Theorem of Perpendicular and Parallel Axis

Theorem of Perpendicular Axis:

According to this theorem, the Moment of inertia of a body about an axis perpendicular to the plane of the body is the sum of the moments of inertia of the body any two mutually perpendicular axes both lying in the same plane.

Moment of inertia along Z = Moment of inertia along Y + Moment of inertia along X

This statement can be proved as follows:

Theorem of Parallel Axis:

According to this theorem, moment of inertia of a body about any axis in its plane and parallel to an axis passing through the centre of mass of the body is equal to its moment of inertia about an axis passing through the centre of mass of the body plus the product of the mass and distance between the axes squared.

Moment of inertia(about any axis) = moment of inertia (along the centre of mass) + (mass of the body  ✕ (distance from the centre of mass)²)

This can be proved as follows: