Momentum and its conservation
Momentum is mass in motion. In any collision or explosion where no outside force acts, the total momentum before equals the total momentum after, and that one idea solves most momentum questions.
AQA puts momentum in the Higher tier only. Check your own board's specification for its tiering.
Part 1 of 3: Learn it
In short
- Momentum = mass × velocity, p = m v, in kg m/s.
- Momentum has a direction: choose one direction as positive and give the other a minus sign.
- In a closed system the total momentum before an event equals the total momentum after it.
Where this is in your specification
Spec points: AQA 4.5.7.1 and 4.5.7.2 (Higher), Edexcel Topic 2, OCR P2.2
| Board | Topic: Momentum |
|---|---|
| AQA 8463 | 4.5.7 (8463); 6.5.5 (8464) |
| Edexcel 1PH0 | Topic 2 |
| OCR J249 | P2.2 |
The equation
Momentum in kg m/s, mass in kg, velocity in m/s. Because velocity is a vector, so is momentum: a 2 kg trolley moving left at 3 m/s has momentum −6 kg m/s if right is positive.
Conservation of momentum
In a closed system (no external forces such as friction), the total momentum before a collision or explosion equals the total momentum after it.
To solve a question, write total momentum before = total momentum after, put each object's m v in with its sign, and solve for the unknown.
- Objects that stick together after a collision move off with one velocity, using their combined mass.
- In an explosion everything starts at rest, so the total momentum before is zero. Afterwards the pieces move in opposite directions with equal and opposite momentum.
Force and changing momentum
A force changes momentum. AQA separate Physics (and some other specifications) use force = change in momentum ÷ time, F = m Δv ÷ Δt. Spreading the change over a longer time means a smaller force, which is how crumple zones, air bags, cycle helmets and crash mats protect people.
What is the momentum of a 0.15 kg ball moving at 20 m/s?
Show the answer
p = 0.15 × 20 = 3 kg m/s.
Part 2 of 3: See it worked
Worked examples
Example 1
A 2.0 kg trolley moving at 3.0 m/s collides with a stationary 1.0 kg trolley. They stick together. How fast do they move afterwards?
- Momentum before = 2.0 × 3.0 + 1.0 × 0 = 6.0 kg m/s
- Momentum after = (2.0 + 1.0) × v = 3.0 v
- 3.0 v = 6.0, so v = 2.0 m/s
Answer: 2.0 m/s, in the direction the first trolley was moving.
Example 2
A 60 kg skater at rest pushes away a 40 kg skater, who moves off at 1.5 m/s. What is the first skater's velocity?
- Total momentum before = 0
- After: 40 × 1.5 + 60 × v = 0
- 60 v = −60, so v = −1.0 m/s
Answer: 1.0 m/s in the opposite direction to the second skater.
Common mistakes
- Ignoring direction, which turns a subtraction into an addition.
- Using only one mass after a 'stick together' collision.
- Forgetting the total momentum is zero before an explosion.
- Giving the unit as kg/m/s or N. Momentum is kg m/s.
A 1000 kg car at 10 m/s hits a stationary 1500 kg car and they lock together. Find their speed.
Show the answer
10 000 = 2500 v, so v = 4 m/s.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
What is the momentum of a 0.15 kg ball moving at 20 m/s?
p = 0.15 × 20 = 3 kg m/s.
A 1000 kg car at 10 m/s hits a stationary 1500 kg car and they lock together. Find their speed.
10 000 = 2500 v, so v = 4 m/s.
Why do air bags reduce injuries?
They increase the time over which the person's momentum changes, so the force on them is smaller.
Jobs that use this
- Mechanical engineer (s'ouvre dans un nouvel onglet)
- Civil engineer (s'ouvre dans un nouvel onglet)
- Airline pilot (s'ouvre dans un nouvel onglet)
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Ces fiches sont en anglais car elles suivent les programmes d'examen britanniques.
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