Suppose a solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on
A) the mass of the sphere.
B) the radius of the sphere.
C) both the mass and the radius of the sphere.
D) neither the mass nor the radius of the sphere.

Question

Quizplus · Accepted Answer

The angular velocity of the sphere at the bottom of the incline only depends on the radius of the sphere. This is because the moment of inertia of a solid sphere is given by (2/5)MR^2, which is only dependent on the radius of the sphere. The mass of the sphere does not affect the moment of inertia in this case, so it does not affect the angular velocity at the bottom of the incline.

Suppose a Solid Sphere of Mass M and Radius R