A system consists of a ball of mass

**M**_{2} and a uniform rod of mass

**M**_{1} and length

**d**. The rod is attached to a horizontal frictionless table by a pivot at point P and initially rotates at an angular speed

, as shown above left. The rotational inertia of the rod about point P is

. The rod strikes the ball, which is initially at rest. As a result of this collision, the rod is stopped and the ball moves in the direction shown above right.

Express all answers in terms of

**M**_{1} ,

**M**_{2} ,

,

**d**, and fundamental constants.