Conservation of momentum

Newton's third law has a consequence so useful it gets its own name. When two objects interact, the forces they exert on each other are equal and opposite. Add up what those forces do over the time of the interaction, and something remarkable falls out: whatever momentum one object loses, the other gains — exactly.

Define the momentum of an object as the product of its mass and velocity:

Now consider two carts on a frictionless track. During a collision, cart A pushes on cart B with force F⃗, and by the third law, B pushes back with −F⃗. Both forces act for the same duration Δt, so the impulses cancel and the total momentum cannot change:

Notice what we did not assume: nothing about the kind of collision, the materials, or whether kinetic energy survives. Momentum conservation holds for bouncing superballs and crumpling cars alike — it needs only the third law and the absence of external forces. That generality is why it's often the first tool a physicist reaches for.