Question

A solid sphere of radius R, a solid cylinder of radius R, and a rod of length R all have the same mass, and all three are rotating with the same angular velocity The sphere is rotating around an axis through its center. The cylinder is rotating around its long axis, and the rod is rotating around an axis through its center but perpendicular to the rod. Which one has the greatest rotational kinetic energy? a. the sphere b. the cylinder c. the rod d. the rod and the cylinder have the same rotational kinetic energy e. they all have the same kinetic energy

Answer 1

b. the cylinder

Step-by-step explanation:

From the information given:

We understood that the mass of the sphere, cylinder, and rod length is the same with the same angular speed.

Taking their moments:

For the solid sphere;
`\text{The moment of inertia :}`
`I_s` =
`(2)/(5) * m * r^2`

The moment of inertia of the cylinder,
`I_c = 0.5* m * r^2`

The moment of inertia of rod,
`I_r =( m * r^2 )/(12)`

The rotational kinetic energy is directly corresponding to the moment of inertia.

Thus, the cylinder has the greatest rotational kinetic energy.