{"id":1292,"date":"2018-03-01T13:18:00","date_gmt":"2018-03-01T05:18:00","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1292"},"modified":"2018-03-01T13:18:00","modified_gmt":"2018-03-01T05:18:00","slug":"angular-momentum-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/angular-momentum-problems-and-solutions.htm","title":{"rendered":"Angular momentum \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. <\/span><\/span>An object with the moment of inertia<\/a> of <\/span><\/span>2 kg <\/span><\/span>m<\/span><\/span>2<\/span><\/span><\/sup> rotates at <\/span><\/span>1 rad\/s. <\/span><\/span>What is the angular momentum<\/a> of the object? <\/span><\/span><\/p>\n

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

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

Angular speed<\/span><\/span><\/a> (<\/span><\/span>\u03c9<\/span><\/span>)<\/span><\/span> = 1 rad\/s<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Angular momentum<\/span><\/span> (L)<\/span><\/span><\/p>\n

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

Formula of angular momentum :<\/span><\/span><\/p>\n

L <\/span><\/span>= I <\/span><\/span>\u03c9<\/span><\/span><\/p>\n

L = <\/i><\/span><\/span>angular momentum <\/i><\/span><\/span>(kg m<\/i><\/span><\/span>2<\/i><\/span><\/span><\/sup>\/s), I = <\/i><\/span><\/span>moment of inertia <\/i><\/span><\/span>(kg m<\/i><\/span><\/span>2<\/i><\/span><\/span><\/sup>), <\/i><\/span><\/span>\u03c9 <\/i><\/span><\/span>= <\/i><\/span><\/span>angular speed <\/i><\/span><\/span>(rad\/s)<\/i><\/span><\/span><\/p>\n

The angular momentum :<\/span><\/span><\/p>\n

L <\/span><\/span>= I <\/span><\/span>\u03c9 = (2)(1) <\/span><\/span>= 2 kg m<\/span><\/span>2<\/span><\/span><\/sup>\/s <\/span><\/span><\/p>\n

<\/p>\n

2. <\/span><\/span>A 2-<\/span><\/span>kg <\/span><\/span>cylinder pulley with radius of <\/span><\/span>0.1 m <\/span><\/span>rotates at a constant angular speed of 2 rad\/s. What is the angular momentum of the pulley ?<\/span><\/span><\/p>\n

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

Mass <\/span><\/span>of pulley <\/span><\/span>(m) <\/span><\/span>= 2 k<\/span><\/span>g<\/span><\/span><\/p>\n

Radius of pulley <\/span><\/span>(r) = 0.1 m<\/span><\/span><\/p>\n

Angular speed <\/span><\/span>(\u03c9) = 2 r<\/span><\/span>ad\/s<\/span><\/span><\/p>\n

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

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

Formula of moment of inertia for solid cylinder :<\/span><\/span><\/p>\n

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

I = <\/i><\/span><\/span>moment of inertia <\/i><\/span><\/span>(kg m<\/i><\/span><\/span>2<\/i><\/span><\/span><\/sup>), m = mass<\/a> (kg), <\/i><\/span><\/span>r = <\/i><\/span><\/span>radius <\/i><\/span><\/span>(m)<\/i><\/span><\/span><\/p>\n

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

I = 1\/2 (2)(0.1)<\/span><\/span>2<\/span><\/span><\/sup> = (1)(0.01) = 0.01 kg m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

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

L <\/span><\/span>= I <\/span><\/span>\u03c9 = (<\/span><\/span>0.01<\/span><\/span>)(<\/span><\/span>2<\/span><\/span>) <\/span><\/span>= 0.02 kg m<\/span><\/span>2<\/span><\/span><\/sup>\/s <\/span><\/span><\/p>\n

<\/p>\n

3. <\/span><\/span>A 2-kg uniform sphere with radius of <\/span><\/span>0.2 m <\/span><\/span>rotates at <\/span><\/span>4 rad\/s. <\/span><\/span>What is the angular momentum of the ball.<\/span><\/span><\/p>\n

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

Mass <\/span><\/span>of ball <\/span><\/span>(m) <\/span><\/span>= 2 <\/span><\/span>kg<\/span><\/span><\/p>\n

Radius of ball <\/span><\/span>(r) = 0.2 m<\/span><\/span><\/p>\n

Angular speed <\/span><\/span>(\u03c9) = 4 ra<\/span><\/span>d\/s<\/span><\/span><\/p>\n

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

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

Formula of moment of inertia for uniform sphere :<\/span><\/span><\/p>\n

I <\/span><\/span>= (2\/5) m r<\/span><\/span>2 <\/span><\/span><\/sup><\/p>\n

I = momen<\/i><\/span><\/span>t of inertia <\/i><\/span><\/span>(kg m<\/i><\/span><\/span>2<\/i><\/span><\/span><\/sup>), m = mass (kg), <\/i><\/span><\/span>r = <\/i><\/span><\/span>radius <\/i><\/span><\/span>(m)<\/i><\/span><\/span><\/p>\n

The moment of inertia for uniform sphere :<\/span><\/span><\/p>\n

I = (2\/5)(2)(0.2)<\/span><\/span>2<\/span><\/span><\/sup> = (4\/5)(0.04) = 0.032 kg m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

The angular momentum of sphere :<\/span><\/span><\/p>\n

L = I <\/span><\/span>\u03c9 = (<\/span><\/span>0.032<\/span><\/span>)(<\/span><\/span>4<\/span><\/span>) <\/span><\/span>= 0.128 kg m<\/span><\/span>2<\/span><\/span><\/sup>\/s <\/span><\/span><\/p>\n

<\/p>\n

4. <\/span><\/span>A <\/span><\/span>1-kg <\/span><\/span>particle rotates at a constant angular speed of <\/span><\/span>2 rad\/s. <\/span><\/span>What is the angular speed if the radius of circle is 1<\/span><\/span>0 cm.<\/span><\/span><\/p>\n

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

Mass <\/span><\/span>of object <\/span><\/span>(m) <\/span><\/span>= 1 k<\/span><\/span>g<\/span><\/span><\/p>\n

The radius of circle <\/span><\/span>(r) = 10 cm = 10\/100 = 0.1 m<\/span><\/span><\/p>\n

The angular speed <\/span><\/span>(\u03c9) = 2 rad\/<\/span><\/span>s<\/span><\/span><\/p>\n

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

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

Formula of moment of inertia for particle :<\/span><\/span><\/p>\n

I <\/span><\/span>= m r<\/span><\/span>2 <\/span><\/span><\/sup>= (1)(0.1)<\/span><\/span>2<\/span><\/span><\/sup> = (1)(0.01) = 0.01 kg m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

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

L = I \u03c9 = (0.01)(2) = 0.02 kg m<\/span><\/span>2<\/span><\/span><\/sup>\/s <\/span><\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

1. An object with the moment of inertia of 2 kg m2 rotates at 1 rad\/s. What is the angular momentum of the object? Known : Moment of inertia (I) = 2 kg m2 Angular speed (\u03c9) = 1 rad\/s Wanted : Angular momentum (L) Solution : Formula of angular momentum : L = I … 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 momentum \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-1292","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\/1292","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=1292"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1292\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}