So the moment of inertia or a ring is MR2 I dont understand why. Here is my reasoning Consider this shape (the ball is a point), the moment of inertia is MR2, there I agree but now what happens when you add another point on the other side since I = ΣMR2 then this is 2MR2 What about a ring or circle, that is nothing more than a bunch of points all the same distance from the center so how many points are there? The circumference so I= πR2MR2 I know that different objects moment of inertia differ by a number in front, like 1/2 or 3/5 Why is their no number prefix for Inertia in front of the formula for a hoop/ hollow cylinder/ circle that represents its circumference? How is this even derived? Second question, How do you represent the angular Kinetic energy of this object? Left Point = A Right point = B ½ I ωA2 + ⅓ I ωB2 ½ I ( ωA2+ωB2 ) both objects have same ω so ½ I 2ω2 Or do I use ω to represent the angular velocity of the whole object and just keep it as ½ I ω2 with whatever I is from the previous question?