homework5sol.20100224.4b85f87e187322.60008504

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online