In physics, the perpendicular axis theorem (or plane figure theorem) can be used to determine the moment of inertia of a rigid object that lies entirely within a plane, about an axis perpendicular 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 in the plane.
Define perpendicular axes
This rule can be applied with the parallel axis theorem and the stretch rule to find moments of inertia for a variety of shapes.
If a planar object (or prism, by the stretch rule) has rotational symmetry such that
Derivation
Working in Cartesian co-ordinates, the moment of inertia of the planar body about the
On the plane,
Note that