Law of Conservation

Question

A rocket is standing by to launch. While sitting on the launching pad the rocket has zero velocity and thus zero initial momentum (p1=0). When the rocket takes off, a bystander proclaims that the law of conservation is broken because the initial momentum of the rocket was zero, but now that it is moving, the final momentum of the rocket is not. Explain whether or the bystander is correct.

Answer 1

To add just a bit to Arturo's splendid answer, the only condition required for conservation of momentum is that no net external force act on the system of interest.  If we were to consider ONLY the solid rocket body and the unexpended fuel as the system, then we would not expect momentum to be conserved, because a net external force acts on that system.  That force comes from the expelled gases pushing (in a Newton's third law scenario) against the rocket.  This is why the rocket, and unexpended fuel, move upward.  But, if we rope the expelled gases into the system with the rocket, then the process of them and and the rocket pushing on each other becomes internal, and we consider no NET EXTERNAL force to have acted on the system in the moment (gravity technically does, but that does not change the conclusion over the instant being considered).  Therefore, as Arturo succinctly stated, the total momentum of the rocket and expelled gases system will remain zero.

Answer 2

The bystander is wrong.  The total momentum of the rocket SYSTEM, which is the rocket body plus propellant, is still zero, and hence conserved.  While the rocket body with unexpended propellant is moving upward, expended propellant is moving downward, with equal and opposite momentum, maintaining a net momentum of zero for the whole system even as parts of the system fly out in opposite directions.