The Perpendicular Axis Theorem
If
and
are the moments of inertia of a lamina about two perpendicular axes
and
in the plane of the lamina, that
is the moment of inertia of the lamina about a third axis
through 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 is
The moments of inertia about diameters in the
and
direction are the same by symmetry.
