Moment of Inertia

A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia, ______

From a disc of radius R a mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through it?

Mention any two physical significance of the moment of inertia.

What is the radius of gyration?

Derive the expression for the moment of inertia of a rod about its centre and perpendicular to the rod.

Derive the expression for the moment of inertia of a uniform ring about an axis passing through the centre and perpendicular to the plane.

Derive the expression for the moment of inertia of a uniform disc about an axis passing through the centre and perpendicular to the plane.

State and prove parallel axis theorem.