University of Alabama in Huntsville
Department of Physics
Fall 2008
PH 601: Classical Dynamics I
Homework Problem Set No. 7
Deadline: 5 November, 2008
Problem 31:
More guidance for problem 30: A thin homogeneous disk of mass mis rolling
without slipping on a horizontal surface. The disk is tilted with respect to
the vertical direction by a small angle θ. Find the minimal speed of the disk
that allows for stable motion.
1. Adapt a coordinate system so that zis the symmetry axis of the disk
and x, y are in the plane of the disk. Make the yaxis parallel to the
plane, and let the disk roll at t= 0 in the direction of y. Don’t forget
to account for all the forces: weight, normal force, and friction.
2. Find convenient Euler angles. (These are not necessarily the standard
ones!) Find the components of the angular velocities in terms of your
Euler angles.
3. Find the principal axes of the disk, and the corresponding moments of
inertia.
4. Find the rate of change of angular momentum.
5. Find the forces in a system co–rotting with the disk.
6. Assume now small angles, and linearize your equations.
7. find a linear inhomogeneous second–order equation for θ, and analyze
the condition for stable solutions.
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