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The Perpendicular Axis Theorem for a Lamina

The Perpendicular Axis Theorem

Ifandare the moments of inertia of a lamina about two perpendicular axesand in the plane of the lamina, thatis the moment of inertia of the lamina about a third axisthrough the point of intersection perpendicular to the lamina, then

Proof

and

The moment of inertia of a disc about an axis through the centre perpendicular to the disc isThe moments of inertia about diameters in theanddirection are the same by symmetry.