{"id":23331,"date":"2026-01-16T16:00:06","date_gmt":"2026-01-16T21:00:06","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?p=23331"},"modified":"2026-01-23T16:38:25","modified_gmt":"2026-01-23T21:38:25","slug":"homework-h1-e-sp-26-2","status":"publish","type":"post","link":"https:\/\/www.purdue.edu\/freeform\/me274\/2026\/01\/16\/homework-h1-e-sp-26-2\/","title":{"rendered":"Homework H1.E – 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 B. 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> (counterclockwise from e<\/strong>R<\/sub><\/em>).<\/p>\n

The first time derivative of \u03b8<\/em>\u00a0 is given to the the constant \u03c9<\/em>. Therefore, the second time derivative of \u03b8<\/em>\u00a0 is zero. The time derivatives of R are found from direct differentiation of the path equation R = b\u03b8<\/em> . These results then are used to find the v<\/em><\/strong>P<\/em><\/sub> and a<\/em><\/strong>P<\/em><\/sub> in terms of their polar coordinates.<\/p>\n

Carefully watch the animation below of the motion of P. As we have seen before, the velocity vector is always tangent to the path, whereas the acceleration vector has both tangent and normal components. The normal component always points inward to the path. Also, as we have seen before, when the angle between v<\/em><\/strong>P<\/em><\/sub> and a<\/em><\/strong>P<\/em><\/sub> is less than 90\u00b0, the speed of P is increasing. As you can see from the animation below, the speed of P is increasing throughout the entire motion.<\/p>\n

<\/p>\n

Please note the orientations and directions of the polar unit vectors e<\/strong><\/em>R<\/sub> and e<\/em><\/strong>\u03b8<\/sub> shown in the figure below for \u03b8 = 30\u00b0.<\/p>\n

\"\"<\/p>\n

\n

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

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