{"id":12329,"date":"2021-09-09T11:08:45","date_gmt":"2021-09-09T15:08:45","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?page_id=12329"},"modified":"2024-10-05T18:09:20","modified_gmt":"2024-10-05T22:09:20","slug":"kinetic-energy-and-joints","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/kinetic-energy-and-joints\/","title":{"rendered":"Kinetic energy and joints"},"content":{"rendered":"<p><em><strong>Pin joint connection<\/strong><\/em><\/p>\n<p>Example 5.B.7 of the lecture book describes a system made up of bar OC pinned to ground at O, and pinned to the center of a disk at C, as shown below. In that problem, we are asked to relate the angular speed of OC to its angular position (using conservation of energy). For this problem, OC rotates about O and the disk translates without rotation. Therefore, the initial potential energy of the system goes into<em><span style=\"text-decoration: underline\"> rotational KE for the bar<\/span><\/em> and <em><span style=\"text-decoration: underline\">translational only KE for the disk<\/span><\/em>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7787 aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2021\/09\/Screen-Shot-2021-09-09-at-11.00.49-AM.jpg\" alt=\"\" width=\"331\" height=\"115\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong><em>Welded joint connection<\/em><\/strong><\/p>\n<p>Consider a problem similar to Example 5.B.7 described above, except here the disk is <em><strong>welded<\/strong><\/em> to arm OC. For this case, OC rotates about O and the disk both rotates and translates. Therefore, the initial potential energy of the system goes into <em><span style=\"text-decoration: underline\">rotational KE for the bar<\/span><\/em> and <em><span style=\"text-decoration: underline\">both translational + rotational KE for the disk<\/span><strong>.<\/strong><\/em><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7787 aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2021\/09\/Screen-Shot-2021-09-09-at-11.01.10-AM.jpg\" alt=\"\" width=\"331\" height=\"115\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"text-decoration: underline\"><em><strong>CONCLUSION<\/strong><\/em><\/span>: For a given angular orientation for OC, OC will be rotating more slowly in the welded joint case than for the pinned connection case. Can you see this in the following animation of the motion simulation for these two systems?<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2021\/09\/welded_jointa.gif\" width=\"569\" height=\"210\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pin joint connection Example 5.B.7 of the lecture book describes a system made up of bar OC pinned to ground at O, and pinned to the center of a disk at C, as shown below. In that problem, we are asked to relate the angular speed of OC to its angular position (using conservation of &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/kinetic-energy-and-joints\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Kinetic energy and joints<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":14,"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-12329","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/12329","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=12329"}],"version-history":[{"count":3,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/12329\/revisions"}],"predecessor-version":[{"id":12336,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/12329\/revisions\/12336"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/14"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=12329"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}