Question #42953

A rigid, non-conducting rotor with moment of inertia $I_0 = 2mR^2$ about its axis of rotation is constrained to rotate freely about the $z$-axis in the horizontal plane $z = R$. A fixed magnetic dipole of magnetic moment $\vec{M} = M_0 \hat{k}$ is located at the origin. Two small beads, each of mass $m$ and charge $+q$, are initially held at the center of the rotor (on the $z$-axis). The entire system is initially rotating with an angular velocity $\omega_0 \hat{k}$. The beads are then released and slide symmetrically outward along the rotor. They come to rest relative to the rotor at its ends, at a radial distance $R$ from the $z$-axis. Assuming no mechanical friction opposes the rotation of the rotor, find the final angular velocity $\omega_f$ of the system.