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## Homework Statement

Suppose, a rod of negligible mass has two balls(A & B) at its two ends. Both the balls have same mass m. The rod is rotating around its center C with a uniform angular velocity ##\omega##. Another ball D (mass M) has a velocity v. At some time, A and D collide with each other. Now, how to apply the law of momentum conservation in this case? (The actual problem was different. But I need to understand how to apply the law of momentum conservation in such case.)[/B]

## Homework Equations

## The Attempt at a Solution

In this case, there are both linear and angular momentum. That confuses me.

Let the length of the rod be 2R.

And the final angular velocity of the rod is ##\omega _f## and final velocity of D is ##v_f##;

Now, I thought,

## m \omega R - m \omega R + Mv = m \omega _f R - m \omega _f R + Mv_f##

So, it becomes, ## v = v_f ##

But, it's not true.