Finding the momentum after a collision

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

A ball is attached to one end of a rod. A second ball hits the ball with velocity u. The collision is inelastic and both balls after the collision travel together with a new velocity v.
The rod is attached to the ceiling at a point with no friction. The moment of inertia for the rod is known and the mass of the rod is known and its length is L. The mass of the two balls are each known.

Find an expression for the momentum before and after the collision.

2. Relevant equations

3. The attempt at a solution
I know how to find the momentum for the balls by simply multiplying their speed with their mass.
My problem is with the rod. I’m not sure how to implement the rod so that I can use this in the equation for momentum. I know that I’m supposed to use the velocity at the center of mass but how do I calculate the velocity of center of mass?

[itex]v_{cm}=\frac{m_{ball1}v_{ball1}+m_{ball2}v_{ball2}+m_{rod}\cdot?}{m_{ba ll1}+m_{ball2}+m_{rod}}[/itex]

You see, I’m not sure what velocity to use for the rod when calculating the velocity of the center of mass.

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