Unformatted text preview: PHYS 3202 Classical Mechanics II - Homework #4 Hints and
Problem 7.5: A is positive, and the additional force is attractive toward the
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
1 ˙2 1 ˙2
M ξ + Iθ .
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
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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