Perpendicular axis theorem

Perpendicular axis theorem

Statement : Moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of moment of inertia about two mutually perpendicular axis concurrent  with perpendicular axis and lying in the plane of laminar body.

I_z = I_x + I_y

Figure A

As shown in fig A, consider a plane lamina body which can rotate about three mutually perpendicular axis x, y, z  respectively. Consider a particle of mass dm situated at point Q. Let us find out moment of inertia of the body about any axis.

Mathematically,

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