Parallel axis theorem - According to this theorem the moment of inertia of a rigid body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass and square of the perpendicular distance between the two parallel axes.

Ix= Moment of inertia of the body about X axis.

Ix¹=  Moment of inertia of the body about X¹ axis.

Both the axes Ix and Ix¹ are parallel to each other, the Ix passing through the body of mass M and the distance between both the parallel axes is a.

Then, Ix¹= Ix+Ma²

Perpendicular axis theorem- According to this theorem the moment of inertia of a plane lamina (A two dimensional body) about an axis is perpendicular to its plane is equal to the sum of the moments of inertia about any two mutually perpendicular axes in the plane of the lamina and concurrent with the perpendicular axis.

Ix= Moment of inertia of the body about axis X in the plane of the lamina.

Iy= Moment of inertia of the body about axis Y in the plane of the lamina.

Iz=Moment of inertia of the body about axis Z which is perpendicular to the plane of the lamina.

Then, Iz=Ix+Iy