HW4 Hints - PHYS 3202 Classical Mechanics II - Homework #4...

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Unformatted text preview: PHYS 3202 Classical Mechanics II - Homework #4 Hints and Clarifications Problem 7.5: A is positive, and the additional force is attractive toward the origin. Problem 7.7: Try to simplify your expression for the kinetic energy first. Depending on your choice of generalized coordinates, Equations (D.12) or (D.11) in the appendices of Thornton and Marion, 5th Edition may be useful. Problem 7.9: If the disk’s center has moved a distance ξ , it will have rotated by an angle θ = ξ/R to avoid slipping. The moment of inertia of the disk about its center is I = 1 M R2 . The kinetic energy of the disk is 2 1 ˙2 1 ˙2 M ξ + Iθ . 2 2 Problem 7.11: The answer to the last question “explain why this is a reasonable result” involves the concept of noninertial reference frame, and is thus OPTIONAL. I have directed your TA not to assign any grade point to this question. You are encouraged to read Chapter 10 if interested in finding an explanation. Problem 7.17: You are encouraged, but not required, to solve the second order differential equation for q (t). However, if you do not solve it, you should verify g that q (t) = 2ω2 (cosh ωt − cos ωt) is THE solution by 1) checking that it satisfies the differential equation you derived, and 2) checking that it satisfies the initial conditions q (0) = q (0) = 0. ˙ In Quiz #1, we mentioned that for fixed constraints, the force of constraint does not do any actual work. What about problem 7.17? This will help you understand your result for the last question in the problem. ...
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