A stationary bar of mass M and length L is mounted to a hori

A stationary bar of mass M and length L is mounted to a horizontal table on a vertical axle through its center. A sticky ball of mass m is thrown horizontally with a speed v and sticks to the bar at the edge.

a. What is the angular velocity of the bar after the ball sticks to it? Below is the top view of this situation.

b. What is the angular velocity of the bar after the ball sticks to it if the axle passes through the edge of the bar instead?

Solution

\"I think its a conservation of energy problem\"
That\'s the easiest approach I see.

mg(L/2) = (1/2)I²

I = m(L/2)² + (1/12)ML²
I = L²[m/4 + M/12]

mg(L/2) = (1/2)L²[m/4 + M/12]²
² = g / {L[1/4 + M/(12m)]}