Example 1: a collision
A 3.0 kg trolley moving at 4.0 m/s hits and sticks to a 1.0 kg trolley at rest. Find their velocity afterwards.
- Momentum before = 3.0 × 4.0 = 12 kg m/s.
- After: (3.0 + 1.0) × v = 12.
- v = 3.0 m/s.
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IB DemystifiedMYP Sciences
Momentum
A slow lorry and a fast cricket ball can both be hard to stop. Momentum combines mass and velocity to tell you how hard, and the way it is shared in collisions explains everything from rocket launches to why airbags and helmets save lives.
Recommended for MYP 5 · eAssessment priority · About 3 lessons · Criteria A, B, C and D
On this page
- Learning objectives
- Before you start
- Key vocabulary
- Understanding the ideas
- Momentum calculations
- Momentum in the real world
- Worked examples
- In the eAssessment
- Check your understanding
- Practice questions
- Investigation
- Criterion-linked questions
- Challenge questions
- Topic check
- Review your mistakes
- Your progress
Learning objectives
By the end of this topic you should be able to:
- calculate momentum using p = mv, including direction
- apply conservation of momentum to collisions and explosions
- calculate force from the rate of change of momentum
- explain safety features using momentum and time
- analyse and evaluate collision experiments
- discuss road-safety decisions using momentum
Before you start
You will use these skills. If any feel shaky, review them first.
- speed, velocity and acceleration (see Speed and Acceleration)
- forces and Newton's laws
- rearranging equations and using negative numbers for direction
Key vocabulary
- Momentum
- Mass × velocity (p = mv), measured in kg m/s; a vector with direction.
- Conservation of momentum
- In a closed system, total momentum before = total momentum after.
- Closed system
- A system on which no external forces act.
- Impulse
- Force × time, equal to the change in momentum.
- Collision / explosion
- Objects hitting each other / objects pushing apart from rest.
Understanding the ideas
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What is it?
Momentum is the product of an object's mass and velocity. Because velocity has a direction, so does momentum: we usually take one direction as positive and the other as negative.
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Why does it happen?
When objects interact, they push on each other with equal and opposite forces for the same time (Newton's third law), so one gains exactly the momentum the other loses. The total stays the same unless an outside force, such as friction, acts.
-
How do we know?
Collisions between trolleys, measured with light gates or video, show the total momentum is the same before and after, within experimental error. The same law is used to analyse particle collisions and spacecraft manoeuvres.
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Why does it matter?
Force equals the rate of change of momentum, so spreading a momentum change over a longer time reduces the force. This is the principle behind crumple zones, airbags, seat belts, helmets and soft landing surfaces.
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What does it connect to?
Momentum links to forces, Newton's laws and energy in physics; to vehicle design and sports science; and to algebra and negative numbers in mathematics.
Momentum calculations
- Momentum: p = m × v (kg m/s).
- Conservation: total momentum before = total momentum after (use + and − for directions).
- Explosions from rest: total momentum is zero, so the parts move apart with equal and opposite momentum.
- Force and momentum: F = change in momentum ÷ time (so F × t = change in momentum).
- Safety: a longer stopping time means a smaller force for the same change in momentum.
Momentum in the real world
Car designers test crumple zones and airbags with crash-test dummies to lengthen stopping times. Cricket and baseball players "give" with their hands when catching. Space agencies use conservation of momentum to steer spacecraft by firing small thrusters.
Worked examples
Example 2: force from momentum
A 60 kg person on a bike stops from 5.0 m/s in 0.30 s. Find the mean force.
- Change in momentum = 60 × 5.0 = 300 kg m/s.
- F = 300 ÷ 0.30 = 1000 N.
In the eAssessment
Momentum questions combine calculations with explanations of safety and design. Expect:
- Calculate momentum, velocities after collisions or explosions, and forces, with units.
- Use direction carefully with + and − signs.
- Explain safety features using time and force.
- Evaluate collision experiments and safety claims.
Common ways to lose marks: forgetting that momentum has direction; forgetting to add masses when objects stick together; saying safety features reduce momentum (they reduce force); and using milliseconds without converting to seconds.
Check your understanding
Quick questions on the ideas above. Try each one before using a hint.
Practice questions
Investigation: bouncing balls and momentum change
Partially guided investigation · about 50 minutes · pairs
- Research question
- How does the type of ball (tennis ball, rubber ball, table-tennis ball, modelling-clay ball of similar size) affect its change in momentum when it is dropped from 1.0 m onto a hard floor?
- Scientific background
- A ball hitting the floor changes direction, so its change in momentum is its mass × (speed just before + speed just after). A ball that bounces higher has a larger change in momentum and experiences a larger impulse from the floor.
- Hypothesis
- Write your own prediction, with a scientific justification.
- Variables
- Identify your independent, dependent and control variables, and explain how you will control them.
- Apparatus
- Four balls, balance, metre rule fixed vertically against a wall, phone camera with slow-motion video, video analysis app or frame-by-frame viewer.
- Method
- Measure the mass of each ball.
- Drop each ball from 1.0 m next to the metre rule while filming in slow motion.
- Use the frames to find the speed just before and just after impact (distance moved ÷ time between frames).
- Calculate the change in momentum; repeat each ball three times and find the mean.
Safety. Keep the drop area clear, clean up any clay, and do not stand on chairs to reach the release height; use a stable stool or a lower height if needed.
Then evaluate: how precise were your speed measurements from the video, and how could you improve them?
Criterion-linked questions
Criterion B: inquiring and designing
Criterion C: processing and evaluating
Criterion D: reflecting on the impacts of science
Challenge questions
Harder problems in unfamiliar contexts. Plan before you calculate.
Topic check
Five questions picked at random from the whole topic. Take a new set whenever you like.
Review your mistakes
Questions you got wrong on this device appear here so you can try them again. Answer one correctly and it leaves the list.
Your progress
Tracked separately for each skill, on this device only.
| Skill | Correct | Status |
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