The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed $\omega$ and (ii) an inner disc of radius 2 R rotating anti-clockwise with angular speed $\omega / 2$. The ring and disc are separated b frictionaless ball bearings. The system is in the x-z plane. The point $P$ on the inner disc is at distance $R$ from the origin, where OP makes an angle of $30^{\circ}$ with the horizontal. Then with respect to the horizontal surface,