Moment of Inertia of a partial disk

[abertram28]

Let me first start by saying that this problem is a challenge problem and the due date has passed (friday). ive still been working on it because it stumped me. in my physics class we did some integration based inertia problems. my calculus isnt all that great so its a bit tough for me. what i did understand was finding the moment of inertia of the rod through calculus. and i followed along to see the moment of inertia of a disk through the axis of revolution. it was a bit confusing on using dTheta instead of a dx and dy.

the teacher asked us to show the moment of inertia of a disk missing one sixth. so i guess the new limits of integration of the dTheta part are going to go from 0 to 5pi/3? is that it? no parallel axis theorem?

if you reply, please try to have a little understanding that my math lags behind my physics a bit. sorry bout that, im taking a strong math semester next to make up for it.

[Gokul43201]

the teacher asked us to show the moment of inertia of a disk missing one sixth. so i guess the new limits of integration of the dTheta part are going to go from 0 to 5pi/3? is that it? no parallel axis theorem?
Correct !

I = \int {\rho (\vec{r})r^2dV
and in cylindrical co-ordinates you have :

dV = r dr d\phi dz