Momentum: conservation, impulse, and collisions
One conservation law solves every collision and explosion you'll be set. Here's momentum, the impulse that changes it, and the difference between elastic and inelastic that decides what's conserved.
Momentum is the quantity that makes collisions solvable. Forces during a crash are violent and unknown, but momentum sidesteps them entirely with one of the most powerful ideas in physics: a conservation law.
What momentum is
Momentum is mass times velocity — a vector, so direction matters and signs count. A heavy slow lorry and a light fast bullet can carry the same momentum. Unit: kg·m/s.
Conservation of momentum
In any collision or explosion, if no external force acts, the total momentum before equals the total momentum after.
This is the master equation. For two objects:
It works for collisions and explosions. In an explosion the total starts at zero, so the pieces must fly apart with momenta that cancel — which is exactly why a gun recoils backwards as the bullet goes forward.
Impulse: what changes momentum
A force acting over a time changes momentum, and that change is the impulse:
This explains safety design beautifully. A crumple zone or an airbag extends the time of a collision, and since the change in momentum is fixed, a longer time means a smaller force. Same , gentler stop.
Elastic vs inelastic — what else is conserved
Momentum is always conserved. Kinetic energy is the variable:
| Collision | Momentum | Kinetic energy |
|---|---|---|
| Elastic | Conserved | Conserved (bounces perfectly) |
| Inelastic | Conserved | Not conserved (some lost to heat/sound) |
| Perfectly inelastic | Conserved | Objects stick together and move as one |
Choose a positive direction and label every velocity with a sign. Momentum is a vector; an object moving left carries negative momentum. The single biggest source of wrong answers here is treating speeds as if direction didn't matter.
Last revised 28 May 2026.