I am considering a problem where there is a rod at rest on a smooth table, and a particle is incident on the end of the rod with some given speed. The particle collides with the rod and sticks to the end of the rod. I am thinking about the subsequent motion of the system. So far, I think:
- The centre of mass of the combined system will now continue at a constant velocity in the same direction as the incident particle, and with a speed such as to conserve the linear momentum.
- Since the centre of mass must continue on at a constant velocity, any rotation, if it occurs, must be about the centre of mass of the new/combined system.
- There must be some rotation because the speed of the particle is reduced. Therefore the incident particle has received an impulse, and must have exerted an impulse on the end of the rod. This would provide an angular impulse about the centre of mass of the system, and therfore there must be rotation about the centre of mass.
However how can this be? The initial angular momentum of the system is zero as there is no rotation, and yet afterwards there is some angular momnetum as the system has rotation. What am I missing here?