{"id":248889,"date":"2025-07-08T19:38:18","date_gmt":"2025-07-08T19:38:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=248889"},"modified":"2025-07-08T19:38:20","modified_gmt":"2025-07-08T19:38:20","slug":"a-wheel-of-radius-14-inches-is-rotating-0-5-rad-s","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/08\/a-wheel-of-radius-14-inches-is-rotating-0-5-rad-s\/","title":{"rendered":"A wheel of radius 14 inches is rotating 0.5 rad\/s."},"content":{"rendered":"\n

A wheel of radius 14 inches is rotating 0.5 rad\/s. What is the linear speed
, the angular speed in RPM, and the angular speed in deg\/s?<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To solve this problem, we need to calculate three things:<\/p>\n\n\n\n

    \n
  1. Linear Speed (v):<\/strong>
    The linear speed of a point on the edge of the rotating wheel is given by the formula: v=r\u22c5\u03c9v = r \\cdot \\omegav=r\u22c5\u03c9 where:
    • rrr is the radius of the wheel (14 inches)<\/li>
    • \u03c9\\omega\u03c9 is the angular speed in radians per second (0.5 rad\/s)<\/li><\/ul>Substituting the given values: v=14\u2009inches\u00d70.5\u2009rad\/s=7\u2009inches\u00a0per\u00a0secondv = 14 \\, \\text{inches} \\times 0.5 \\, \\text{rad\/s} = 7 \\, \\text{inches per second}v=14inches\u00d70.5rad\/s=7inches\u00a0per\u00a0second So, the linear speed is 7 inches per second<\/strong>.<\/li>\n\n\n\n
    • Angular Speed in RPM (Revolutions per Minute):<\/strong>
      To convert the angular speed from radians per second (rad\/s) to revolutions per minute (RPM), we can use the conversion factor: 1\u2009rev=2\u03c0\u2009radians1 \\, \\text{rev} = 2\\pi \\, \\text{radians}1rev=2\u03c0radians 1\u2009minute=60\u2009seconds1 \\, \\text{minute} = 60 \\, \\text{seconds}1minute=60seconds So the angular speed in RPM is: RPM=\u03c9\u00d7602\u03c0\\text{RPM} = \\frac{\\omega \\times 60}{2\\pi}RPM=2\u03c0\u03c9\u00d760\u200b Substituting the given value of \u03c9=0.5\u2009rad\/s\\omega = 0.5 \\, \\text{rad\/s}\u03c9=0.5rad\/s: RPM=0.5\u2009rad\/s\u00d7602\u03c0=30\u03c0\u22489.55\u2009RPM\\text{RPM} = \\frac{0.5 \\, \\text{rad\/s} \\times 60}{2\\pi} = \\frac{30}{\\pi} \\approx 9.55 \\, \\text{RPM}RPM=2\u03c00.5rad\/s\u00d760\u200b=\u03c030\u200b\u22489.55RPM So, the angular speed is approximately 9.55 RPM<\/strong>.<\/li>\n\n\n\n
    • Angular Speed in deg\/s:<\/strong>
      To convert the angular speed from radians per second (rad\/s) to degrees per second (deg\/s), we can use the following conversion factor: 1\u2009radian=180\u2218\/\u03c01 \\, \\text{radian} = 180^\\circ\/\\pi1radian=180\u2218\/\u03c0 So, the angular speed in degrees per second is: deg\/s=\u03c9\u00d7180\u2218\u03c0\\text{deg\/s} = \\omega \\times \\frac{180^\\circ}{\\pi}deg\/s=\u03c9\u00d7\u03c0180\u2218\u200b Substituting the given value of \u03c9=0.5\u2009rad\/s\\omega = 0.5 \\, \\text{rad\/s}\u03c9=0.5rad\/s: deg\/s=0.5\u00d7180\u2218\u03c0\u224828.65\u2218\/s\\text{deg\/s} = 0.5 \\times \\frac{180^\\circ}{\\pi} \\approx 28.65^\\circ\/\\text{s}deg\/s=0.5\u00d7\u03c0180\u2218\u200b\u224828.65\u2218\/s So, the angular speed is approximately 28.65 degrees per second<\/strong>.<\/li>\n<\/ol>\n\n\n\n

      Summary:<\/h3>\n\n\n\n
        \n
      • Linear Speed:<\/strong> 7 inches per second<\/li>\n\n\n\n
      • Angular Speed in RPM:<\/strong> 9.55 RPM<\/li>\n\n\n\n
      • Angular Speed in deg\/s:<\/strong> 28.65 degrees per second<\/li>\n<\/ul>\n\n\n\n

        This shows how a rotating wheel’s linear and angular speeds are related through the radius and angular velocity.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        A wheel of radius 14 inches is rotating 0.5 rad\/s. What is the linear speed, the angular speed in RPM, and the angular speed in deg\/s? The Correct Answer and Explanation is: To solve this problem, we need to calculate three things: Summary: This shows how a rotating wheel’s linear and angular speeds are related […]<\/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-248889","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248889","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=248889"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248889\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248889"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248889"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248889"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}