Explosions and Recoil

Think of a system at rest, then something inside it pushes the parts apart: a rifle firing a bullet, a spring release, two skaters shoving off each other. Before the push, total momentum is zero because nothing is moving. Newton's third law says the forces the pieces exert on each other are equal and opposite at every instant, and those forces act for the same amount of time, so the impulses are equal and opposite too. Equal and opposite impulses mean equal and opposite changes in momentum. Add the final momenta of the two pieces together and they cancel, so total momentum is still zero after the push. Nothing about the internal push can change the total, only external forces could do that, and there usually aren't any during the brief moment of the explosion.

Momentum balances because it is a vector: one piece's momentum points left, the other's points right, equal in size, and they cancel in the sum. Kinetic energy cannot cancel that way because it only takes positive values. Before the explosion there is no motion, so kinetic energy is zero. After, both pieces move, so total kinetic energy is positive. That energy came from somewhere real: compressed gas, a stretched spring, a chemical reaction, stored potential energy converted into motion.

This sits right next to ordinary collisions in the unit, but runs the film backward: instead of two objects merging or bouncing and losing kinetic energy, one object splits and gains it. The same momentum bar charts and conservation setup apply either way, just with energy flowing the opposite direction.