The moment of inertia of a solid cylinder is equal to one half of the mass multiplied by the square of the radius. This equation should be used to find the cylinder's moment of inertia with respect to the z-axis, or the plane parallel to the cylinder's height.

The moment of inertia for a cylinder with respect to x-axis is the same as moment of inertia for the y-axis because they both lie in the plane parallel to the cylinder's radius. It's equal to the mass multiplied by the sum of three times the square of the radius and the square of the height, divided by twelve.