QP12

A small marble of mass M is placed in a hemispherical bowl of radius R as shown in the figure. If the bowl is spun (around its vertical axis) with the constant speed , the marble eventually settles at a distance r₀ from the axis.

 

(3 points)  (a) Find the magnitude and the angle with respect to the vertical axis of the force exerted by the bowl on the marble.

(2 points)  (b) Find r₀ as a function of .

(2 points) (c) Note that if is too small, the answer to part (b) does not make sense. What happens if the angular velocity is too small?