Conservation of Momentum

A small mass is thrown with a velocity of \(\SI[per-mode=symbol]{2}{\meter\per\second}\) toward a rod, a distance of \(\ell/3\) from its center. The rod is hinged at the centre.

You are given that the mass is \(\SI{6}{\kilo\gram}\), and its length \(\ell = \SI{3}{\meter}\) and the mass of the small object is \(\SI{3}{\kilo\gram}.\) Upon collision, the small mass sticks to the rod.

Find the angular velocity of the rod after this impact (in \(\si[per-mode=symbol]{\radian\per\second}\)).

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