{"id":23685,"date":"2026-04-17T08:00:13","date_gmt":"2026-04-17T12:00:13","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?p=23685"},"modified":"2026-04-23T11:44:24","modified_gmt":"2026-04-23T15:44:24","slug":"homework-h6-d-sp26","status":"publish","type":"post","link":"https:\/\/www.purdue.edu\/freeform\/me274\/2026\/04\/17\/homework-h6-d-sp26\/","title":{"rendered":"Homework H6.D – Sp26"},"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

<\/p>\n

The derivation of the dynamical equation of motion (EOM) for a system is a straight-forward application of what we have learned from Chapter 5 in using the Newton-Euler equations. The goal in deriving the EOM is to end up with a single differential equation in terms of a single dependent variable that describes the motion of the system. Here in this problem, we want our EOM to be in terms of x(t).<\/p>\n

Recall the following f<\/em>our-step plan<\/em><\/span> outline in the lecture book and discussed in lecture:<\/p>\n

Step 1: FBDs<\/strong><\/em>
\nDraw a FBD of the disk. Define a rotation coordinate for the disk.<\/p>\n

Step 2: Kinetics (Newton\/Euler)
\n<\/strong><\/em>Write down the Newton\/Euler equations for the disk.<\/p>\n

Step 3: Kinematics<\/strong><\/em>
\nUse the no-slip condition between the disk and the ramp to relate x to the rotational coordinate that you chose above.<\/p>\n

Step 4: EOM<\/strong><\/em>
\nCombine your Newton\/Euler equations along with your kinematics to arrive at a single differential equation in terms of the dependent variable x<\/em>.<\/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":[7],"tags":[],"class_list":["post-23685","post","type-post","status-publish","format-standard","hentry","category-chapter-6-homework"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23685","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=23685"}],"version-history":[{"count":3,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23685\/revisions"}],"predecessor-version":[{"id":24923,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23685\/revisions\/24923"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=23685"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/categories?post=23685"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/tags?post=23685"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}