Momentum Calculator
Momentum measures how hard something is to stop. It combines mass and velocity, and in any closed system the total is conserved.
Formula
p = m × v
- p in kg·m/s, m in kilograms, v in metres per second
- Impulse: F × t = change in momentum
1,500 kg at 20 m/s: 30,000 kg·m/s
The Formula
p = m × v
Momentum in kilogram metres per second, mass in kilograms, velocity in metres per second.
A 1,500 kg car at 20 m/s carries 30,000 kg·m/s. A 10 g bullet at 400 m/s carries just 4 kg·m/s — despite the speed, the mass difference dominates.
Momentum is a vector: direction matters, and opposing momenta cancel.
Conservation in Collisions
In a closed system, total momentum before a collision equals total momentum after. This holds whether the objects bounce apart or stick together.
It is why a rifle recoils: the forward momentum of the bullet is matched by backward momentum of the rifle. The rifle moves slowly only because it is far more massive.
Momentum Versus Kinetic Energy
Both involve mass and velocity, but they scale differently. Momentum is proportional to v; kinetic energy to v².
Doubling speed doubles momentum but quadruples energy. A 1,500 kg car at 30 m/s carries 675 kJ; at 60 m/s it carries 2,700 kJ. That is why stopping distances grow so sharply with speed, and why crashes at motorway speeds are so much worse than the speed difference suggests.
Momentum is always conserved in collisions; kinetic energy is only conserved in perfectly elastic ones, which real crashes are not.
Quick Reference
| Object | Mass | At 10 m/s | Force to stop in 1 s |
|---|---|---|---|
| Tennis ball | 0.058 kg | 0.58 kg·m/s | 0.58 N |
| Cyclist and bike | 90 kg | 900 kg·m/s | 900 N |
| Small car | 1,200 kg | 12,000 kg·m/s | 12,000 N |
| Lorry | 20,000 kg | 200,000 kg·m/s | 200,000 N |
Frequently Asked Questions
- How do I calculate momentum?
- Multiply mass by velocity. A 1,500 kg car travelling at 20 m/s has 30,000 kg·m/s of momentum.
- What is conservation of momentum?
- In a closed system, total momentum before an event equals total momentum after it. It holds in every collision, whether objects bounce apart or stick together.
- What is the difference between momentum and kinetic energy?
- Momentum scales with velocity, kinetic energy with velocity squared. Doubling speed doubles momentum but quadruples energy.
- Why does a gun recoil?
- Conservation of momentum. The bullet's forward momentum is matched by equal backward momentum in the gun, which moves slowly because it is much heavier.