A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid
Sphere is
A) less than the total kinetic energy of the cylinder.
B) more than the total kinetic energy of the cylinder.
C) equal to the total kinetic energy of the cylinder.

Question

Quizplus · Accepted Answer

The total kinetic energy of a rolling object is the sum of its translational kinetic energy ($KE_{trans} = \frac{1}{2}mv^2$) and its rotational kinetic energy ($KE_{rot} = \frac{1}{2}I\omega^2$). For both the sphere and the cylinder, the translational kinetic energies are the same because they have the same mass and speed. However, the moment of inertia ($I$) for a solid sphere ($\frac{2}{5}mr^2$) is less than that for a solid cylinder ($\frac{1}{2}mr^2$), making the sphere's rotational kinetic energy less than the cylinder's. Therefore, the total kinetic energy of the sphere is less than that of the cylinder.

A Solid Sphere and a Solid Cylinder, Both Uniform and of the Same