$19-70*$ Two $2-$kg balls A and $B$ are connected by a lightweight, rigid, $400-mm$ long rod that is free to rotate in the $xy-$plane about a ball$-$andsocket at $O$ as shown. The rod is initially stationary. If a $2-kg$ ball with a velocity of $5j\frac{m}{s}$ collides with ball $A($the collision is perfectly plastic, $e=0)$ and causes the system of three balls to rotate about the $z-$axis, determine the angular velocity of the rod immediately after the collision.