Momentum Explained With Examples
Momentum explained simply: p = mv, conservation of momentum in collisions and explosions, impulse and why crumple zones and airbags work, with worked examples.
Key takeaways
- Momentum is mass times velocity: p = mv, measured in kg·m/s.
- In a closed system, total momentum before a collision equals total momentum after.
- Impulse (force × time) changes momentum, which is why longer impact times reduce injury.
On this page
Momentum describes how hard it is to stop a moving object. A slow truck and a fast baseball can both be hard to stop, for different reasons.
The formula
p = m × v
- p = momentum (kg·m/s)
- m = mass (kg)
- v = velocity (m/s), including direction
Because velocity has direction, momentum does too: it’s a vector.
Conservation of momentum
In a closed system with no external forces, total momentum stays the same. This lets you predict what happens in collisions and explosions.
Worked example: collision
A 1,000 kg car at 10 m/s hits a stationary 1,500 kg car and they move together. Before: 1,000 × 10 = 10,000 kg·m/s. After: (1,000 + 1,500) × v = 10,000, so v = 4 m/s.
Worked example: recoil
When a skater throws a heavy ball forwards, they move backwards: the momenta are equal and opposite. This is Newton’s third law in action; see Newton’s laws of motion.
Impulse
Impulse = force × time = change in momentum. For the same change in momentum, a longer impact time means a smaller force. That’s why:
- Crumple zones and airbags reduce injuries
- You bend your knees when you land a jump
- Catching a ball means moving your hands back with it
Elastic and inelastic collisions
- Elastic: kinetic energy is conserved (close to true for billiard balls).
- Inelastic: some kinetic energy becomes heat, sound or deformation (car crashes).
Momentum is conserved in both. See kinetic vs potential energy for the energy side.
Momentum is a vector quantity, so its direction matters; see vectors and scalars.
Frequently asked questions
What is the unit of momentum?
Kilogram metres per second (kg·m/s), equivalent to newton-seconds (N·s).
Is momentum the same as inertia?
No. Inertia is resistance to changes in motion (related to mass); momentum depends on both mass and velocity.
Is momentum always conserved?
In a closed system with no external forces, yes.
Sources
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