A small ball of mass \(m\) moves horizontally with speed \(v\) toward a uniform thin rod of mass \(M\) and length \(L\) that is hanging vertically from a frictionless pivot attached to the ceiling. The ball strikes the bottom end of the rod and sticks to it. During the collision, the ball-rod system is analyzed.

Which of the following correctly describes the conservation of linear momentum and the conservation of angular momentum about the pivot for the ball-rod system during the collision?