# Rocking Bowl Oscillations

1. Apr 29, 2010

### Fuzzy Static

1. The problem statement, all variables and given/known data
A hemispherical shell with its curved surface resting on a table will rock back and forth. To derive the period, use $$\sum$$T=I$$\alpha$$$$_{}z$$. Sum the torques about the instantaneous point of contact and make the small angle approximation sin $$\theta$$$$\approx$$$$\theta$$.
You will need to know the location of the center of mass. It can be shown that the center of mass of the shell is halfway between the center of curvature and surface. (You don't have to show it.)
You will also need the moment of inertia. Since we will restrict ourselves to small angle oscillations, just use the moment of inertia about the equilibrium point of contact.

2. Relevant equations

$$\sum$$T=I$$\alpha$$$$_{}z$$
sin $$\theta$$$$\approx$$$$\theta$$

3. The attempt at a solution
Um... Using the sum of Torque = the moment of Inertia times alpha. No clue.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution