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[itex]m=\frac{1}{5}Q \omega a^2[/itex]. the question doesn't say but i'm assuming a is the radius.

Anyway, so far I have:

[itex]m=\frac{1}{2} \int_V dV (\mathbf{r \wedge J})[/itex]

but [itex]\mathbf{J}= \rho \mathbf{v} = \rho \mathbf{\omega \wedge r}[/itex]

and so [itex]m=\frac{\rho}{2} \int_V r^2 \mathbf{\omega} - (\mathbf{r \cdot \omega})\mathbf{r}[/itex]

but i don't really know where to go from here?