physicscatalyst.com\/mech\/parallel-axis-theorem.php\" >Theorem of parallel axis<\/a>     \\[I=I_{CM}+Md^2\\]     Rotational Kinetic Energy     \\[K.E.=\\frac{1}{2}I\\omega ^2\\]     Total Kinetic Energy = Rotational K.E. + Translational K.E.     \\[\\text{Total K.E.} = \\frac{1}{2}I\\omega ^2+\\frac{1}{2}Mv^2\\]     <\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p><strong>Units and notations Used<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>mass \\(M\\) is in \\(Kg\\)<\/li><li> Radius \\(R\\) in meters \\(\\left( m \\right) \\)<\/li><li> <a href=\"https:\/\/physicscatalyst.com\/mech\/radius-of-gyration.php\"  rel=\"noreferrer noopener\" aria-label=\"Radius of gyration (opens in a new tab)\">Radius of gyration<\/a> \\(K\\) in meter \\(\\left( m \\right)\\) <\/li><li> <a href=\"https:\/\/physicscatalyst.com\/mech\/kinetic-energy-of-rotation.php\"  rel=\"noreferrer noopener\" aria-label=\"Rotational Kinetic Energy (opens in a new tab)\">Rotational Kinetic Energy<\/a> in \\(Joule\\)<\/li><li> Angular velocity \\(\\omega\\) in \\(rad\\,\\, s^{-1}\\)<\/li><\/ul>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Relations between torque, angular momentum and M.I. \\(I\\)<\/h3>\n\n\n\n<p>Torque = M.I \\(\\times\\) angular acceleration<br>or,\\[\\tau=I\\alpha\\] Work done by torque,\\[W=\\tau \\theta\\] Angular momentum = M.I. \\(\\times\\) angular Velocity<br>or, \\[L=I\\omega\\] <\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p><strong>Unit and terms Used<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Torque \\(\\tau\\) is in \\(N\\,\\,m\\).<\/li><li>Moment of inertia \\(I\\) is in \\(Kg\\,\\,m^2\\).<\/li><li>Angular momentum \\(L\\) is in \\(Kg\\,\\,m^2s^{-1}\\). <\/li><\/ul>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Rolling without slipping<\/h3>\n\n\n\n<p>For a cylinder of mass \\(M\\) and radius \\(R\\), <a rel=\"noreferrer noopener\" aria-label=\"rolling motion (opens in a new tab)\" href=\"https:\/\/physicscatalyst.com\/mech\/rolling-motion.php\" >rolling motion<\/a> without slipping down a plane inclined at an angle \\(\\theta\\) with the horizontal,<br>1. <a rel=\"noreferrer noopener\" aria-label=\"Force of friction (opens in a new tab)\" href=\"https:\/\/physicscatalyst.com\/mech\/force-of-friction.php\" >Force of friction<\/a> between the plane and the cylinder<br>\\(f=\\frac{1}{3}Mg\\sin \\theta\\)<br>2. Linear acceleration,<br>\\(a=\\frac{2}{3}g \\sin \\theta\\) <br>3. Conditions for rolling without slipping is<br>\\(\\mu_s &gt;  \\frac{1}{3}  \\tan \\theta\\)<br>Here \\(a\\) and \\(g\\) are in \\(m\\,\\,s^{-1}\\) and  \\(\\mu_s \\) has no units.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This Rotational motion formulas list has a list of frequently used rotational motion equations. These equations involve trigonometry and vector products.Rotational motion is the motion of a body around a fixed axis (see types of motion). Variables of motion in case of rotational motion are 1. angular displacement \\(\\theta\\)2. angular velocity \\(\\omega\\)3. angular acceleration \\(\\alpha\\)Also [&hellip;]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[14],"tags":[],"class_list":["post-5698","post","type-post","status-publish","format-standard","hentry","category-physics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Rotational Motion Formulas list - physicscatalyst&#039;s Blog<\/title>\n<meta name=\"description\" content=\"These Rotational motion formulas list has a list of frequently used rotational motion equations. 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These equations involve trigonometry and vector products.Rotational motion is the motion of a body around a fixed axis (see types of motion). Variables of motion in case of rotational motion are 1. angular displacement \\(\\theta\\)2. angular velocity \\(\\omega\\)3. angular acceleration \\(\\alpha\\)Also&hellip;","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/5698","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/comments?post=5698"}],"version-history":[{"count":1,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/5698\/revisions"}],"predecessor-version":[{"id":6873,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/5698\/revisions\/6873"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=5698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=5698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=5698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}