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?