# Inelastic collision between ball and rotating system.

**1. The problem statement, all variables and given/known data**

A homogenous, thin stick with the mass m and the length l is hanging from the ceiling and can rotate freely around the point P.

A small ball with the mass of M is attached to the end of the stick.

The small ball on the end of the stick gets hit by another small ball with the mass of M in a completely inelastic collision. Before the two balls hit, the ball not touching the stick is moving with the speed of u.

What is the sum of the angular momentum before and after the collision?

**2. Relevant equations**

The moment of inertia for the stick itself is I = 1/3*m*l^{2}.

I figured the total moment of inertia for the system after the balls collide would be (1/3*m+2M)*l^{2}.

**3. The attempt at a solution**

My initial attempt was to simply say that "Conservation of angular momentum must mean, that since the ball initially has the angular moment L = l*M*u around the point P. Therefore the resulting angular momentum must be equal that."

I however realized that I didn’t understand what I was answering.

From this: http://ift.tt/1k8tZPR

I found that the linear AND angular momentum must be conserved, but since the ball moves in exactly the same direction as it’s angular momentum and the resulting system not moving in the direction of u, what happened to the linear momentum?

Of course, I would’ve happily solved it myself and found my own solution to these questions, but I am at a loss.

http://ift.tt/1k8u2el

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