Determine the direction and magnitude of the rotational velocity w which will leave the relative position of the three stars unchanged. The sphere and step are perfectly rough and inelastic. An infinitely massive wedge of fixed angle a has a rough horizontal surface and a smooth inclined surface. A uniform solid sphere of radius a and mass m , spinning with an angular velocity w 0 about a horizontal axis normal to the plane of the paper, is gently placed in contact with the wedge as shown in the figure. The coefficient of sliding friction between the sphere and the horizontal surface is m and is 0 for the smooth inclined surface.
Gravity acts vertically downward.
You may answer this question qualitatively, but more credit will be granted for a quantitative solution.