According to the parallel axis theorem, a moment of inertia of a body about any axis is equal to the sum of the moment of inertia about a parallel axis through the centre of gravity and the product of the mass of the body and the square of the perpendicular distance between the two axis.
Let Ic be the moment of inertia of a body of mass M about an axis (PQ) passing through the centre of gravity C. According to the theorem moment of inertia of a body an axis AB is I = lc + Mr2 According to the theorem on perpendicular axis, the moment of inertia of a plane about an axis perpendicular to the plane is equal to the sum of the moment of inertia about two perpendicular axes in the plane of the lamina such that the three mutually perpendicular axes have common point of intersection.
If IX, IY and IZ represent the moment of inertia of the body about the axes OX, OY & OZ, then according to perpendicular axes theorem IX + IZ = IY.
