{"id":1281,"date":"2018-02-28T17:28:36","date_gmt":"2018-02-28T09:28:36","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1281"},"modified":"2018-02-28T17:28:36","modified_gmt":"2018-02-28T09:28:36","slug":"rotational-dynamics-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/rotational-dynamics-problems-and-solutions.htm","title":{"rendered":"Rotational dynamics \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. A force F applied to a cord wrapped around a cylinder pulley. The torque<\/a> is <\/span><\/span>2 <\/span><\/span>N m and the moment of inertia<\/a> is <\/span><\/span>1 kg <\/span><\/span>m<\/span><\/span>2<\/span><\/span><\/sup>,<\/span><\/span> what is the angular acceleration<\/a> of the cylinder. <\/span><\/span><\/p>\n

\"RotationalKnown :<\/u><\/span><\/span><\/p>\n

Torque (<\/span><\/span>\u03c4<\/span><\/span>) = 2 N m<\/span><\/span><\/p>\n

The moment of inertia (I) = <\/span><\/span>1 kg m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

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

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

\u03a3\u03c4<\/span><\/span> = I <\/span><\/span>\u03b1<\/span><\/span><\/p>\n

\u03a3\u03c4 <\/i><\/span><\/span>= net torque, I = moment of inertia, <\/i><\/span><\/span>\u03b1 = angular acceleration<\/i><\/span><\/span><\/p>\n

Angular acceleration of cylinder :<\/span><\/span><\/p>\n

\u03b1 = \u03a3\u03c4 \/ I = 2 \/ 1 = 2 rad\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

<\/p>\n

2. A force F applied to a cord wrapped around a cylinder pulley. The magnitude of the force is 10 <\/span><\/span>N, the radius of the cylinder is 0.2 m and the moment of inertia is <\/span><\/span>1 kg <\/span><\/span>m<\/span><\/span>2, W<\/span><\/span>hat is the angular acceleration of the cylinder?<\/span><\/span><\/p>\n

\"RotationalKnown :<\/u><\/span><\/span><\/p>\n

Force (F) = 10 N<\/span><\/span><\/p>\n

Radius of cylinder (R) = 0.2 m<\/span><\/span><\/p>\n

The moment of inertia (I) = <\/span><\/span>1 kg m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Wanted:<\/u><\/span><\/span> The angular acceleration of the cylinder.<\/span><\/span><\/p>\n

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

\u03c4<\/span><\/span> = F R <\/span><\/span><\/p>\n

\u03c4<\/i><\/span><\/span> = torque, F = force, R = radius of cylinder<\/i><\/span><\/span><\/p>\n

Torque :<\/span><\/span><\/p>\n

\u03c4 <\/span><\/span>= F R = (1<\/span><\/span>0 N)(0.2 m) = 2 N m<\/span><\/span><\/p>\n

\u03a3\u03c4<\/span><\/span> = I <\/span><\/span>\u03b1<\/span><\/span><\/p>\n

\u03a3\u03c4 <\/i><\/span><\/span>= net torque, I = moment of inertia, <\/i><\/span><\/span>\u03b1 = angular acceleration<\/i><\/span><\/span><\/p>\n

Angular acceleration of cylinder :<\/span><\/span><\/p>\n

\u03b1 = \u03a3\u03c4 \/ I = <\/span><\/span>2 \/ 1 = 2 rad\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

<\/p>\n

3. A force F applied to a cord wrapped around a cylinder pulley. The magnitude of force is 10 <\/span><\/span>N, the radius of cylinder is 0.2 m and the mass of cylinder is 20 <\/span><\/span>kg <\/span><\/span>m<\/span><\/span>2,<\/span><\/span><\/sup>. W<\/span><\/span>hat is the angular acceleration of the cylinder.<\/span><\/span><\/p>\n

\"RotationalKnown :<\/u><\/span><\/span><\/p>\n

Force (F) = 10 N<\/span><\/span><\/p>\n

Radius of cylinder (R) = 0.2 m<\/span><\/span><\/p>\n

Mass of cylinder (M) = 2<\/span><\/span>0 <\/span><\/span>kg<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Angular acceleration of cylinder<\/span><\/span><\/p>\n

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

\u03c4 <\/span><\/span>= F R = (1<\/span><\/span>0 N)(0.2 m) = 2 N m<\/span><\/span><\/p>\n

