conservation of momentum

Here is one of the most reliable rules in all of physics: in a group of objects left to interact among themselves, the total momentum never changes. Push two ice skaters apart and they glide off in opposite directions; add up their momenta and you get exactly what you started with — zero. Nature keeps the books balanced.

Precisely: if the net external force on a system is zero, the total momentum of the system is constant, p_total before = p_total after. The reason is Newton's third law — every internal push comes in an equal-and-opposite pair, so the forces objects exert on each other cancel when you add up the whole system, leaving the total momentum untouched. Because momentum is a vector, this holds direction by direction: the total in the x-direction is conserved, and separately the total in the y-direction.

This law is the master key to collisions, explosions, and recoil: you rarely know the messy forces during a crash, but you always know that the total momentum afterward equals the total before. The catch is the word 'external' — an outside force such as strong friction or a wall CAN change a system's momentum, so the law applies only to an isolated (closed) system, or over a time so short that outside forces have not yet mattered.