{"id":391,"date":"2018-02-01T08:50:00","date_gmt":"2018-02-01T00:50:00","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=391"},"modified":"2018-02-01T08:50:00","modified_gmt":"2018-02-01T00:50:00","slug":"uniform-circular-motion-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/uniform-circular-motion-problems-and-solutions.htm","title":{"rendered":"Uniform circular motion – problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. An object moves in a circle with the constant angular speed of 10 rad\/s. Determine (a) Angular speed<\/a> after 10 seconds (b) Angular displacement<\/a> after 10 seconds. <\/span><\/span><\/p>\n

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

Angular speed <\/span><\/span>(\u03c9) =10 rad\/s<\/span><\/span><\/p>\n

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

(a) Angular speed (\u03c9) after 10 seconds.<\/span><\/span><\/p>\n

(b) Angle <\/span><\/span>(\u03b8) after 10 seconds<\/span><\/span><\/p>\n

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

(a) <\/span><\/span>Angular speed (\u03c9) after 10 seconds<\/span><\/span><\/p>\n

Object in uniform circular motion<\/a> so that angular speed is constant, 10 rad\/s.<\/span><\/span><\/p>\n

(b) Angular displacement <\/span><\/span>(\u03b8)<\/span><\/span><\/p>\n

Constant angular speed 10 radians\/second means the object around 10 radians each second. After 10 seconds, the object around 10 x 10 radians = 100 radians.<\/span><\/span><\/p>\n

<\/p>\n

2. A particle moves in a circle with the constant speed of 10 m\/s. Radius of circle = 1 meter. Determine (a) Particle’s speed after 5 seconds (b) Particle’s displacement<\/a> after 5 seconds (c) Centripetal acceleration<\/a>.<\/span><\/span><\/p>\n

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

Radius of circle (r) = 1 meter<\/span><\/span><\/p>\n

Particle’s speed (v) = 10 m\/s<\/span><\/span><\/p>\n

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

(a) <\/span><\/span> Particle’s speed after 5 seconds<\/u><\/span><\/span><\/p>\n

The motion of object is in the uniform circular motion so that speed is constant, 10 m\/s.<\/span><\/span><\/p>\n

(b)<\/span><\/span> Particle’s displacement after 5 seconds<\/u><\/span><\/span><\/p>\n

10 meters\/second means each 1 second, particle’s displacement = 10 meters. After 5 seconds, particle’s displacement = 5 x 10 meters = 50 meters.<\/span><\/span><\/p>\n

(c)<\/span><\/span> Centripetal acceleration (a<\/u><\/span><\/span>r<\/u><\/span><\/sub>)<\/u><\/span><\/span><\/p>\n

a<\/span><\/span>r<\/span><\/sub> = v<\/span><\/span>2<\/span><\/span><\/sup> \/ r = 10<\/span><\/span>2<\/span><\/span><\/sup> \/ 1 = 100 \/ 1 = 100 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

3. A ball attached to one end of a cord, is revolved in a circle with radius of 2 meters at the constant speed of 60 rpm. Determine (a) the magnitude of the angular speed after 2 seconds (b) the angular displacement after 1 minute.<\/span><\/span><\/p>\n

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

Radius of circle (r) = 2 meters<\/span><\/span><\/p>\n

Angular speed (\u03c9) = 60 rpm = 60 revolutions \/ 1 minute<\/span><\/span><\/p>\n

= 60 revolutions \/ 60 seconds = 1 revolution \/ second = 2\u03c0 <\/span><\/span>radians \/ second<\/span><\/span><\/p>\n

= 2(3.14) radians \/ second= 6.28 radians \/ second<\/span><\/span><\/p>\n

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

(a) <\/span><\/span>Angular speed (\u03c9) after 2 seconds<\/u><\/span><\/span><\/p>\n

The angular speed is constant so after 2 seconds, the angular speed (\u03c9) = 6.28 radians \/ second<\/span><\/span><\/p>\n

(b) <\/span><\/span>Angular displacement (\u03b8) <\/u><\/span><\/span><\/p>\n

The angular speed = 1 revolution\/second means each 1 second, ball experience 1 revolution. After 60 seconds, ball moves 60 revolutions.<\/span><\/span><\/p>\n

The angular speed = 6.28 radians\/second means each 1 second, the ball moves with the angle of 6.28 radians. After 60 seconds, the ball moves 376.8 radians.<\/span><\/span><\/p>\n

<\/p>\n

4. A bike wheel rotates 120 revolutions in 60 seconds. What is the angular speed?<\/span><\/span><\/p>\n

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

(a) revolutions per minute (rpm)<\/span><\/span><\/u><\/p>\n

120 revolutions \/ 60 seconds = 120 revolutions \/ 1 minute = 120 revolutions \/ minute = 120 rpm<\/span><\/span><\/p>\n

(b) <\/span><\/span>degrees per second (<\/u><\/span><\/span>o<\/u><\/span><\/span><\/sup>\/s)<\/u><\/span><\/span><\/p>\n

1 revolution = 360<\/span><\/span>o<\/span><\/span><\/sup>, 120 revolutions = 43200<\/span><\/span>o<\/span><\/span><\/sup><\/p>\n

120 revolutions \/ 60 seconds = (120)(360<\/span><\/span>o<\/span><\/span><\/sup>) \/ 60 seconds = 43200<\/span><\/span>o<\/span><\/span><\/sup> \/ 60 seconds = 720<\/span><\/span>o<\/span><\/span><\/sup>\/second<\/span><\/span><\/p>\n

(c) <\/span><\/span>radians per second (rad\/s)<\/u><\/span><\/span><\/p>\n

1 revolution = 6.28 radians<\/span><\/span><\/p>\n

120 revolutions \/ 60 seconds = (120)(6.28) radians \/ 60 seconds = 753.6 radians \/ 60 seconds = 12.56 radians\/second.<\/span><\/span><\/p>\n

<\/p>\n

[wpdm_package id=’432′]<\/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. An object moves in a circle with the constant angular speed of 10 rad\/s. Determine (a) Angular speed after 10 seconds (b) Angular displacement after 10 seconds. Known : Angular speed (\u03c9) =10 rad\/s Wanted : (a) Angular speed (\u03c9) after 10 seconds. (b) Angle (\u03b8) after 10 seconds Solution : (a) Angular speed … 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":"Uniform circular motion - 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-391","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\/391","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=391"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/391\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=391"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=391"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=391"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}