Question

Imagine a spinning disk of uniform density, with mass M and radius R. Except where noted, it is rotating about an axis through its center and perpendicular to its plane. What is its moment of inertia if the axis of rotation is moved to a line 2R from the center of the disk? (There’s no rotation of the axis, it remains parallel to its original position).

Could someone explain what this question is asking in a diagram?

Answer 1

Mass of disk= M

Radius of disk=R

Mass moment of inertia about the axis passing through the centroid of the disk perpendicular to the disk=0.5MR²

But, the new axis is shifted by 2R

Therefore, the probelm can be solved using parallel axes theorem

Distance between center of mass of disk and the new axis=2R

Moment of inertia about new shifted axis from parallel axes theorem=0.5MR²+M*(2R)²=4.5MR²

This is the required answer