Why does the point mass and the ring have the same formula for computing the moment of inertia

Question

Why does the point mass and the ring have the same formula for
computing the moment of inertia?

 

 

formula: MR²

Answer 1

All that matters is how far the mass is located from the axis of rotation.  For both the point mass M at a distance R from the axis, and a ring of mass M and radius R, all of the mass is at the same distance R from the axis, so the moment of inertia will just be MR^2 in both cases.  The same is true of a hollow cylinder of radius R and mass M with both ends open.  It too will have a moment of inertia of MR^2.