{"id":8153,"date":"2023-04-30T23:48:35","date_gmt":"2023-04-30T23:48:35","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=8153"},"modified":"2024-05-25T06:50:26","modified_gmt":"2024-05-25T06:50:26","slug":"angular-velocity-equation","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/angular-velocity-equation.htm","title":{"rendered":"Angular velocity equation","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

3 questions about Angular velocity equation<\/span><\/p>\n

1. An object moving in a circular path has a radius of 0.5 m. The particle is able to cover an angle of 60\u03c0 rad in 15 seconds. Determine the angular speed of the object.<\/span><\/p>\n

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

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

Angle (\u03b8) = 60\u03c0 rad<\/span><\/p>\n

Time interval (t) = 15 seconds<\/span><\/p>\n

Wanted:<\/u> Angular velocity (\u03c9)<\/span><\/p>\n

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

\u03b8 = \u03c9 t <\/span><\/p>\n

60\u03c0 = \u03c9 (15)<\/span><\/p>\n

\u03c9 = 60\u03c0 \/ 15 = 4\u03c0 rad\/s <\/span><\/p>\n

2. A bicycle wheel with a radius of 30 cm rotates at a constant speed. The tire valve can rotate at an angle of 120\u03c0 rad for 10 seconds. Determine the angular speed.<\/span><\/p>\n

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

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

Angle (\u03b8) = 120\u03c0 rad<\/span><\/p>\n

Time interval (t) = 10 s<\/span><\/p>\n

Wanted:<\/u> Angular velocity (\u03c9)<\/span><\/p>\n

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

\u03b8 = \u03c9 t <\/span><\/p>\n

120\u03c0 = \u03c9 (10)<\/span><\/p>\n

\u03c9 = 120\u03c0 \/ 10 = 12\u03c0 rad\/s <\/span><\/p>\n

3. The rope is wrapped around a wheel with radius R = 25 cm as shown. If a point on the rope (point A) has a speed of 5 m\/s then the rotational speed of the wheel is…<\/span><\/p>\n

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

Radius (r) = 25 cm = 0.25 meters<\/span><\/p>\n

Speed (v) = 5 m\/s<\/span><\/p>\n

Wanted:<\/u> Angular velocity (\u03c9)<\/span><\/p>\n

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

The formula for the relation between angular speed, linear speed and radius:<\/span><\/p>\n

v = r \u03c9<\/span><\/p>\n

5 = (0,25) \u03c9<\/span><\/p>\n

\u03c9 = 5 \/ 0,25 = 20 rad\/s<\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

3 questions about Angular velocity equation 1. An object moving in a circular path has a radius of 0.5 m. The particle is able to cover an angle of 60\u03c0 rad in 15 seconds. Determine the angular speed of the object. Known: Radius (r) = 0.5 meters Angle (\u03b8) = 60\u03c0 rad Time interval (t) … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"closed","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":"3","_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 velocity equation","_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-8153","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\/8153","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=8153"}],"version-history":[{"count":7,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/8153\/revisions"}],"predecessor-version":[{"id":9845,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/8153\/revisions\/9845"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=8153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=8153"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=8153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}