# Moment of inertia tensor of hollow cone

#### dpqb29

I am having trouble right now with the same problem (finding Ixx and Iyy).

I_{yy} = \int(x^2 + z^2)dm

where

dm = \frac{2M}{R^2 + H^2} q dq

and q is my generalized coordinate that is measured from the origin down the length of the cone. I am able to integrate z^2 since it can simply be related to q by

z = \frac{Hq}{\sqrt{R^2 + H^2}} ,

but I am unable to simply relate x to q. I know that
\begin{eqnarray}
\rho^2 = x^2 + y^2\\
\rho = \frac{Rq}{\sqrt{R^2 + H^2}}
\end{eqnarray}
by the way.

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