homework5sol.20100224.4b85f87e187322.60008504

# homework5sol.20100224.4b85f87e187322.60008504 - TAM 412,...

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TAM 412, Homework 5, Selected answers Harry Dankowicz Mechanical Science and Engineering University of Illinois at Urbana-Champaign danko@illinois.edu 3. Let R denote a reference frame f xed relative to the wire. Let e R denote an inertial reference frame and suppose that R rotates (but does not translate) relative to e R with constant angular velocity. Let P be an arbitrary point on the wire. It follows that the position vector to P from the origin O is given by r OP = x ( q ) e x + y ( q ) e y + z ( q ) e z for some q ,where e x , e y ,and e z are basis vectors in R . If the particle moves along the wire, it follows that its position is given by r = x ( q ( t )) e x + y ( q ( t )) e y + z ( q ( t )) e z and thus ˙ r = μ dx dq ( q ( t )) e x + dy dq ( q ( t )) e y + dz dq ( q ( t )) e z ˙ q = d r dq ˙ q It follows that ˙ q 2 2 d r dq · d r dq = 1 2 ˙ r · ˙ r whereas ˙ q d r dq · ¨ r = ˙ r · ¨ r From the second equation on page 21, it follows that m ¨ r +2 m ω × ˙ r

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## This note was uploaded on 11/17/2011 for the course TAM 412 taught by Professor Weaver during the Spring '08 term at University of Illinois, Urbana Champaign.

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homework5sol.20100224.4b85f87e187322.60008504 - TAM 412,...

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