Question
From a circular disc of radius R and mass 9M, a small disc of radius R/3 is removed from the disc as shown in figure. Find the moment of inertia of remaining disc about an axis perpendicular to the plane of the disc and passing through center.
Solution
The moment of inertia of complete disc about a perpendicular axis passing through center O is,
The mass of cut out disc if radius R/3 is,
Now, using the theorem of parallel axis, the moment of inertia of cut out disc about the perpendicular axis passing through center O is,
The moment of inertia of residue disc is,
The mass of cut out disc if radius R/3 is,
Now, using the theorem of parallel axis, the moment of inertia of cut out disc about the perpendicular axis passing through center O is,
The moment of inertia of residue disc is,
