Imagine you had a long heavy rod in space with no significant gravity acting upon it. And a projectile is flying towards it, perpendicular to the orientation of the rod, with the impact some between the centre of mass of the rod and an end of the rod. Upon impact there is no deflection (for whatever reason the bodies fuse together).
Basic preservation of momentum says the centre of mass this fused body will continue to travel in the same direction of the original projectile. But will it also be rotating? And at what rate? If there were a fixed point of rotation I would know how to calculate the rate of rotation. But since it is moving I am confused.