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 2R rotating anti-clockwisewith angular speed $$\frac{\omega}{2}$$. 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,