Quantum theory has taught us that virtually everything to do with the nature of matter in the universe is a random process. The decay of atomic nuclei is something that makes that randomness "visible" with appropriate instrumentation. As such, the rate of decay will vary over the "short" term. Consequently, it is not surprising to see a variation of a few counts in an activity measurement over a period of a few minutes.
__
Safety with respect to radioactive materials involves staying as far away from them as possible. The use of long tongs for handling would be appropriate.
In a system with no energy loss, momentum is conserved if the mass remains constant. The system described has no change in mass, and energy loss is considered negligible. Hence the product of the total mass and the velocity of its center will be a constant. The center of mass stays the same speed.
