We all know that M.I of a Uniform rigid rod about an axis perpendicular to it's length and passing through it's center is MLsquare/12.Where M is mass and L is length of the rod. If it is broken to half such that M becomes M/2 and L becomes L/2,we can't apply ML square /12 formula to it.We have to apply the equation of M.I of rod about an axis passing through one of the ends and perpendicular to the length of it.That is MLsquare/3.If we apply the condition that M/2 and L/2 ,we could get ML square /24. That is exactly half of original moment of inertia. I know well this much. But my confusion begins Suppose a ring of mass M and radius R.We know M.I of it is MR square. But if 90degree sector of it breaks,such that it's mass becomes 3/4M. My Physics teacher says the broken ring's M.I then will be 3/4MR square. My question is,as in the case of rigid rod,when it breaks, we just need another formula to find its MI. Similarly for this too,we have to use another formula right? I have the same problem with circular disk too.