Probability — practice question

A rough horizontal rod $AB$ with length $0.45\,\text{m}$ turns at a steady angular speed of $6\,\text{rad s}^{-1}$ about a vertical axis through $A$. A small ring $R$ of mass $0.2\,\text{kg}$ is able to slide along the rod. A particle $P$ of mass $0.1\,\text{kg}$ is fixed at the midpoint of a light inextensible string of length $0.6\,\text{m}$. One end of the string is fastened to $R$ and the other end is fastened to $B$, with angle $RPB = 60^\circ$ (see diagram). As the system rotates, $R$ and $P$ each travel in horizontal circles. $R$ is in limiting equilibrium.