{"id":15675,"date":"2022-06-01T17:42:48","date_gmt":"2022-06-01T21:42:48","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?p=15675"},"modified":"2024-10-05T18:06:52","modified_gmt":"2024-10-05T22:06:52","slug":"homework-h3-b-9","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me274\/chapter-3-discussion\/homework-h3-b-9\/","title":{"rendered":"Homework H3.B.09"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-14417 aligncenter\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2022\/05\/Screen-Shot-2022-05-15-at-10.36.07-AM-300x192.jpg\" alt=\"\" width=\"323\" height=\"207\" srcset=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2022\/05\/Screen-Shot-2022-05-15-at-10.36.07-AM-300x192.jpg 300w, https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2022\/05\/Screen-Shot-2022-05-15-at-10.36.07-AM.jpg 573w\" sizes=\"auto, (max-width: 323px) 100vw, 323px\" \/><\/p>\n<p>Ask and answer questions here. And, learn from both.<\/p>\n<hr \/>\n<p><em><strong>DISCUSSION and HINTS<\/strong><\/em><\/p>\n<p>For your work on this problem, it is recommended that you use an observer attached to the disk. The observer\/disk has two components of rotation:<\/p>\n<ul>\n<li>One component of <em>\u03c9<\/em><sub>0<\/sub>\u00a0about the <span style=\"text-decoration: underline\"><em>fixed<\/em><\/span> <em><strong>K<\/strong><\/em>-axis.<\/li>\n<li>The second component of <em>\u03c9<\/em><sub>disk\u00a0<\/sub>about the <em><span style=\"text-decoration: underline\">moving<\/span><\/em> <em><strong>j<\/strong><\/em>-axis.<\/li>\n<\/ul>\n<p>Write out the angular velocity vector <strong>\u03c9<\/strong> in terms of the two components described above.<\/p>\n<p>Take a time derivative of <strong>\u03c9<\/strong>\u00a0to get the angular acceleration <strong>\u03b1<\/strong>\u00a0of the observer\/disk. When taking this derivative, you will need to find the time derivative of the unit vector <em><strong>j<\/strong><\/em>. How do you do this? Read back over Section 3.2 of the lecture book. There you will see: <em><strong>j<\/strong><\/em>_dot = <strong>\u03c9\u00a0<\/strong>x <em><strong>j<\/strong><\/em>, where <strong>\u03c9\u00a0<\/strong>is the total angular velocity vector of the disk that you found above.<\/p>\n<p><em><span style=\"text-decoration: underline\">Acceleration of point A<br \/>\n<\/span><\/em>The motion of A is quite complicated. To better understand the motion of A, consider first the view of point A by our observer who is attached to the disk &#8211; what does this observer see in terms of relative velocity and relative acceleration: (<em><strong>v<\/strong><sub>A\/B<\/sub><\/em>)<sub>rel<\/sub> and (<em><strong>a<\/strong><sub>A\/B<\/sub><\/em>)<sub>rel<\/sub>?<\/p>\n<p>With this known relative motion, we can use the moving reference frame acceleration equation:<\/p>\n<p><em><strong>a<\/strong><sub>A<\/sub><\/em>\u00a0= <em><strong>a<\/strong><sub>B<\/sub><\/em>\u00a0+ (<em><strong>a<\/strong><sub>A\/B<\/sub><\/em>)<sub>rel<\/sub>\u00a0+<em><strong>\u03b1<\/strong><\/em> x <em><strong>r<\/strong><sub>A\/B<\/sub><\/em>\u00a0+ 2 <strong>\u03c9<\/strong>\u00a0x\u00a0(<em><strong>v<\/strong><sub>A\/B<\/sub><\/em>)<sub>rel<\/sub>\u00a0+ <strong>\u03c9<\/strong>\u00a0x\u00a0(<strong>\u03c9<\/strong>\u00a0x\u00a0<em><strong>r<\/strong><sub>A\/B<\/sub><\/em>)<\/p>\n<p>In finding the acceleration of B, <em><strong>a<\/strong><sub>B<\/sub><\/em>, note that B moves with a constant speed on a circular path centered on point O. Use the path description to find <em><strong>a<\/strong><sub>B<\/sub><\/em>. <em>WARNING<\/em>: Although B moves with a constant speed, its acceleration is NOT zero.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ask and answer questions here. And, learn from both. DISCUSSION and HINTS For your work on this problem, it is recommended that you use an observer attached to the disk. The observer\/disk has two components of rotation: One component of \u03c90\u00a0about the fixed K-axis. The second component of \u03c9disk\u00a0about the moving j-axis. Write out the &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me274\/chapter-3-discussion\/homework-h3-b-9\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Homework H3.B.09<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":14895,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-15675","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/15675","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/comments?post=15675"}],"version-history":[{"count":2,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/15675\/revisions"}],"predecessor-version":[{"id":16373,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/15675\/revisions\/16373"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/14895"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=15675"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}