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AQA GCSE Physics · Topic 4.5 Forces · Higher tier
Edexcel International GCSE Physics · Section 1 Forces and motion · Physics only
Momentum — Conservation and Rate of Change
Physics only The whole of momentum is Physics only — Double Award
students can skip this page.
Higher tier Momentum and conservation of momentum are Higher tier, for
Combined and Triple. Triple only Rate of change of momentum is
Triple (Physics) only.
In this lesson you'll learn to: use momentum = mass × velocity; explain why momentum
is a vector; use conservation of momentum in collisions and explosions; and use
force = change in momentum ÷ time to explain crash mats, crumple zones and why golfers hit
hard.
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Prefer to watch? Scroll to the bottom for the video on this topic
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A video walkthrough is coming soon — it will appear at the bottom of this page
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Start here — have a play
Don't read anything yet. Send the trolley round a corner at a steady speed — is its momentum changing? Then crash two trolleys together, bounce them apart and blow them apart from rest, and watch the total momentum. Finally, land a gymnast on the floor and on a crash mat, and compare the force.
speed changing
direction changing
momentum changing
momentum = mass × velocity p = m × v (kg m/s). Velocity is a vector, so momentum is too: it changes if the speed changes or if the direction changes. The gold arrows left behind show the momentum every 0.6 s.
Set it up
right = + left = −
How long does the change take?
force = change in momentum ÷ time F = (mv − mu) ÷ t. The change in momentum is fixed by the masses and speeds — the time is what safety features (and golfers) change.
Physics With Kate · physicswithkate.com — GCSE & International GCSE Physics
▲ In the conservation tab, keep an eye on the total — it never changes.
Total momentum before = total momentum after.
And force = change in momentum ÷ time. Those two ideas answer almost every momentum question. The notes show you how to set them out for the marks.
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Revision notes
Momentum
⭐ The equation
momentum = mass × velocity p = m × v p in kg m/s, m in kg, v in m/s.
Velocity is a vector, so momentum is a vector too. An object's momentum changes if its speed changes or its direction changes:
| Situation | Momentum | Why |
|---|---|---|
| a puck sliding across smooth ice at a steady 3.0 m/s in a straight line | stays the same | same speed, same direction |
| a car speeding up from 8 m/s to 20 m/s | changes (increases) | speed changes |
| suitcases going round a corner on a baggage belt at a steady speed | changes | direction changes |
Conservation of momentum
⭐ Learn this
In a closed system (no external forces, like friction), the total momentum before an event is equal to the total momentum after it. This is true for every collision and every explosion.
- Pick a direction to be positive (usually right). Anything moving the other way has a negative velocity and a negative momentum.
- Add up the momentum of every object before. At GCSE there are at most two.
- Momentum alone can't tell you whether objects stick together or move off separately — the question has to tell you.
Explosions
If everything starts still, the total momentum before is zero, so the total after must be zero too. The two parts move off in opposite directions with equal and opposite momentum: the lighter part moves faster and the heavier part moves slower. That's why a gun recoils, and why a rifle is much heavier than its bullet.
⚠ Trap 1 — signs
An object moving left has a negative velocity. In a head-on collision, a 1.0 kg trolley at 2 m/s to the left has momentum −2 kg m/s, not +2. Forgetting the minus sign is the most common lost mark.
Force and rate of change of momentum Triple onlyPhysics only
⭐ The equation
force = change in momentum ÷ time taken F = (mv − mu) ÷ t
A force is how quickly momentum changes. The force on an object is equal to its rate of change of momentum.
Safety: make the time longer
In a crash, the change in momentum is fixed — the person or car goes from moving to stopped either way. What safety features change is the time it takes:
- crash mats and soft playground surfaces
- crumple zones, airbags and seat belts (which stretch slightly)
- cycle and climbing helmets, which crush on impact
- bending your knees when you land
The three-step answer that gets the marks
The time taken to stop increases, so the
rate of change of momentum decreases, so the
impact force decreases (force = rate of change of momentum).
what changes which way the effect on the force
Sport and tools: make the time shorter
Sometimes you want a big force: driving a golf ball, hitting a nail with a hammer, kicking a ball. A hard club head or steel hammer gives a short contact time, so a large rate of change of momentum, so a large impact force. A rubber mallet makes the time longer and the force smaller — useful when you don't want to dent something.
How to write it in the exam
Calculate the momentum of a 1200 kg car travelling at 15 m/s.
p = m × v = 1200 × 15 = 18 000 kg m/s
A 3.0 kg trolley at 4.0 m/s hits a stationary 1.0 kg trolley. They stick together. Calculate their velocity.
Total momentum before = 3.0 × 4.0 + 1.0 × 0 = 12 kg m/s. Total after = (3.0 + 1.0) × v = 12, so v = 12 ÷ 4.0 = 3.0 m/s
A 2.0 kg toy cannon fires a 0.050 kg ball at 20 m/s. Calculate the recoil velocity of the cannon.
Total before = 0 (all still). After: 0.050 × 20 + 2.0 × v = 0, so 2.0 v = −1.0 and v = −0.50 m/s — 0.50 m/s backwards.
A 1000 kg car at 12 m/s stops in a crash in 0.30 s. Calculate the average force on it.
Change in momentum = 1000 × 0 − 1000 × 12 = −12 000 kg m/s. F = 12 000 ÷ 0.30 = 40 000 N
Explain how a crash mat reduces the risk of injury. (3 marks)
The mat increases the time taken for the gymnast to stop. The change in momentum is the same, so the rate of change of momentum is smaller. Force = rate of change of momentum, so the impact force is smaller.
✅ Check your answer
Units kg m/s for momentum · a direction (or sign) on every velocity · total before and total after written out · grams and milliseconds converted · in "explain" answers: time → rate of change of momentum → force, in that order.
📘 Now do it in your workbook
Conservation of Momentum: is there a change in momentum, collisions and explosions. Rate of Change of Momentum: safety features, hitting a ball, and the crash-mat exam question.
Edexcel iGCSE Forces and Motion Workbook · pages 13–14 AQA GCSE Physics Workbook · FORCES · pages 17–18✅ Can you do it? Tick as you go
0% complete🎉 Nice work! You've ticked off every objective for this topic.
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Prefer to watch? Here's the whole thing
Video walkthrough — coming soon
Everything above, explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it.
Everything above, explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it. The video is on its way.
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Video coming soon
The walkthrough for this lesson is being filmed and will appear right here. Until then, the notes and the free workbook pages above cover every mark.
Now put it into practice
Pages 13 and 14 of the Forces and Motion workbook are free: momentum, conservation, safety features and the crash-mat exam question.
Pages 17 and 18 of the Forces workbook are free: momentum, conservation, safety features and the crash-mat exam question.
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