Solution
= Solution
The total hoop charge is $Q=2\pi R\eta$. One revolution takes $2\pi/\omega$, so the current is
$$
I=\frac{Q\omega}{2\pi}=\eta R\omega.
$$
Multiplying by the enclosed area gives
$$
\boxed{m=I\pi R^2\hat n
=\pi\eta\omega R^3\hat n}.
$$