{"id":407,"date":"2018-02-02T00:53:59","date_gmt":"2018-02-01T16:53:59","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=407"},"modified":"2018-02-02T00:53:59","modified_gmt":"2018-02-01T16:53:59","slug":"angular-velocity-and-linear-velocity-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/angular-velocity-and-linear-velocity-problems-and-solutions.htm","title":{"rendered":"Angular velocity and linear velocity \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. <\/span><\/span>A ball at the end of a string is revolving uniformly in a horizontal circle of radius 2 meters at constant angular speed 10 rad\/s. Determine the magnitude of the linear velocity of a point located :<\/span><\/span><\/p>\n

(a) 0.5 meters from the center <\/span><\/span><\/p>\n

(b) 1 meter from the center<\/span><\/span><\/p>\n

(c) 2 meters from the center<\/span><\/span><\/p>\n

Known :<\/span><\/span><\/u><\/p>\n

Radius <\/span><\/span>(r) = <\/span><\/span>0.5 <\/span><\/span>meter<\/span><\/span>s, 1 meter, 3 meters<\/span><\/span><\/p>\n

The angular speed <\/span><\/span>= 10 radian<\/span><\/span>s<\/span><\/span>\/se<\/span><\/span>cond<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The linear velocity<\/a><\/span><\/span><\/p>\n

Solution :<\/span><\/span><\/u><\/p>\n

v = r <\/span><\/span>\u03c9<\/span><\/span><\/p>\n

v = <\/span><\/span>the linear velocity<\/span><\/span>, r = <\/span><\/span>radius<\/span><\/span>, \u03c9 = <\/span><\/span>the angular velocity<\/span><\/span><\/i><\/p>\n

(a) <\/span><\/span>The linear velocity (v) of a point located at r = 0.5 meters<\/u><\/span><\/span><\/p>\n

v = r <\/span><\/span>\u03c9 <\/span><\/span>=<\/span><\/span> (0.5 meter<\/span><\/span>s<\/span><\/span>)(10 rad\/s) = 5 meter<\/span><\/span>s<\/span><\/span>\/se<\/span><\/span>cond<\/span><\/span><\/p>\n

(b) <\/span><\/span>The linear velocity <\/u><\/span><\/span>(v) <\/u><\/span><\/span>of a point located at <\/u><\/span><\/span>r = 1 meter<\/u><\/span><\/span><\/p>\n

v = r <\/span><\/span>\u03c9 <\/span><\/span>=<\/span><\/span> (1 meter)(10 rad\/s) = 10 meter<\/span><\/span>s<\/span><\/span>\/se<\/span><\/span>cond<\/span><\/span><\/p>\n

(c) <\/span><\/span>The linear velocity <\/u><\/span><\/span>(v) <\/u><\/span><\/span>of a point located at <\/u><\/span><\/span>r = 2 meter<\/u><\/span><\/span>s<\/u><\/span><\/span><\/p>\n

v = r <\/span><\/span>\u03c9 <\/span><\/span>=<\/span><\/span> (2 meter<\/span><\/span>s<\/span><\/span>)(10 rad\/s) = 20 meter<\/span><\/span>s<\/span><\/span>\/se<\/span><\/span>cond<\/span><\/span><\/p>\n

<\/p>\n

2. <\/span><\/span>The blades in a blender rotate at a rate of 5000 rpm. Determine the magnitude of the linear velocity :<\/span><\/span><\/p>\n

(a) <\/span><\/span>a point located 5 cm from the center<\/span><\/span><\/p>\n

(b) <\/span><\/span>a point located 10 cm from the center<\/span><\/span><\/p>\n

Known :<\/span><\/span><\/u><\/p>\n

Radius <\/span><\/span>(r) = <\/span><\/span>5 cm and <\/span><\/span>10 cm<\/span><\/span><\/p>\n

The angular speed <\/span><\/span>(<\/span><\/span>\u03c9) = 5000 <\/span><\/span>revolutions<\/span><\/span> \/ 60 s<\/span><\/span>econds<\/span><\/span> = 83.3 <\/span><\/span>revolutions<\/span><\/span> \/ se<\/span><\/span>cond<\/span><\/span> = (83.3)(6.28 radian) \/ se<\/span><\/span>cond<\/span><\/span> = 523.3 radian<\/span><\/span>s<\/span><\/span> \/ se<\/span><\/span>cond<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The magnitude of the linear velocity<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

(a) <\/span><\/span>The magnitude of the linear velocity of a point located 0.05 m from the center<\/span><\/span><\/p>\n

v = r <\/span><\/span>\u03c9 <\/span><\/span>= <\/span><\/span>(0.05 m)(<\/span><\/span>523.3 <\/span><\/span>rad\/s) = 26 m\/s<\/span><\/span><\/p>\n

(b) <\/span><\/span>The magnitude of the linear velocity of a point located 0,1 m from the center<\/u><\/span><\/span><\/p>\n

v = r <\/span><\/span>\u03c9 <\/span><\/span>= <\/span><\/span>(0.1 m)(<\/span><\/span>523.3 <\/span><\/span>rad\/s) = 52 m\/s<\/span><\/span><\/p>\n

