{"id":12371,"date":"2021-09-14T18:03:50","date_gmt":"2021-09-14T22:03:50","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?page_id=12371"},"modified":"2024-10-05T18:09:21","modified_gmt":"2024-10-05T22:09:21","slug":"out-of-balance-forces","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/out-of-balance-forces\/","title":{"rendered":"Out-of-balance forces"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7686 aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2021\/09\/Screen-Shot-2021-09-14-at-5.55.06-PM.jpg\" alt=\"\" width=\"300\" height=\"196\" \/><\/p>\n<p>A disk is supported by a shaft through its geometric center O. The mass center G is not coincident with O, leading to a mass imbalance as the disk rotates. How does the mass imbalance influence the reactions on the disk at the shaft O as the shaft turns at a constant rate of \u03a9?<\/p>\n<p><em><strong>Analysis<\/strong><\/em><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7686 aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2021\/09\/Screen-Shot-2021-09-14-at-5.57.22-PM.jpg\" alt=\"\" width=\"325\" height=\"214\" \/><\/p>\n<p>From the above, we see that:<\/p>\n<ul>\n<li>When a<sub>Gy<\/sub> &lt; 0 (G is above O), F<sub>y<\/sub> &lt; mg. Therefore, the vertical component of the reaction at O is less than the weight of the disk.<\/li>\n<li>When a<sub>Gy<\/sub> &gt; 0 (G is below O), F<sub>y<\/sub> &gt; mg. Therefore, the vertical component of the reaction at O is greater than the weight of the disk.<\/li>\n<li>When a<sub>Gy<\/sub> = 0 (G is at same level as O): \u00a0F<sub>y<\/sub> = mg.<\/li>\n<\/ul>\n<p>Watch the animation to the right to see how F<sub>y<\/sub> varies with position.<\/p>\n<div class=\"page\" title=\"Page 3\">\n<div class=\"layoutArea\">\n<div class=\"column\">\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\/out_of_balance.gif\" width=\"573\" height=\"244\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>A disk is supported by a shaft through its geometric center O. The mass center G is not coincident with O, leading to a mass imbalance as the disk rotates. How does the mass imbalance influence the reactions on the disk at the shaft O as the shaft turns at a constant rate of \u03a9? &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/out-of-balance-forces\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Out-of-balance forces<\/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-12371","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/12371","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=12371"}],"version-history":[{"count":1,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/12371\/revisions"}],"predecessor-version":[{"id":12376,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/12371\/revisions\/12376"}],"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=12371"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}