{"id":411,"date":"2018-02-05T08:56:30","date_gmt":"2018-02-05T00:56:30","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=411"},"modified":"2018-02-05T08:56:30","modified_gmt":"2018-02-05T00:56:30","slug":"angular-acceleration-and-linear-acceleration-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/angular-acceleration-and-linear-acceleration-problems-and-solutions.htm","title":{"rendered":"Angular acceleration and linear acceleration \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. A wheel 3<\/span><\/span>0 cm in radius rotates at constant <\/span><\/span>5 rad\/s<\/span><\/span>2<\/span><\/span><\/sup>. What is the magnitude of the linear acceleration<\/a> of a point located at (a) 10 cm from the center (b) 20 cm from the center (c) on the edge of the wheel?<\/span><\/span><\/p>\n

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

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

Angular acceleration (<\/span><\/span>\u03b1<\/span><\/span>) = 5 rad\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Wanted :<\/u><\/span><\/span> linear acceleration <\/span><\/span> (a) r = 0.1 m (b) r = 0.2 m (c) r = 0.3 m<\/span><\/span><\/p>\n

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

Relation between linear acceleration (a) and angular acceleration :<\/span><\/span><\/p>\n

a = r <\/span><\/span>\u03b1<\/span><\/span><\/p>\n

(a) <\/span><\/span>linear acceleration, r = 0.1 m<\/u><\/span><\/span><\/p>\n

a = (0.1 m)(5 rad\/s<\/span><\/span>2<\/span><\/span><\/sup>) = 0.5 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

(b)<\/span><\/span> linear acceleration, r = 0.2 m<\/u><\/span><\/span><\/p>\n

a<\/span><\/span> = (0.2 m)(5 rad\/s<\/span><\/span>2<\/span><\/span><\/sup>) = 1 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

(c) <\/span><\/span>linear acceleration, r = 0.3 m<\/u><\/span><\/span><\/p>\n

a<\/span><\/span> = (0.3 m)(5 rad\/s<\/span><\/span>2<\/span><\/span><\/sup>) = 1.5 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

<\/p>\n

2. A pulley 50 cm in radius. If the linear acceleration of a point located on the edge of the pulley is 2 m\/s<\/span><\/span>2<\/span><\/span><\/sup>, determine the angular acceleration of the pulley! <\/span><\/span><\/p>\n

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

Radius (r) = 50 cm = 0,5 m<\/span><\/span><\/p>\n

linear acceleration (a) = 2 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

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

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

\u03b1 <\/span><\/span>= a<\/span><\/span> \/ r =<\/span><\/span> 2 \/ 0.5 = 4 rad\/s<\/span><\/span>2 <\/span><\/span><\/sup><\/p>\n

3. The blades in a blender 20 cm in radius, initially at rest. After 2 seconds, the blades rotates 10 rad\/s. Determine the magnitude of linear acceleration (a) a point located at 10 cm from the center (b) a point located at the edge of the blades.<\/span><\/span><\/p>\n

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

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

The initial angular velocity (<\/span><\/span>\u03c9<\/span><\/span>o<\/span><\/sub>) <\/span><\/span>= 0<\/span><\/span><\/p>\n

The final angular velocity (<\/span><\/span>\u03c9<\/span><\/span>t<\/span>) <\/span><\/sub>= 10 radians\/second<\/span><\/span><\/p>\n

Time interval (t) = 2 seconds<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> the linear accelera<\/span><\/span>tion of a point located at (a) r = 0.1 m (b) r = 0.2 m<\/span><\/span><\/p>\n

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

\u03c9<\/span><\/span>t<\/sub> <\/span><\/span>= <\/span><\/span>\u03c9<\/span><\/span>o <\/span><\/sub>+ <\/span><\/span>\u03b1 t<\/span><\/span><\/p>\n

10 = 0 + \u03b1 (2)<\/span><\/span><\/p>\n

10 = 2 \u03b1 <\/span><\/span><\/p>\n

\u03b1 = 10 \/ 2<\/span><\/span><\/p>\n

\u00a0\u03b1 = 5 rad\/s<\/span><\/span><\/p>\n

(a) <\/span><\/span>linear acceleration of r = 0.1 m<\/u><\/span><\/span><\/p>\n

a = r <\/span><\/span>\u03b1 <\/span><\/span>= (0.1 m)(5 rad\/s<\/span><\/span>2<\/span><\/span><\/sup>) = 0.5 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

(b)<\/span><\/span> linear acceleration of r = 0.2 m<\/u><\/span><\/span><\/p>\n

a<\/span><\/span> = r <\/span><\/span>\u03b1 <\/span><\/span>= (0.2 m)(5 rad\/s<\/span><\/span>2<\/span><\/span><\/sup>) = 1 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

<\/p>\n

4. A wheel 20 cm in radius is accelerated for 2 seconds from 20 rad\/s to rest. Determine the magnitude of linear acceleration (a) a point located at 10 cm from the center (b) a point located at 10 cm from the center.<\/span><\/span><\/p>\n

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

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

The initial angular speed (<\/span><\/span>\u03c9<\/span><\/span>o<\/span><\/sub>) <\/span><\/span>= 20 rad\/s<\/span><\/span><\/p>\n

The final angular speed (<\/span><\/span>\u03c9<\/span><\/span>t<\/span><\/sub>) = 0<\/span><\/span><\/p>\n

Time interval (t) = 2 seconds<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The linear acceleration (a) r = 0.1 m (b) r = 0.2 m<\/span><\/span><\/p>\n

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

\u03c9<\/span><\/span>t <\/span><\/sub>= <\/span><\/span>\u03c9<\/span><\/span>o <\/span><\/sub>+ <\/span><\/span>\u03b1 t<\/span><\/span><\/p>\n

0 = 20 + \u03b1 (2)<\/span><\/span><\/p>\n

-20 = 2 \u03b1 <\/span><\/span><\/p>\n

\u03b1 = -20 \/ 2<\/span><\/span><\/p>\n

\u00a0\u03b1 = -10 rad\/s<\/span><\/span><\/p>\n

Negative sign mean the angular speed<\/a> is decrease.<\/span><\/span><\/p>\n

(a) <\/span><\/span>linear acceleration of r = 0.1 m<\/u><\/span><\/span><\/p>\n

\u00a0a<\/span><\/span> = r <\/span><\/span> \u03b1 <\/span><\/span>= (0.1 m)(-10 rad\/s<\/span><\/span>2<\/span><\/span><\/sup>) = -1 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

(b) <\/span><\/span>linear acceleration of r = 0.2 m<\/u><\/span><\/span><\/p>\n

a = r <\/span><\/span>\u03b1 <\/span><\/span>= (0.2 m)(-10 rad\/s<\/span><\/span>2<\/span><\/span><\/sup>) = -2 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

<\/p>\n

[wpdm_package id=’429′]<\/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 wheel 30 cm in radius rotates at constant 5 rad\/s2. What is the magnitude of the linear acceleration of a point located at (a) 10 cm from the center (b) 20 cm from the center (c) on the edge of the wheel? Known : Radius (r) = 30 cm = 0.3 m Angular … 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 acceleration and linear 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-411","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\/411","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=411"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/411\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=411"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=411"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=411"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}