{"id":400,"date":"2018-02-01T09:02:48","date_gmt":"2018-02-01T01:02:48","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=400"},"modified":"2018-02-01T09:02:48","modified_gmt":"2018-02-01T01:02:48","slug":"angular-displacement-and-linear-displacement-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/angular-displacement-and-linear-displacement-problems-and-solutions.htm","title":{"rendered":"Angular displacement and linear displacement \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Converting angle units (degree, radian, revolution)<\/strong><\/p>\n

1. \u00bc <\/span><\/span>rev <\/span><\/span>= ….. <\/span><\/span>o<\/span><\/span><\/sup> (<\/span><\/span>degree<\/span><\/span>) ?<\/span><\/span><\/p>\n

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

1 <\/span><\/span>rev<\/span><\/span> = 360<\/span><\/span>o<\/span><\/span><\/sup><\/p>\n

\u00bd <\/span><\/span>rev<\/span><\/span> = 180<\/span><\/span>o<\/span><\/span><\/sup><\/p>\n

\u00bc <\/span><\/span>rev<\/span><\/span> = 90<\/span><\/span>o<\/span><\/span><\/sup><\/p>\n

2. \u00bd <\/span>rev<\/span> = …….. r<\/span>ad<\/span> ?<\/span><\/span><\/p>\n

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

1 <\/span>rev<\/span> = 2<\/span>\u03c0<\/span> rad = 2(3.14) rad = 6.28 rad<\/span><\/span><\/p>\n

\u00bd <\/span>rev<\/span> = pi rad = 3.14 rad<\/span><\/span><\/p>\n

3. 180<\/span>o<\/span><\/sup> = ….. <\/span>rev ?<\/span><\/span><\/p>\n

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

360<\/span>o<\/span><\/sup> = 1 <\/span>rev<\/span><\/span><\/p>\n

180<\/span>o<\/span><\/sup> = \u00bd <\/span>rev<\/span><\/span><\/p>\n

<\/p>\n

4. 90<\/span>o<\/span><\/sup> = ….. rad ?<\/span><\/span><\/p>\n

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

360<\/span>o<\/span><\/sup> = 2<\/span>\u03c0 <\/span>rad = 2(3.14) rad = 6.28 ra<\/span>d<\/span><\/span><\/p>\n

180<\/span>o<\/span><\/sup> = <\/span>\u03c0 <\/span>rad = 3.14 rad<\/span><\/span><\/p>\n

90<\/span>o<\/span><\/sup> = \u00bd <\/span>\u03c0<\/span> rad = \u00bd (3.14) = 1.57<\/span><\/span><\/p>\n

5. 60 rad = ….. <\/span>rev<\/span> ?<\/span><\/span><\/p>\n

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

6.28 rad = 1 <\/span><\/span>rev<\/span><\/span><\/p>\n

60 rad\/6.28 = 9.55 <\/span><\/span>rev<\/span><\/span><\/p>\n

6. 40 rad= ….. <\/span><\/span>o<\/span><\/span><\/sup> ?<\/span><\/span><\/p>\n

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

6.28 rad = 360<\/span><\/span>o<\/span><\/span><\/sup><\/p>\n

40 rad\/6.28 = (6.37)(360<\/span><\/span>o<\/span><\/span><\/sup>) = 2292.99<\/span><\/span>o<\/span><\/span><\/sup><\/p>\n

<\/p>\n

Angular displacement and linear displacement <\/strong><\/p>\n

1. A bike wheel 60 cm in diameter rotates 10 radians. What is the linear displacement<\/a> of a point 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

Angle (\u03b8<\/span><\/span>) = 10 radians<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> linear displacement (l)<\/span><\/span><\/p>\n

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

l = r <\/span><\/span>\u03b8<\/span><\/span><\/p>\n

l = (0.3 m)(10 rad) <\/span><\/span><\/p>\n

l = 3 meters<\/span><\/span><\/p>\n

2. A wheel 50 cm in radius rotates 360<\/span><\/span>o<\/span><\/span><\/sup>. What is the linear displacement of a point on the edge of the wheel ?<\/span><\/span><\/p>\n

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

Radius (r) = 50 cm = 0.5 meters<\/span><\/span><\/p>\n

Angle (<\/span><\/span>\u03b8<\/span><\/span>) = 360<\/span><\/span>o <\/span><\/span><\/sup>= 6.28 radians<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> linear displacement (l)<\/span><\/span><\/p>\n

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

l = r <\/span><\/span>\u03b8<\/span><\/span><\/p>\n

l = (0.5 m)(6.28 rad) <\/span><\/span><\/p>\n

l = 3.14 meters<\/span><\/span><\/p>\n

<\/p>\n

3. A wheel 50 cm in radius rotates 2 revolutions. What is the linear displacement of a point on the edge of the wheel ?<\/span><\/span><\/p>\n

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

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

Angle (<\/span><\/span>\u03b8<\/span><\/span>) = 2 revolutions = (2)(6.28 radians) = 12.56 radians<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> linear displacement (l) ?<\/span><\/span><\/p>\n

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

l = r <\/span><\/span>\u03b8<\/span><\/span><\/p>\n

l = (0.5 m)(12.56 rad) <\/span><\/span><\/p>\n

l = 6.28 m<\/span><\/span><\/p>\n

4. A point on the edge of a wheel 2 meters in radius, moves 100 meters. Determine the angular displacement. <\/span><\/span><\/p>\n

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

Radius (r) = \u00bd (diameter) = \u00bd (2 meters) = 1 meter<\/span><\/span><\/p>\n

linear displacement (l) = 100 meters<\/span><\/span><\/p>\n

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

(a) Angular displacement (in radian)<\/span><\/span><\/p>\n

\u03b8 <\/span><\/span>= s \/ r = 100 \/ 1 = 100 radians<\/span><\/span><\/p>\n

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

1 radian = 360<\/span><\/span>o<\/span><\/span><\/sup><\/p>\n

100 radians = 100(360<\/span><\/span>o<\/span><\/span><\/sup>) = 36,000 radians<\/span><\/span><\/p>\n

(c) Angular displacement (in revolution)<\/span><\/span><\/p>\n

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

36,000 \/ 6.28 = 5732,484 revolutions<\/span><\/span><\/p>\n

<\/p>\n

5. A particle round a circle 10 meters and rotates 180<\/span><\/span>o<\/span><\/span><\/sup>. What is the radius ?<\/span><\/span><\/p>\n

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

Linear displacement (l) = 10 meters<\/span><\/span><\/p>\n

Angle (<\/span><\/span>\u03b8<\/span><\/span>) = 180<\/span><\/span>o<\/span><\/span><\/sup> = 3.14 radians<\/span><\/span><\/p>\n

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

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

r = l \/ <\/span><\/span>\u03b8 <\/span><\/span>= 10 \/ 3.14 = 3.18 meters<\/span><\/span><\/p>\n

<\/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":"

    Converting angle units (degree, radian, revolution) 1. \u00bc rev = ….. o (degree) ? Solution 1 rev = 360o \u00bd rev = 180o \u00bc rev = 90o 2. \u00bd rev = …….. rad ? Solution 1 rev = 2\u03c0 rad = 2(3.14) rad = 6.28 rad \u00bd rev = pi rad = 3.14 rad 3. … 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 displacement and linear displacement \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-400","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\/400","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=400"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/400\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=400"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=400"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}