The Parallel Axis Theorem
If the moment of inertia of a body of mass M about an axis through its centre of mass is
then the moment of inertia of the body about a parallel axis at a distance
from the first axis is
Proof
The moment of inertia about axis Az is given by :
|Separate into distinct integrals
The coordinates of the centre of mass are
and
and
as the axes are chosen so that the centre of gravity lies on the z axis so
From the diagram
and
and substituting in the equation for I, we have:
