How do I calculate moment of inertia for a disk and ring combination?

[Tom McCurdy]

I was wondering how to start a. If I can get (a) I am pretty sure I can get b and c with not too much trouble

http://www.quantumninja.com/hw/random/problem6.jpg


I am really lost to how to even start this problem

 

[Davorak]

You did to do an integral over the volume $\int \,dm*r^2 \,dv$ where $\,dm$ is just the density of the material. The easiest way to do this I think would be to only do the above integral for one of the 4 quadrates and then times that answer by 4. r for one axes would be x and for the other would be y.

 

[Tom McCurdy]

Ok I think I found the answer

for Moment of Inertia for

$$x= \frac{mab^3}{3}$$

$$y= \frac{ma^3b}{4}$$

Could someone show me how to derive these though??

 

[dextercioby]

How did u find those results...?

Daniel.

 

[Tom McCurdy]

A website... I don't have the url anymore... why is it incorrect?

 

[dextercioby]

So they only gave the results and not how to get them,huh...?It looks weird,because one may expect the same denominator for both.

Daniel.