Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?

Why is it easier to rotate a disc than a ring of the same mass and size, about an axis passing through their centres?

The moment of inertia of a solid sphere of density rho and radius R about its diameter is given by :

Find the expression for moment of inertia of a thin uniform rod about an axis passing through its centre and perpendicular to its length

Find the moment of inertia of a thin circular ring about an axis passing through the centre and perpendicular to the plane of the ring

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

Find the expression for moment of inertia of a thin uniform rod about an axis passing through its one end and perpendicular to its length.

Three thin metal rods,each of mas M and length dL,are welded to form an equilateral triangle.The moment of inertia of the composite structure about an axis passing through the centre of mas of the structure and perpendicualr to its plane is :