{"id":23458,"date":"2026-02-16T08:00:59","date_gmt":"2026-02-16T13:00:59","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?p=23458"},"modified":"2026-02-21T22:16:11","modified_gmt":"2026-02-22T03:16:11","slug":"homework-h3-h-sp-26","status":"publish","type":"post","link":"https:\/\/www.purdue.edu\/freeform\/me274\/2026\/02\/16\/homework-h3-h-sp-26\/","title":{"rendered":"Homework H3.H – 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

Any questions??<\/p>\n

\n

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

It is recommended that you use an observer attached to the wheel. As we have discussed in class, your choice of observer directly affects four terms in the acceleration equation: \u03c9\u00a0<\/strong><\/em>and \u03b1<\/strong><\/em>\u00a0 (how the observer moves<\/em>), and the relative velocity and relative acceleration terms (what the observer sees<\/em>). Note that the remainder of the discussion here is based on having the observer attached to the wheel.<\/p>\n

The wheel shown above has TWO components of rotation:<\/p>\n

    \n
  • a rotation rate of \u03c91<\/sub> about a fixed axis (the “+” Y<\/em>-axis), and,<\/li>\n
  • a rotation rate of \u03c92<\/sub> about a moving axis (the “+” z-axis)<\/li>\n<\/ul>\n

    (Be sure to make a clear distinction between the lower case and upper case symbols.)<\/p>\n

    Therefore, the angular velocity of the wheel is given by:<\/p>\n

    \u03c9<\/strong><\/em>\u00a0= \u03c91<\/sub>J<\/strong><\/em>\u00a0+ \u03c92<\/sub> k<\/strong><\/em><\/p>\n

    The angular acceleration vector\u00a0\u03b1<\/strong><\/em>\u00a0is simply the time derivative of the angular velocity vector \u03c9<\/em><\/strong> : \u03b1 = <\/strong>d\u03c9<\/strong>\/dt. <\/em>In taking this time derivative,<\/p>\n

      \n
    • Recall that the J<\/strong><\/em>-axis is fixed. Since J<\/strong><\/em>\u00a0is fixed, then dJ<\/strong><\/em>\/dt = 0<\/strong><\/em>.<\/li>\n
    • Recall that the k<\/strong><\/em>-axis is NOT fixed. Knowing that, how do you find\u00a0dk<\/strong><\/em>\/dt?<\/li>\n<\/ul>\n

      With the observer attached to the wheel, what motion does the observer see for points A and B? That is, what are (v<\/strong>A\/O<\/sub>)rel<\/sub><\/em> and (a<\/strong>A\/O<\/sub>)rel<\/sub>,<\/em>\u00a0and (v<\/strong>B\/O<\/sub>)rel<\/sub><\/em> and (a<\/strong>B\/O<\/sub>)rel<\/sub><\/em>?<\/p>\n

      NOTE<\/em>: Pay particular attention to the motion of the reference point O. What path does O follow? And, based on that, how do you write down the acceleration vector of O, a<\/strong>O<\/sub><\/em>?<\/p>\n

      \n

       <\/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":"open","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":[2,4],"tags":[],"class_list":["post-23458","post","type-post","status-publish","format-standard","hentry","category-chapter-1-homework","category-chapter-3-homework"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23458","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=23458"}],"version-history":[{"count":2,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23458\/revisions"}],"predecessor-version":[{"id":24054,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23458\/revisions\/24054"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=23458"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/categories?post=23458"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/tags?post=23458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}