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Moment of inertia tensor of hollow cone

  • Thread starter dpqb29
  • Start date
1
0
I am having trouble right now with the same problem (finding Ixx and Iyy).
\begin{equation}
I_{yy} = \int(x^2 + z^2)dm
\end{equation}
where
\begin{equation}
dm = \frac{2M}{R^2 + H^2} q dq
\end{equation}
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
\begin{equation}
z = \frac{Hq}{\sqrt{R^2 + H^2}} ,
\end{equation}
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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