Question

Find com of non uniform hemisphere whose density

Answer 1

Consider a sphere of non-uniform density with radius R=0.5m and mass M=1 kg. The rotational inertia of this sphere can be taken to be I=BMR^2 where B is unknown.

The sphere is initially rotating with angular velocity w0=4.00rad/s and is placed on a rough horizontal surface. The velocity of the center of mass of the sphere as it is placed on the surface is 0.

The sphere at first rolls and slips. Just as it begins to roll without slipping, the velocity of the center of mass is found to be 1.5 m/s.