Question

A solid cylinder and a hollow cylinder of the same mass and radius, both initially at rest, roll down the same inclined plane without slipping.

How do their rotational kinetic energies about the center of mass compare at the bottom?

If the plane were frictionless which would reach the bottom first?

Answer 1

this is what i put

a) The solid cylinder, the moment of inertia of a hollow cylinder is I = mr^2, and if a solid cylinder is I = 1/2 mr^2.
B) Since both objects started with the same potential energy, both have the same total kinetic energy at the bottom. But since both objects have the same mass and the hollow cylinder is moving slower, the hollow cylinder has the smaller translational KE and thus the greater rotational KE.

Answer 2

c) the solid one

Answer 3

The second part: both would reach the bottom at the same time as they would not have to rotate, just slide down (assuming equal air resistance).