{"id":245692,"date":"2025-07-06T11:11:52","date_gmt":"2025-07-06T11:11:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245692"},"modified":"2025-07-06T11:11:54","modified_gmt":"2025-07-06T11:11:54","slug":"calculate-the-rotational-inertia-of-a-wheel-that-has-a-kinetic-energy-of-25-000-j-when-rotating-at-500-rev-min","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/calculate-the-rotational-inertia-of-a-wheel-that-has-a-kinetic-energy-of-25-000-j-when-rotating-at-500-rev-min\/","title":{"rendered":"Calculate the rotational inertia of a wheel that has a kinetic energy of 25, 000 J when rotating at 500 rev\/min"},"content":{"rendered":"\n<p>Calculate the rotational inertia of a wheel that has a kinetic energy of 25, 000 J when rotating at 500 rev\/min:&#8217;<\/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 (III) of the wheel, we can use the formula for the kinetic energy of rotational motion: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 of the wheel (25,000 J),<\/li>\n\n\n\n<li>III is the moment of inertia (which we need to find),<\/li>\n\n\n\n<li>\u03c9\\omega\u03c9 is the angular velocity in radians per second.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Convert the rotational speed from revolutions per minute (rev\/min) to radians per second.<\/h3>\n\n\n\n<p>The formula to convert from revolutions per minute (rev\/min) to radians per second is:\u03c9=2\u03c0\u00d7rev\/min60\\omega = \\frac{2\\pi \\times \\text{rev\/min}}{60}\u03c9=602\u03c0\u00d7rev\/min\u200b<\/p>\n\n\n\n<p>Given that the rotational speed is 500 rev\/min:\u03c9=2\u03c0\u00d750060=1000\u03c060\u224852.36\u2009rad\/s\\omega = \\frac{2\\pi \\times 500}{60} = \\frac{1000\\pi}{60} \\approx 52.36 \\, \\text{rad\/s}\u03c9=602\u03c0\u00d7500\u200b=601000\u03c0\u200b\u224852.36rad\/s<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Rearrange the kinetic energy equation to solve for the moment of inertia.<\/h3>\n\n\n\n<p>KE=12I\u03c92KE = \\frac{1}{2} I \\omega^2KE=21\u200bI\u03c92I=2KE\u03c92I = \\frac{2KE}{\\omega^2}I=\u03c922KE\u200b<\/p>\n\n\n\n<p>Substitute the values for KE=25,000KE = 25,000KE=25,000 J and \u03c9=52.36\\omega = 52.36\u03c9=52.36 rad\/s:I=2\u00d725,000(52.36)2I = \\frac{2 \\times 25,000}{(52.36)^2}I=(52.36)22\u00d725,000\u200bI=50,0002743.6\u224818.22\u2009kg\u22c5m2I = \\frac{50,000}{2743.6} \\approx 18.22 \\, \\text{kg} \\cdot \\text{m}^2I=2743.650,000\u200b\u224818.22kg\u22c5m2<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The rotational inertia (III) of the wheel is approximately <strong>18.22 kg\u00b7m\u00b2<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The key to solving this problem lies in the relationship between kinetic energy and rotational motion. The formula KE=12I\u03c92KE = \\frac{1}{2} I \\omega^2KE=21\u200bI\u03c92 directly connects the kinetic energy to the moment of inertia and angular velocity. By first converting the rotational speed into radians per second, we can then isolate III in the equation and solve for it. The result gives the moment of inertia, which is a measure of the wheel&#8217;s resistance to changes in rotational motion, depending on both its mass and the distribution of that mass relative to the axis of rotation.<\/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-banner5-693.jpeg\" alt=\"\" class=\"wp-image-245693\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the rotational inertia of a wheel that has a kinetic energy of 25, 000 J when rotating at 500 rev\/min:&#8217; The Correct Answer and Explanation is: To calculate the rotational inertia (III) of the wheel, we can use the formula for the kinetic energy of rotational motion:KE=12I\u03c92KE = \\frac{1}{2} I \\omega^2KE=21\u200bI\u03c92 Where: Step 1: [&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-245692","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245692","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=245692"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245692\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245692"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245692"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245692"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}