How do we know that moment of inertia cannot exceed MR2 for a solid body like solid cylinder, solid sphere, hollow sphere etc? R is the radius of the object in consideration. I know it has something to do with- that for solid bodies (in some cases hollow also) there are a lot of point masses in the body which are not at a distance of R from the axis of rotation. They are closer (less than R) to the axis of rotation than the point masses on the boundary of the body (at a distance of R from the body). Still, how does it prove that in such cases the moment of inertia would be less than MR2? ∑miri = or So how do the above two equations show that if there are masses which are located at a distance of less than R from the axis of rotation then the moment of inertia would be less than MR2?