Rigid Body
Two identical particles of the mass

are connected to the
two ends of a rigid massless rod of the length

. The system
initially rotates around the center-of-mass with the angular
velocity

. One of the particles encounters a third one (with
the same mass) at rest, which momentarily sticks to it. What is the
angular velocity of the rotation around the center-of-mass after the
collision ? (No gravity.)