Systems of Many Particles in Physics

Once a system holds more than a couple of parts, tracking each one becomes hopeless, so the trick is to stop trying. All of its momentum still sits in one place, at the center of mass, and if nothing pushes in from outside then that single value cannot change, however violently the parts rearrange themselves inside. This is why an explosion and a collision are the same problem in reverse. The blocks give that pooled momentum, the conservation statement that follows from it, and the two relations that describe a rocket, which is simply a system that throws part of its own mass away to move.