How Do You Calculate the Moment of Inertia for a Cone?

[RivalDestiny]

Homework Statement

A cone with height h and radius R. The radius R is located at the top of the cone. We have to find moment of inertia of the cone. The disc has a radius r, height of dz, and is located z below the circular surface with radius R.

Homework Equations

$$dI = \frac{1}{2}\ dm\ r^2$$

dm=pdV

The Attempt at a Solution

I found dV first

dV = Area * dz
dV= pi*r^2 * dz

dm=p(pi*r^2*dz)

then I found r using ratios:

r/R=z/h
r=Rz/h

Substitued into

$$dI = \frac{1}{2}\ dm\ r^2$$

I don't know what to do after I sub them all in...This is the first time I've looked at these sort of problems.

 

[rock.freak667]

Try reading this thread, it might help you

https://www.physicsforums.com/showthread.php?t=269934"

In which I don't remember how to do it without a triple integral.