A uniform solid circular disk of mass $m$ and radius $R$ is on a flat, frictionless horizontal table. The center of the disk is initially at rest, and the disk is spinning with angular velocity $\omega_0$ about its center. A stone, modeled as a point mass also of mass $m$, is placed on the edge of the disk with zero initial velocity relative to the table. A rim built into the disk constrains the stone to slide, with friction, along the disk's edge. After the stone stops sliding with respect to the disk, the system rotates as a rigid body. What is the magnitude of the horizontal force exerted by the rim on the stone at this time? (Answer in terms of $m$, $R$, and $\omega_0$)