# Moment of inertia of a cone

1. Oct 22, 2008

### ehilge

1. The problem statement, all variables and given/known data

Calculate the moment of inertia of a uniform solid cone about an axis through its center. The cone has mass M and altitude h. The radius of its circular base is R. (see attached photo)

2. Relevant equations
I know I need to somehow use the equation I= intergral r^2 dm
also, I have an equation from my proffessor, dm=rho dv I'm not sure if I need this though since its unifrom density so it doesn't seem like $$\rho$$ should matter.

3. The attempt at a solution
I don't have a solution right now. I know the answer is 3/10 MR2 but I don't know how to get there. From class, since we did some examples, I think I need an equation that has a triple integral in it but I don't know what to integrate and to where. Do I need to get dm in terms of something like d$$\vartheta$$, dr, and dh?

Thanks for your help. Also, if you have any general suggestions on how to complete moment of inertia problems like this that would be great. I know we're gonna be doing a lot of them.

Thanks again!!!

Last edited: Oct 22, 2008
2. Oct 23, 2008

### hage567

Yes dm = $$\rho$$dV will be used. Have you tried setting up dV in cylindrical coordinates? Then try to look for your limits of integration.