Physics 422 -- Fall 2007

Homework #6, due Wednesday Oct. 17 at beginning of class

1. [4pts]    Marion & Thornton problem 11.14. Hint: Using the parallel axis theorem and the moment of inertia tensor of a sphere can save you a lot of integration.

2. [4pts]    Marion & Thornton problem 11.18

3. [4pts]    Marion & Thornton problem 11.24. Do part (b) only.

4. [4pts]    Marion & Thornton problem 11.25. Again a bit of thought can save a lot of integration in calculating the moment of inertia.
Use the angle theta of the wheel as the generalized coordinate in the Lagrangian.

Part (b): After you find the Lagrangian, use it to obtain the equation of motion.

5. [4pts]    Find the frequency of oscillation of a simple pendulum that is released from rest at angles of 30, 60, 90, 120, 150 degrees relative to straight down, in units where the frequency of small oscillations is equal to 1. You will need to use some numerical method, e.g. Mathematica or one of its rivals (or for the truly hard-core, c++ or fortran) to do this problem.