{"id":23361,"date":"2026-01-23T16:00:33","date_gmt":"2026-01-23T21:00:33","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?p=23361"},"modified":"2026-04-22T16:26:20","modified_gmt":"2026-04-22T20:26:20","slug":"homework-h1-j-sp-26","status":"publish","type":"post","link":"https:\/\/www.purdue.edu\/freeform\/me274\/2026\/01\/23\/homework-h1-j-sp-26\/","title":{"rendered":"Homework H1.J – Sp 26"},"content":{"rendered":"\n\n\n
Problem statement<\/strong><\/em><\/span><\/a>
\nSolution video<\/a>
\n<\/strong><\/em><\/span><\/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

<\/p>\n

An observer riding along on block A will describe the motion of P relative to themself in terms of the radial distance r<\/em> and the cable angle \u03b8<\/em>. Because of this, it is convenient to use the relative motion kinematics equations to write down the velocity and acceleration of particle P: \u00a0v<\/strong>P<\/sub> = v<\/strong>A<\/sub> + v<\/strong>P\/A<\/sub><\/em> and a<\/strong>P<\/sub> = a<\/strong>A<\/sub> + a<\/strong>P\/A<\/sub><\/em> , where the relative velocity and relative acceleration terms are written in polar form:<\/p>\n

v<\/strong>P\/A\u00a0<\/sub><\/em>= r_dot e<\/strong>r\u00a0<\/sub>+ r*theta_dot e<\/strong>\u03b8<\/sub><\/em><\/p>\n

a<\/strong>P\/A\u00a0<\/sub><\/em>= (r_ddot -r*theta_dot2<\/sup>)\u00a0e<\/strong>r\u00a0<\/sub>+ (r*theta_ddot + 2r_dot*theta_dot)\u00a0e<\/strong>\u03b8<\/sub><\/em><\/p>\n

You will need to write the polar unit vectors\u00a0e<\/strong>r\u00a0<\/sub><\/em>and\u00a0e<\/strong>\u03b8\u00a0<\/sub><\/em>in terms of the Cartesian unit vectors, i<\/strong><\/em> and j<\/strong><\/em>, at some point before you can add together terms.<\/p>\n

QUESTION<\/em>: What is the relationship between xA<\/sub> and r<\/em>? (Recall that the cable remains taut at all times.)<\/p>\n

An animation showing the path of point P corresponding to \u03b8<\/em>_dot = constant is provided below. How does this true path differ from the view of the path as seen by the observer on A? Can you visualize that? HINT<\/strong><\/em>: The path seen by the observer on A is an inward spiral centered on the observer (point A).<\/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-23361","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\/23361","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=23361"}],"version-history":[{"count":6,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23361\/revisions"}],"predecessor-version":[{"id":23803,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23361\/revisions\/23803"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=23361"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/categories?post=23361"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/tags?post=23361"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}