Forces and motion · GCSE Physics
Momentum
Teacher-written GCSE Physics revision on momentum: p = mv, conservation in a closed system, F = Δp/t, and crumple zones — Higher-tier Combined and Triple content, so check your paper.
Momentum p = mv, in kg m/s, is a vector. In a closed system it is conserved. A longer collision time means a smaller force: F = Δp / t.
The important bits
What you need to know
- 1
Momentum p = mv. Mass in kilograms, velocity in m/s, momentum in kg m/s. It is a vector: direction matters, so opposite motions have opposite signs.
- 2
This is Higher-tier on AQA Combined Science and is required on GCSE Physics. If you sit Foundation Combined, check whether momentum appears on your paper.
- 3
Conservation of momentum: in a closed system (no external resultant force), total momentum before a collision or explosion equals total momentum after.
- 4
Explosions start with zero total momentum if the system was at rest; the pieces fly in opposite directions so that m₁v₁ + m₂v₂ = 0.
- 5
A force causes a change in momentum: F = Δp / t = (mv − mu) / t. This is Newton’s second law written for changing momentum, including when mass is constant (then F = ma).
- 6
Safety: airbags, crumple zones and seat belts increase the time over which Δp happens, so F falls. The change in momentum is set by the change in velocity; time is what you can design.
- 7
Elastic and inelastic collisions both conserve momentum in a closed system. Kinetic energy is conserved only in elastic collisions; most everyday crashes are inelastic and heat and deform materials.
- 8
Always assign a positive direction. A +8 kg m/s and a −3 kg m/s add to +5 kg m/s. Dropping the sign invents momentum from nowhere.
Quotations worth analysing
Short evidence. Real method.
“Momentum = mass × velocity”
Velocity, not speed, if the objects can go opposite ways. Units kg m/s, not newtons. Newtons are for force.
“Force equals the rate of change of momentum”
Same change in momentum in twice the time is half the force. That is the whole crumple-zone sentence.
“Momentum is conserved in a closed system.”
Closed means you have included every object in the interaction and there is no external resultant. The Earth-plus-jumper system is closed; the jumper alone is not.
Go deeper
Collisions are accounting with signs
Write total p before = total p after. Example: a 2.0 kg trolley at 3.0 m/s catches a 1.0 kg trolley at rest and they stick (inelastic). Before: 2.0 × 3.0 + 1.0 × 0 = 6.0 kg m/s. After: (2.0 + 1.0) × v = 6.0, so v = 2.0 m/s in the original direction. Kinetic energy fell from 9.0 J to 6.0 J; the missing 3.0 J went to thermal and deformation stores. Momentum still balanced. If they bounce, you need another fact (or energy if it is elastic) because two unknowns remain. Students add speeds without masses, or forget that a recoil velocity is negative. In gun-and-bullet questions the system starts at rest, so m_b v_b + m_g v_g = 0, and the gun’s smaller speed is a larger mass sharing the opposite momentum.
Go deeper
Crumple zones are F = Δp/t in sheet metal
A 1000 kg car stopping from 20 m/s has Δp = 20 000 kg m/s, whatever the design. Hit a wall in 0.10 s and F = 20 000 / 0.10 = 200 000 N. Crumple for 0.40 s and F = 50 000 N. The occupants still have to lose the same momentum; they do it more gently. Seat belts stretch, airbags deflate, helmets crush: all increase t. The exam sentence is “increases the time taken for the change in momentum, which decreases the force”. Do not say they “absorb the impact” without the time. Newton 3 still holds: the wall feels an equal and opposite force. Conservation of momentum of car-plus-Earth is true but not helpful; the useful system for the force on the driver is the driver’s Δp and the time the belt is taut.
See the idea in action
A 0.0050 kg bullet at 400 m/s embeds in a 2.0 kg block at rest on ice (almost no external horizontal force). Momentum before = 0.0050 × 400 = 2.0 kg m/s. After, (2.0 + 0.0050) × v = 2.0, so v ≈ 1.00 m/s. The pair slides together. If that stop of the bullet happened in 0.0010 s, the average force on the bullet F = Δp/t = 2.0 / 0.0010 = 2000 N (opposite to the velocity). Stretching the collision to 0.010 s would drop that force to 200 N. Kinetic energy is not conserved: ½ × 0.0050 × 160 000 = 400 J before, versus about 1.0 J after; the rest is thermal and deformation.
Exam technique
Turn knowledge into marks
Choose a positive direction, write p = mv for each object, then total before = total after. For safety, quote F = Δp/t and say that increasing t decreases F. Keep mass in kg. Flag this as Higher if you are on Combined Foundation.
Common mistakes
Do not give these marks away
- 01
Treating momentum as a scalar, or quoting it in newtons.
- 02
Using conservation of kinetic energy in a sticky inelastic collision, or forgetting opposite signs.
- 03
Saying crumple zones “reduce momentum” rather than increasing the time for the same Δp.
A 4.0 kg skateboarder moving at 2.5 m/s picks up a 1.0 kg bag at rest and they move off together. What is their speed?
A2.0 m/s
B2.5 m/s
C3.1 m/s
D10 m/s
Show the answer
2.0 m/s. Momentum before = 4.0 × 2.5 = 10 kg m/s. After, 5.0 × v = 10, so v = 2.0 m/s. Mass increased, speed fell; momentum was conserved.
Quick questions
If this is the bit you searched
What is momentum?
The product of mass and velocity, p = mv, a vector in kg m/s. It is conserved in a closed system.
How do crumple zones protect drivers?
They increase the time taken for the occupant’s momentum to change to zero, so the average force F = Δp/t is smaller.
Do all collisions conserve kinetic energy?
No. Momentum is conserved in a closed system. Kinetic energy is conserved only if the collision is elastic. Most crashes are inelastic.
Is momentum on Combined Science?
On AQA it is Higher-tier Combined and part of GCSE Physics. Foundation Combined students should check their specification and past papers.