Moment inertia - theoretical problem

AI Thread Summary
The discussion centers on calculating the moment of inertia for a hollow cylinder with inner radius a and outer radius b, specifically for its center axis. Participants suggest using the known formula for a solid cylinder and modifying it for the hollow case by considering it as a composite of two overlapping cylinders. There is a focus on the importance of correctly accounting for mass in the calculations. One user expresses initial confusion about using definite integration but ultimately finds a solution. The thread concludes with a successful resolution to the problem.
silenzer
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Moment inertia -- theoretical problem

Homework Statement



Show that the moment inertia of a hollow cylinder with inner radius a and outer radius b is (1/2)*M*(a^2+b^2), calculated for the center axis.

Homework Equations



I know that the moment inertia of a non-hollow cylinder is I = (1/2) MR^2, but I don't know the moment inertia of a hollow one.

I = MR^2, generally.

Krotation = (1/2)Iw^2

The Attempt at a Solution



I'm not entirely certain on where to start. Should I split the cylinder into two parts and work from there?
 
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silenzer said:
Should I split the cylinder into two parts and work from there?
Yes. Consider overlapping cylinders. Subtract!

Be careful with the mass.
 
I'm sorry but I'm still having problems... I googled the problem and all of the solutions use definite integration. Can I solve this problem without using that?
 
silenzer said:
I'm sorry but I'm still having problems... I googled the problem and all of the solutions use definite integration. Can I solve this problem without using that?
All you need to know is the formula for the moment of inertia of a solid cylinder--which you already know.

Hint: For a composite body with parts a and b, Itotal = Ia + Ib.
 
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Sorry for the late reply. I did it! :D Thanks a lot.
 
silenzer said:
Sorry for the late reply. I did it! :D Thanks a lot.
:thumbs:
 
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