# What do I do next after finding the linear velocities?

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A rod of length $l$ falls on two metal pads of same height from a height $h$. The coefficients of restitution of the metal pads are $e_1$ and $e_2$ $e_1>e_2$. The angular velocity of the rod after it recoils is?

Attempt:

I have calculated the velocities after collision to be $e_1\sqrt{2gh}$ and $e_2 \sqrt{2gh}$.
I feel there's certainly going to be rotation but I am not able to calculate the angular velocity. Will the rod rotate about the centre of mass? If yes, why is it so?

Immediately after the collision the line joining the 2 points of contact A, B is initially horizontal. Because end A is moving upwards faster than end B the line AB rotates. The angular velocity $\omega$ of the rod is the rate at which line AB rotates. You can find this from $\omega=(v_A-v_B)/l$ assuming the distance AB is $l$.