A thin, flat, uniform disk has mass M and radius R_ A circular hole of radius R/4, centered at a point R/2 from the disk's center, is then punched in the disk.
(a) Find the moment of inertia of the disk with the hole about an axis through the original center of the disk, perpendicular to the plane of the disk. (Hint: Find the moment of inertia of the piece punched from the disk.)
(b) Find the moment of inertia of the disk with the hole about an axis through the center of the hole, perpendicular to the plane of the disk.