Momentum
📖Definition
Momentum (p) is a measure of how much "motion" an object has. It depends on both mass and velocity.
p = m × v
- m = mass (kg)
- v = velocity (m/s)
- p = momentum (kg m/s)
Momentum is a vector — it has direction. By convention, take one direction as positive (e.g. right = +) and the opposite direction as negative.
Conservation of momentum
In any closed system (no external forces), the total momentum before an interaction = total momentum after.
total momentum before = total momentum after
This applies to collisions, explosions and recoil.
Collisions
There are two main types:
- Elastic — kinetic energy is also conserved (rare; ideal billiard balls).
- Inelastic — kinetic energy is not conserved (some becomes heat / sound / deformation). Momentum is always conserved.
A common question type is two trolleys colliding and sticking together (perfectly inelastic).
✦Worked example— Worked example — collision
A 2 kg trolley moves at 6 m/s and collides with a stationary 4 kg trolley. They stick together. Find their combined velocity after the collision.
Before: p = (2 × 6) + (4 × 0) = 12 kg m/s. After: p = (2 + 4) × v = 6v. Conservation: 6v = 12 → v = 2 m/s.
Recoil / explosion
A stationary object that bursts apart starts with zero momentum, so the pieces must have momenta that add to zero — equal and opposite.
Example: a 0.020 kg bullet leaves a 4 kg gun at 400 m/s. Find recoil velocity of the gun.
0 = (0.020 × 400) + (4 × v) → v = −2 m/s. The gun recoils at 2 m/s in the opposite direction.
Force = rate of change of momentum (Higher tier)
Newton’s second law in its general form:
F = (m × v − m × u) / t = Δp / t
This is why crumple zones, airbags, padded helmets and bend-knees-when-landing all reduce the force in a collision: by increasing the time over which momentum changes, the same Δp gives a smaller force.
Edexcel exam tip
Always include direction — write momentum to the right as positive and to the left as negative. A collision answer with a negative velocity simply means the object now moves the other way; do not "drop the minus sign". Always state final velocity with its direction.
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