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I know I need to find each individual pieces' moment of inertia, using (0.5)mr^2, (0.5)m(r1^2 +r2^2). I don't know how to find the shaft's moment of inertia though...

And for the angular velocity, do you need to find each pieces separate angular velocity and add them together or do you just need it once because they would all be the same...?

See, I tried finding the answer using just the moment of inertia of the ring and the thin disk (cover) but I got a very very small number....