# Moment inertia - theoretical problem

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?

Doc Al
Mentor
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?

Doc Al
Mentor
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.

1 person
Sorry for the late reply. I did it!! :D Thanks a lot.

Doc Al
Mentor
Sorry for the late reply. I did it!! :D Thanks a lot.
:thumbs: