You are working at a billiard parlor and one of your customers
complains that a fellow customer is using a ?trick? ball. Trick
billiard balls have the same diameter and weight as a regular billiard
ball, but are hollow.  Your boss tells you to use an inclined plane to
determine if the ball is hollow.

a)	Calculate (show your calculations) the moment of inertia for both
the solid and hollow balls.
b)	Write the Lagrangian for a ball rolling down the inclined plane.
Find the equation(s) of motion.
c)	How will you tell if the ball is ?trick??

The moment of inertia for the hollow ball will be greater than the
moment of inertia for the solid ball.  This is because the center of
mass for the hollow ball is closer to the circumfrence than is the
case with the solid ball.

When you put the balls on an inclined plane, the hollow ball should roll slower.

As for the othe two, sound like homework problems - you're on your own
for those -- well, for $5, anyways...

Please correct me if I'm wrong here...but wouldnt the center of mass
still be in the center (assuming that hollow center of the trick ball
is spherical and positioned in the middle) for both the trick and the
regular ball.

-Fractl