How to find the moment of inertia of a cube?

[geekie weekie]

Hello,

If I have a rigid cube rotated about an axis with dimensions L x W x H centimeters, how can we find the moment of inertia?

Thank you.

 

[Jolb]

You can calculate the moment of rotational inertia of a body rotating about an axis passing through a point $P$ using the formula:$$I_P = \int_V \rho(\mathbf{r})\,\mathbf{r}^2 \, dV$$ where $\mathbf{r}$ is the radius vector to a point in the body from the axis passing through $P$. See here: http://en.wikipedia.org/wiki/Moment_of_inertia

You can often look up the moments of inertia for some typical bodies rotating around typical axes:
http://en.wikipedia.org/wiki/List_of_moments_of_inertia