IGCSE Physics Momentum Notes
Momentum measures how hard it is to stop a moving object. It is conserved in collisions, which lets you solve collision and explosion problems.
Key concepts
- Momentum
- The product of mass and velocity: p = mv, measured in kg m/s. A vector.
- Conservation of momentum
- In a closed system, total momentum before a collision equals total momentum after.
- Force and momentum
- Force equals the rate of change of momentum: F = (mv − mu) ÷ t.
- Momentum is conserved in all collisions and explosions when no external force acts.
- A larger contact time reduces the force in a collision (crumple zones, air bags).
- Momentum is a vector, so direction (and sign) matters in calculations.
Key formulas
Momentum
p = m × v
kg m/s.
Conservation
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Force
F = (mv − mu) ÷ t
rate of change of momentum.
Worked example
A 2 kg trolley at 3 m/s hits a stationary 1 kg trolley and they stick together. Find their common velocity.
- 1Momentum before: (2 × 3) + (1 × 0) = 6 kg m/s.
- 2Momentum after: (2 + 1) × v = 3v.
- 3Conserve momentum: 3v = 6.
- 4Solve: v = 2 m/s.
Answer: v = 2 m/s
Common mistakes
✗ Ignoring direction when momentum is a vector.
✓ Assign one direction positive and the other negative before adding.
✗ Forgetting to combine masses when objects stick together.
✓ After a 'stick together' collision the mass is the sum of both objects.
✗ Confusing momentum (kg m/s) with force (N).
✓ Force is the rate of change of momentum, not momentum itself.
Quick check
Try these, then reveal the answers.
State the equation for momentum.Reveal answer
p = m × v.
What is conserved in a collision with no external force?Reveal answer
Total momentum.
Why do air bags reduce injury?Reveal answer
They increase the contact time, reducing the force on the passenger.
Exam tips
- Write 'momentum before = momentum after' explicitly to earn the method mark.
- Take care with signs when objects move in opposite directions.
- Link crumple zones and air bags to F = change in momentum ÷ time.
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Frequently asked questions
Is momentum always conserved?+
Total momentum is conserved whenever no external resultant force acts on the system.
How do safety features use momentum?+
By extending the time over which momentum changes, they reduce the force experienced (F = Δp ÷ t).
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