Consider a frictionless plane. A particle of known mass and velocity (say a lump of clay) strikes a uniform rod (for simplicity let the rod be stationary in the lab frame) and sticks to it somewhere other than at the rod's center of mass. I wish to describe the linear and angular velocity of the particle-rod system after the collision. In the absence of an external force, the center of mass of the particle-rod system continues with the same velocity despite the collision. I presume then that the particle-rod system will begin to rotate about its center of mass with angular momentum equal to r x p, with p being the initial momentum of the particle and r the moment arm from the cm to point of contact. I'm almost certain this can't be right since angular momentum of the system about its cm ought to be conserved also--and in this case that initial angular momentum is zero. Further, it would seem that I've made the kinetic energy of the post collision system dependent on the point the particle strikes the rod. I think I'm confused with something very fundamental here. Any help would be greatly appreciated.