Perpendicular axes rule

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In physics, the perpendicular axes rule can be used to determine the moment of inertia of a rigid object, which lies entirely within a plane, about an axis at right angles to the plane, given the moments of inertia of the object about two perpendicular axes lying within the plane. The axes must all pass through a single point on the plane.

Let I be the moment of inertia of the object about the axis perpendicular to the plane within which the object lies through a point O, IX be the moment of inertia of the object about an axis within the plane through O and IY be the moment of inertia of the object about the axis within the plane perpendicular to IX through O. Then the moment of inertia about the new axis through O is given by:

I = IX + IY

This rule can be applied with the stretch rule and parallel axes rule to find moments of inertia for a variety of shapes.

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