PHYSICS 5200 Problem Set #11 due 4/28/98

1.

(10 points): A solid uniform sphere of radius a has a spherical cavity of radius a/2 centered at a point a/2 from the center of the sphere.

(a)

Find the center of mass. Hint, if you consider the cavity as being created by the addition of a negative density sphere to the uniform sphere, this problem can be done with simple algebra.

(b)

Find the moment of inertia of the sphere about an axis passing through the center of the sphere and the center of the cavity.

2.

(10 points): A billiard ball is given initial speed v₀. Initially it slides without rolling, but due to friction, it begins to roll. Show that the speed when it rolls without sliding is (5/7)v₀.