A child's toy consists of a small wedge that has an acute angle θ, as shown in the figure. The sloping side of the wedge is frictionless, and an object of mass m on it remains at constant height if the wedge is spun at a certain constant speed.

a. Show that for the object to be at rest with respect to the rotating wedge
at a distance L up along the wedge, the speed of the object must be =√sin.

b. Now assume that the coefficient of static friction between the object and the wedge is μs, and the object is still a distance L up the wedge, but just about to slide down the surface of the rotating wedge. What would be the expression describing the speed v of the object in this case? Would v be smaller or larger than what you found in part a)? Explain why.