A large 3-lb sphere with a radius r = 3 in. is thrown into a light basket at the end of a thin, uniform rod weighing 2 lb and length L = 10 in. as shown. Immediately before the impact the angular velocity of the rod is 3 rad/s counterclockwise and the velocity of the sphere is 2 ft/s down. Assume the sphere sticks in the basket. Determine after the impact
(a) the angular velocity of the bar and sphere,
(b) the components of the reactions at A