A solid sphere,a solid cylinder,and a hoop each have the same mass and radius.If they are spinning at the same angular velocity,which one has the greatest rotational kinetic energy?
A)the sphere
B)the cylinder
C)the hoop
D)They all have the same rotational kinetic energy.

Question

Quizplus · Accepted Answer

The rotational kinetic energy of an object is given by the formula $KE_{rot} = \frac{1}{2}I\omega^2$, where $I$ is the moment of inertia and $\omega$ is the angular velocity. The moment of inertia depends on the mass distribution relative to the axis of rotation. For objects with the same mass and radius, the hoop has the greatest moment of inertia ($I = mR^2$ for a hoop), making its rotational kinetic energy the highest among the given options.

A Solid Sphere,a Solid Cylinder,and a Hoop Each Have the Same