Why Is My Rotation Problem Still Unanswered?

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Well, the moment of inertia of a hoop is M*R^2. So the moment of inertia of any portion of a hoop is also M*R^2 where M is the mass of that portion. Why are you making up problems, aren't there enough already? :)
 
But this hoop is not the same axis.

haha, I'm crazy, sorry.
 
Ok. My confusion suggests a picture might be nice. Everything else seems ok.
 

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