{"id":23337,"date":"2026-01-16T16:00:01","date_gmt":"2026-01-16T21:00:01","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?p=23337"},"modified":"2026-04-22T16:26:20","modified_gmt":"2026-04-22T20:26:20","slug":"homework-h1-f-sp-26","status":"publish","type":"post","link":"https:\/\/www.purdue.edu\/freeform\/me274\/2026\/01\/16\/homework-h1-f-sp-26\/","title":{"rendered":"Homework H1.F – Sp 26"},"content":{"rendered":"\n\n\n
Problem statement<\/strong><\/em><\/span><\/a>
\nSolution video<\/strong><\/em><\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

DISCUSSION THREAD<\/span><\/strong><\/em><\/p>\n

\"\"<\/p>\n

Discussion and hints:<\/strong><\/em><\/p>\n

For the polar description to be used here, the radial unit vector e<\/strong>R\u00a0<\/sub><\/em>points from O toward P. The transverse unit vector e<\/strong>\u03b8<\/sub><\/em>\u00a0is perpendicular to e<\/strong>R\u00a0<\/sub><\/em>and points in the direction of increasing angle \u03b8<\/em> (clockwise from e<\/strong>R<\/sub><\/em>).<\/p>\n

The solution of this problem comes down to trig – can you do the projections of v<\/em><\/strong>P<\/em><\/sub> and a<\/em><\/strong>P<\/em><\/sub>\u00a0onto the polar unit vectors e<\/strong>R\u00a0<\/sub><\/em>and\u00a0e<\/strong>\u03b8<\/sub><\/em>\u00a0? For example, the velocity of P can be written as v<\/em><\/strong>P<\/em><\/sub>\u00a0= v<\/em>P<\/em><\/sub>\u00a0sin\u03b8 e<\/strong>R<\/sub>\u00a0+ vP\u00a0<\/sub>cos\u03b8 e<\/strong>\u03b8<\/sub><\/em>. And, the acceleration of P can be written as a<\/em><\/strong>P<\/em><\/sub>\u00a0= –a<\/em>P<\/em><\/sub>\u00a0cos\u03b2\u00a0e<\/strong>R<\/sub>\u00a0– aP\u00a0<\/sub>sin\u03b2\u00a0e<\/strong>\u03b8 <\/sub>. No formulas to remember, just look at the figure and do the trig!\u00a0<\/span><\/em>From these results, you can identify the time derivatives of R<\/em> and \u03b8<\/em>.<\/p>\n

<\/p>\n

\n

Any questions??<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Problem statement Solution video DISCUSSION THREAD<\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-23337","post","type-post","status-publish","format-standard","hentry","category-chapter-1-homework"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23337","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/types\/post"}],"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=23337"}],"version-history":[{"count":6,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23337\/revisions"}],"predecessor-version":[{"id":23760,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23337\/revisions\/23760"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=23337"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/categories?post=23337"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/tags?post=23337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}