Question

A solid sphere is rotating about an axis through its center at a constant rotation rate. Another hollow sphere of the same mass and radius is rotating about its axis through the center at the same rotation rate. Which sphere has a greater rotational kinetic energy?

a) Solid sphere
b) Hollow sphere
c) Both have the same rotational kinetic energy.
d) It depends on the material of the spheres.

Answer 1

The hollow sphere has a greater rotational kinetic energy than the solid sphere when both are rotating at the same rate because the hollow sphere has a larger moment of inertia.

Step-by-step explanation:

When comparing the rotational kinetic energy of two spheres of the same mass and radius rotating at the same rotation rate, we must consider their moments of inertia. The hollow sphere has a greater moment of inertia than the solid sphere because the mass of the hollow sphere is distributed further from the axis of rotation.

Since rotational kinetic energy is ½Iω², where I is the moment of inertia and ω is the angular velocity, the hollow sphere with the larger moment of inertia will have a greater rotational kinetic energy when rotating at the same angular velocity as the solid sphere.