3. <\/span><\/span>A point on the edge of a wheel <\/span><\/span>30 cm <\/span><\/span>in radius, <\/span><\/span>around a circle at constant speed <\/span><\/span>10 meters\/second.<\/span><\/span><\/p>\n

What is the magnitude of the angular velocity?<\/span><\/span><\/p>\n

Known :<\/span><\/span><\/u><\/p>\n

Radius (<\/span><\/span>r) = 30 cm = 0.3 meter<\/span><\/span>s<\/span><\/span><\/p>\n

The linear velocity <\/span><\/span>(v) = 10 meter<\/span><\/span>s<\/span><\/span>\/se<\/span><\/span>cond<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> the angular velocity<\/span><\/span><\/p>\n

Solution :<\/span><\/span><\/u><\/p>\n

\u03c9 = v \/ r = 10 \/ 0.3 = 33 radian<\/span><\/span>s<\/span><\/span>\/se<\/span><\/span>cond<\/span><\/span><\/p>\n

<\/p>\n

4. <\/span><\/span>A car with tires 50 cm in diameter <\/span><\/span>trave<\/span><\/span>l<\/span><\/span>s 10 meters in <\/span><\/span>1<\/span><\/span> second. <\/span><\/span>What is the angular speed ?<\/span><\/span><\/p>\n

Known :<\/span><\/span><\/u><\/p>\n

Radius <\/span><\/span>(r) = 0.25 meter<\/span><\/span><\/p>\n

The linear speed of a <\/span><\/span>point on the edge of tires <\/span><\/span>(v) = 10 meter<\/span><\/span>s<\/span><\/span>\/se<\/span><\/span>cond<\/span><\/span><\/p>\n

Wanted:<\/u><\/span><\/span> The angular speed<\/span><\/span><\/p>\n

Solution :<\/span><\/span><\/u><\/p>\n

\u03c9 = v \/ r = 10 \/ 0.25 = 40 radian<\/span><\/span>s<\/span><\/span>\/se<\/span><\/span>cond<\/span><\/span><\/p>\n

5. <\/span><\/span>The angular speed of wheel 20 cm in radians is 120 rpm. What is the distance<\/a> if the car travels in 10 seconds. <\/span><\/span><\/p>\n

Known :<\/span><\/span><\/u><\/p>\n

Radius <\/span><\/span>(r) = 20 cm = 0.2 meter<\/span><\/span>s<\/span><\/span><\/p>\n

The angular speed <\/span><\/span>= 120 <\/span><\/span>rev <\/span><\/span>\/ 60 se<\/span><\/span>conds<\/span><\/span> = 2 <\/span><\/span>rev<\/span><\/span> \/ se<\/span><\/span>cond <\/span><\/span>= (2)(6.28) radian<\/span><\/span>s<\/span><\/span> \/ se<\/span><\/span>cond<\/span><\/span> = 12.56 radian<\/span><\/span>s<\/span><\/span> \/ se<\/span><\/span>cond<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> distance<\/span><\/span><\/p>\n

Solution :<\/span><\/span><\/u><\/p>\n

Velocity<\/a> of the edge of wheel :<\/span><\/span><\/p>\n

v = r <\/span><\/span>\u03c9 = (0.2 meter<\/span><\/span>s<\/span><\/span>)(12.56 radian<\/span><\/span>s<\/span><\/span>\/se<\/span><\/span>cond<\/span><\/span>) = 2.5 meter<\/span><\/span>s<\/span><\/span>\/se<\/span><\/span>cond<\/span><\/span><\/p>\n

2.5 meter<\/span><\/span>s<\/span><\/span> \/ se<\/span><\/span>cond means a point on the edge of wheel travels <\/span><\/span>2.5 meter<\/span><\/span>s<\/span><\/span> each 1 second<\/span><\/span>. <\/span><\/span>After <\/span><\/span>10 se<\/span><\/span>conds<\/span><\/span>, <\/span><\/span>the point travels <\/span><\/span>25 meter<\/span><\/span>s<\/span><\/span>. <\/span><\/span><\/p>\n

So the distance is <\/span><\/span>25 meter<\/span><\/span>s<\/span><\/span>. <\/span><\/span><\/p>\n

<\/p>\n

[wpdm_package id=’427′]<\/p>\n

[wpdm_package id=’439′]<\/p>\n

    \n
  1. Converting angle units sample problems with solutions<\/a><\/li>\n
  2. Angular displacement and linear displacement sample problems and solutions<\/a><\/li>\n
  3. Angular velocity and linear velocity sample problems with solutions<\/a><\/li>\n
  4. Angular acceleration and linear acceleration sample problems with solutions<\/a><\/li>\n
  5. Uniform circular motions sample problems with solutions<\/a><\/li>\n
  6. Centripetal acceleration sample problems with solutions<\/a><\/li>\n
  7. Nonuniform circular motions sample problems with solutions<\/a><\/li>\n<\/ol>\n

    <\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

    1. A ball at the end of a string is revolving uniformly in a horizontal circle of radius 2 meters at constant angular speed 10 rad\/s. Determine the magnitude of the linear velocity of a point located : (a) 0.5 meters from the center (b) 1 meter from the center (c) 2 meters from the … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Angular velocity and linear velocity \u2013 problems and solutions","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-407","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/407","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=407"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/407\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=407"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=407"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=407"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}