# Moment of inertia tensor about y-axis of a cylinder.

1. May 12, 2013

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

What must the ratio of height to radius of a cylinder be so that every axis
is a principal axis (with the CM as the origin)?

2. Relevant equations

Moment of inertia tensor.
I need I_yy = $\sum m *(x^2 + z^2)$

3. The attempt at a solution

I calculated I_zz = MR^2 /12 . Now I change the principal axis to y-axis. I need to determine the moment of inertia tensor of it. Polar coordinates won't work. If I go for cartesian, I do not know the limits for the dx.

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2. May 12, 2013

### TSny

You can perform the integral using cylindrical coordinates $\vec{r} = (r\cos\theta, r\sin\theta, z)$.

3. May 13, 2013

### TSny

Also, the result for $I_{zz}$ is not correct. You should get a different factor than 12 in the denominator.