{"id":245688,"date":"2025-07-06T11:09:22","date_gmt":"2025-07-06T11:09:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245688"},"modified":"2025-07-06T11:09:24","modified_gmt":"2025-07-06T11:09:24","slug":"calculate-the-rotational-rotational-inertia-of-a-wheel-that-has-a-kinetic-energy-of-24400-j-when-rotating-at-602-rev-min","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/calculate-the-rotational-rotational-inertia-of-a-wheel-that-has-a-kinetic-energy-of-24400-j-when-rotating-at-602-rev-min\/","title":{"rendered":"Calculate the rotational rotational inertia of a wheel that has a kinetic energy of 24,400 J when rotating at 602 rev\/min."},"content":{"rendered":"\n<p>Calculate the rotational rotational inertia of a wheel that has a kinetic energy of 24,400 J when rotating at 602 rev\/min.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To calculate the rotational inertia (moment of inertia) of the wheel, we can use the formula for rotational kinetic energy:KE=12I\u03c92KE = \\frac{1}{2} I \\omega^2KE=21\u200bI\u03c92<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>KEKEKE is the kinetic energy,<\/li>\n\n\n\n<li>III is the moment of inertia,<\/li>\n\n\n\n<li>\u03c9\\omega\u03c9 is the angular velocity in radians per second.<\/li>\n<\/ul>\n\n\n\n<p>We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>KE=24,400\u2009JKE = 24,400 \\, \\text{J}KE=24,400J,<\/li>\n\n\n\n<li>rev\/min=602\u2009rev\/min\\text{rev\/min} = 602 \\, \\text{rev\/min}rev\/min=602rev\/min.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Convert the angular velocity from rev\/min to rad\/s.<\/h3>\n\n\n\n<p>To convert the angular velocity from revolutions per minute to radians per second, use the following conversion factors:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1\u2009rev=2\u03c0\u2009radians1 \\, \\text{rev} = 2\\pi \\, \\text{radians}1rev=2\u03c0radians,<\/li>\n\n\n\n<li>1\u2009min=60\u2009seconds1 \\, \\text{min} = 60 \\, \\text{seconds}1min=60seconds.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the angular velocity \u03c9\\omega\u03c9 in radians per second is:\u03c9=602\u2009rev\/min\u00d72\u03c0\u2009rad1\u2009rev\u00d71\u2009min60\u2009seconds=62.97\u2009rad\/s\\omega = 602 \\, \\text{rev\/min} \\times \\frac{2\\pi \\, \\text{rad}}{1 \\, \\text{rev}} \\times \\frac{1 \\, \\text{min}}{60 \\, \\text{seconds}} = 62.97 \\, \\text{rad\/s}\u03c9=602rev\/min\u00d71rev2\u03c0rad\u200b\u00d760seconds1min\u200b=62.97rad\/s<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Rearrange the formula for moment of inertia.<\/h3>\n\n\n\n<p>Now that we know KE=24,400\u2009JKE = 24,400 \\, \\text{J}KE=24,400J and \u03c9=62.97\u2009rad\/s\\omega = 62.97 \\, \\text{rad\/s}\u03c9=62.97rad\/s, we can rearrange the equation to solve for III:I=2KE\u03c92I = \\frac{2KE}{\\omega^2}I=\u03c922KE\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Substitute the known values.<\/h3>\n\n\n\n<p>Substitute the values for kinetic energy and angular velocity:I=2\u00d724,400(62.97)2I = \\frac{2 \\times 24,400}{(62.97)^2}I=(62.97)22\u00d724,400\u200bI=48,8003965.1\u224812.3\u2009kg\u22c5m2I = \\frac{48,800}{3965.1} \\approx 12.3 \\, \\text{kg} \\cdot \\text{m}^2I=3965.148,800\u200b\u224812.3kg\u22c5m2<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The rotational inertia of the wheel is approximately <strong>12.3 kg\u00b7m\u00b2<\/strong>.<\/p>\n\n\n\n<p>This calculation assumes that the wheel&#8217;s mass is uniformly distributed, and that the moment of inertia depends only on the wheel&#8217;s angular velocity and kinetic energy. If the shape or mass distribution of the wheel were more specific (e.g., a solid disk or hoop), the formula for III would change accordingly.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-692.jpeg\" alt=\"\" class=\"wp-image-245689\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the rotational rotational inertia of a wheel that has a kinetic energy of 24,400 J when rotating at 602 rev\/min. The Correct Answer and Explanation is: To calculate the rotational inertia (moment of inertia) of the wheel, we can use the formula for rotational kinetic energy:KE=12I\u03c92KE = \\frac{1}{2} I \\omega^2KE=21\u200bI\u03c92 Where: We are given: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"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":"","ast-disable-related-posts":"","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":[25],"tags":[],"class_list":["post-245688","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245688","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=245688"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245688\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245688"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245688"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245688"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}