{"id":414,"date":"2018-02-05T11:13:16","date_gmt":"2018-02-05T03:13:16","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=414"},"modified":"2018-02-05T11:13:16","modified_gmt":"2018-02-05T03:13:16","slug":"centripetal-acceleration-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/centripetal-acceleration-problems-and-solutions.htm","title":{"rendered":"Centripetal acceleration \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. <\/span><\/span>A ball, attached to the end of a horizontal cord, is revolved in a circle of radius 20 cm. The ball around 360<\/span><\/span>o<\/span><\/span><\/sup> each second. Determine the magnitude of the centripetal acceleration<\/a>!<\/span><\/span><\/p>\n

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

Angular speed (\u03c9<\/span><\/span>) = 360<\/span><\/span>o<\/span><\/span><\/sup>\/second = 1 revolution\/second = 6.28 radians\/second<\/span><\/span><\/p>\n

Radius (r) = 20 cm = 0.<\/span><\/span>2 m<\/span><\/span><\/p>\n

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

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

a<\/b><\/span><\/span>r<\/b><\/span><\/sub> = v<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup> \/ r<\/b><\/span><\/span> —> v = r <\/span><\/span>\u03c9<\/span><\/span><\/p>\n

a<\/span><\/span>r<\/span><\/sub> = (r <\/span><\/span>\u03c9)<\/span><\/span>2 <\/span><\/span><\/sup>\/ r = r<\/span><\/span>2 <\/span><\/span><\/sup>\u03c9<\/span><\/span>2<\/span><\/span><\/sup> \/ r<\/span><\/span><\/p>\n

a<\/b><\/span><\/span>r<\/b><\/span><\/sub> = r <\/b><\/span><\/span>\u03c9<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup> <\/b><\/p>\n

a<\/i><\/span><\/span>s<\/i><\/span><\/span><\/sub> = centripetal acceleration, v = linear velocity, r = radius, <\/i><\/span><\/span>\u03c9 <\/i><\/span><\/span>= angular velocity<\/a><\/i><\/span><\/span><\/p>\n

The magnitude of the centripetal acceleration <\/u><\/span><\/span>:<\/span><\/span><\/p>\n

ar<\/sub><\/span><\/span> = r <\/span><\/span>\u03c9<\/span><\/span>2 <\/span><\/span><\/sup>a<\/span><\/span>r<\/span><\/sub> = (0,2 m)(<\/span><\/span>6.28 rad\/s) <\/span><\/span><\/p>\n

a<\/span><\/span>r<\/span><\/sub> = 1.256 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

<\/p>\n

2. A wheel 30 cm in radius rotate at a rate of 180 rpm. Determine the centripetal acceleration of a point on the edge of wheel! <\/span><\/span><\/p>\n

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

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

Angular speed (<\/span><\/span>\u03c9<\/span><\/span>) = 180 revolutions \/ 60 seconds = 3 revolutions \/ second = (3)(6.28 radians) \/ second = 18.84 radians\/second<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> centripetal acceleration (<\/span><\/span>a<\/span><\/span>r<\/span><\/sub>) of r = 0.3 m<\/span><\/span><\/p>\n

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

The magnitude of the centripetal acceleration :<\/span><\/span><\/p>\n

a<\/span><\/span>r<\/sub> <\/span><\/span>= r <\/span><\/span>\u03c9<\/span><\/span>2 <\/span><\/span><\/sup><\/p>\n

a<\/span><\/span>r <\/span><\/sub>= (0.3 m)(18.84 <\/span><\/span>rad\/s) <\/span><\/span><\/p>\n

a<\/span><\/span>r<\/span><\/sub> = 5.65 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

3. A race car moving on a circular track of radius 50 meters. If car’s speed is 72 km\/h, determine the magnitude of the centripetal acceleration!<\/span><\/span><\/p>\n

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

Radius (r) = 50 meters<\/span><\/span><\/p>\n

Speed (v) = 72 km\/h = (72)(1000 meters) \/ 3600 seconds = 20 meters\/second<\/span><\/span><\/p>\n

Wanted <\/u><\/span><\/span>: the magnitude of the centripetal acceleration (a<\/span><\/span>r<\/span><\/sub>) <\/span><\/span><\/p>\n

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

ar<\/sub><\/span><\/span> = v<\/span><\/span>2<\/span><\/span><\/sup> \/ r = 20<\/span><\/span>2<\/span><\/span><\/sup> \/ 50 = 400 \/ 50 = 8 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

<\/p>\n

4. A car has the maximum centripetal acceleration 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>, so the car can turn without skidding out of a curved path. If the car is moving at a constant 108 km\/h, what is the radius of unbanked curve ?<\/span><\/span><\/p>\n

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

Centripetal acceleration <\/span><\/span>(a<\/span><\/span>r<\/span><\/sub>) = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Car’s speed <\/span><\/span>(v) = 108 km\/<\/span><\/span>h <\/span><\/span>= (108)(1000) \/ 3600 = 30 meter<\/span><\/span>s<\/span><\/span>\/se<\/span><\/span>c<\/span><\/span>on<\/span><\/span>d<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> radius <\/span><\/span>(r)<\/span><\/span><\/p>\n

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

r<\/span><\/span> = v<\/span><\/span>2<\/span><\/span><\/sup> \/ a<\/span><\/span>r<\/span><\/sub><\/p>\n

r = 30<\/span><\/span>2<\/span><\/span><\/sup> \/ 10 = 900 \/ 10 = 90 meter<\/span><\/span>s<\/span><\/span><\/p>\n

<\/p>\n

[wpdm_package id=’433′]<\/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, attached to the end of a horizontal cord, is revolved in a circle of radius 20 cm. The ball around 360o each second. Determine the magnitude of the centripetal acceleration! Known : Angular speed (\u03c9) = 360o\/second = 1 revolution\/second = 6.28 radians\/second Radius (r) = 20 cm = 0.2 m Wanted … 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":"Centripetal acceleration \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-414","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\/414","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=414"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/414\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=414"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=414"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=414"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}