Moment of Inertia--Spherical Shell -- from Eric Weisstein's World of Physics

The moment of inertia of a sphere of uniform density and radius R is

so the moment of inertia of the shell created by removing a small sphere from within a big one is

But

so

Define

and assume that , so (5) can be expanded in a series. Therefore,

Moment of Inertia, Moment of Inertia--Sphere