What momentum is
Momentum measures how hard it is to stop a moving object. It combines mass and velocity:
p = m × v
with mass in kilograms and velocity in meters per second, giving kg·m/s. A heavy truck and a fast baseball can both carry a lot of momentum.
Impulse and stopping force
To change momentum, a force must act for some time. The impulse equals the change in momentum:
F × t = Δp
So the average force needed to stop an object is F = p ÷ t. Stopping over a longer time means a smaller force, which is the idea behind airbags, crumple zones, bike helmets and bending your knees when you land.
Worked example
A car weighing 3,300 lb (1,497 kg) travels at 30 mph (13.4 m/s) and brakes to a stop in 3 seconds.
- Momentum: 1,497 × 13.4 = 20,075 kg·m/s.
- Kinetic energy: ½ × 1,497 × 13.4² = 134.6 kJ.
- Average stopping force: 20,075 ÷ 3 = 6,692 N, about 1,500 lbf.
- Average deceleration: 13.4 ÷ 3 = 4.47 m/s², or 0.46 g.
In a crash that stops the car in 0.1 second, the average force would be 30 times higher, about 200,000 N.
Momentum versus kinetic energy
| Momentum | Kinetic energy | |
|---|---|---|
| Formula | m × v | ½ m v² |
| Type | vector (has a direction) | scalar |
| Doubling the speed | doubles it | quadruples it |
| Conserved in collisions | always, in a closed system | only in elastic collisions |
Conservation of momentum
In a closed system with no outside forces, total momentum stays constant. In a collision between two carts, the momentum lost by one is gained by the other. In an explosion or a rocket launch, parts fly apart with momenta that add up to zero, which is why a gun recoils and a rocket moves forward when it ejects gas backward.
Units
- 1 kg·m/s = 1 N·s.
- In US customary units, momentum can be expressed in slug·ft/s or lb·ft/s, but physics problems almost always use SI units.