Moment of inertia :<\/span><\/span><\/p>\n

I = 1\u20442 M R<\/span><\/span>2 <\/span><\/span><\/sup>= 1\u20442 (20)(0.2)<\/span><\/span>2 <\/span><\/span><\/sup>= 1\u20442 (20)(0.04) = 0.4 kg m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Angular acceleration of cylinder :<\/span><\/span><\/p>\n

\u03b1 = \u03a3\u03c4 \/ I = <\/span><\/span>2 \/ <\/span><\/span>0.4 <\/span><\/span>= 5 rad\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

<\/p>\n

4. A 1-kg block hanging from a cord wrapped around a cylinder pulley. The moment of inertia of pulley is 1 kg <\/span><\/span>m<\/span><\/span>2<\/span><\/span><\/sup> and the radius of pulley is 0.2 m. What is the angular acceleration of the pulley. Acceleration due to gravity<\/a> is 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>. <\/span><\/span><\/p>\n

\"RotationalKnown :<\/u><\/span><\/span><\/p>\n

Moment of inertia of pulley (I) = 1 kg m<\/span><\/span>2 <\/span><\/span><\/sup><\/p>\n

Mass<\/a> of block (m) = 1 kg<\/span><\/span><\/p>\n

Acceleration due to gravity (g) = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Weight<\/a> (w) = m g = (1 kg)(10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>) = 10 kg m\/s<\/span><\/span>2<\/span><\/span><\/sup> = 10 N<\/span><\/span><\/p>\n

Radius of pulley (R) = 0.2 m<\/span><\/span><\/p>\n

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

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

Torque :<\/span><\/span><\/p>\n

\u03c4 <\/span><\/span>= F R = w R = (1<\/span><\/span>0 N)(0.2 m) = 2 N m<\/span><\/span><\/p>\n

Moment of inertia :<\/span><\/span><\/p>\n

I = 1 kg m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Angular acceleration :<\/span><\/span><\/p>\n

\u03b1 = \u03a3\u03c4 \/ I = <\/span><\/span>2 \/ 1<\/span><\/span> = 2 rad\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

<\/p>\n

5. A 1-kg block hanging from a cord wrapped around a cylinder pulley. The mass of pulley is 20 kg <\/span><\/span>and the radius of pulley is 0,2 m. What is the angular acceleration of the pulley and the free fall<\/a> acceleration of the block. Acceleration due to gravity is 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>.<\/span><\/span><\/p>\n

\"RotationalKnown :<\/u><\/span><\/span><\/p>\n

Mass of pulley (M) = 2<\/span><\/span>0 <\/span><\/span>kg<\/span><\/span><\/p>\n

Radius of pulley (R) = 0,2 m<\/span><\/span><\/p>\n

Mass of block (m) = 1 kg<\/span><\/span><\/p>\n

Acceleration due to gravity (g) = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Weight (w) = m g = (1 kg)(10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>) = 10 kg m\/s<\/span><\/span>2<\/span><\/span><\/sup> = 10 N<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> the angular acceleration of the pulley and the free fall acceleration of the block.<\/span><\/span><\/p>\n

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

The torque :<\/span><\/span><\/p>\n

\u03c4 <\/span><\/span>= F R = w R = (1<\/span><\/span>0 N)(0.2 m) = 2 N m<\/span><\/span><\/p>\n

The moment of inertia of cylinder pulley :<\/span><\/span><\/p>\n

I = 1\u20442 M R<\/span><\/span>2 <\/span><\/span><\/sup>= 1\u20442 (20)(0.2)<\/span><\/span>2 <\/span><\/span><\/sup>= (10)(0.04) = 0.4 kg m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

The angular acceleration of the pulley :<\/span><\/span><\/p>\n

\u03b1 = \u03a3\u03c4 \/ I = 2<\/span><\/span> \/ <\/span><\/span>0.4 <\/span><\/span>= 5 <\/span><\/span>rad\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

The free fall acceleration of the block :<\/span><\/span><\/p>\n

a = R \u03b1 = (0.2)(5) = 1 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

1. A force F applied to a cord wrapped around a cylinder pulley. The torque is 2 N m and the moment of inertia is 1 kg m2, what is the angular acceleration of the cylinder. Known : Torque (\u03c4) = 2 N m The moment of inertia (I) = 1 kg m2 Wanted: 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":"Rotational dynamics \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-1281","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\/1281","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=1281"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1281\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1281"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1281"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}