IB Physics Momentum and Collisions: A Clear Guide
In every IB Physics collision question, the same idea does most of the work: if no external resultant force acts on a system, its total momentum stays the same. Use that to find the unknown velocity. Then use kinetic energy to decide what type of collision it was. This guide shows you how, with worked numbers and the slips examiners see most often.
TL;DR
- Momentum is p = mv, measured in kg·m/s, and it is a vector, so direction and sign matter.
- Total momentum is conserved in every collision of an isolated system, elastic or inelastic.
- Kinetic energy is conserved only in elastic collisions. Compare it before and after to classify the collision.
- Impulse is the change in momentum (J = FΔt = Δp), and the area under a force-time graph gives it.
- Practise with exam-style questions, not just notes: the marks come from clear setup and sign conventions.
Table of Contents
- Where momentum sits in the IB Physics course
- The core ideas: momentum and impulse
- Conservation of momentum in collisions
- Elastic, inelastic and totally inelastic: how to classify
- Worked example 1: objects that stick together
- Worked example 2: an elastic collision
- Collisions in two dimensions and explosions
- Mistakes that cost marks
- Our perspective: practise with the exam in mind
- A study plan for momentum and collisions
- Getting started with Tiber Tutor
- FAQ
- Sources
Where momentum sits in the IB Physics course
In the current course (first assessment 2025), momentum belongs to theme A, Space, time and motion. The IB physics subject brief lists A.2 Forces and momentum alongside kinematics, work, energy and power, and rigid body mechanics. You can read the IB’s own overview on its Physics in the DP page.
If your school still uses older notes, check the topic numbers. The content is familiar, but the numbering has changed, and your teacher’s syllabus reference should be your anchor.
The core ideas: momentum and impulse
Momentum is the product of mass and velocity. OpenStax defines it as p = mv, and the SI unit is kg·m/s. Because velocity has a direction, so does momentum. Pick a positive direction at the start and stick to it.
Impulse is the change in momentum caused by a net force acting over a time. In symbols, J = FΔt = Δp. This is the same as saying force is the rate of change of momentum, which links Newton’s second law to everything in this topic.
Two practical consequences come up again and again:
- A longer collision time means a smaller average force for the same change in momentum. This is why crumple zones, airbags and padded dashboards work.
- On a force-time graph, the area under the curve is the impulse. Count squares or use geometry, then divide by mass to get the change in velocity.
Conservation of momentum in collisions
For two objects in an isolated system:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
This holds whatever happens to the energy. The textbook treatment in OpenStax on types of collisions makes the same point: momentum is conserved in all interactions, but kinetic energy is not.
In an exam answer, state the condition. Write that there is no external resultant force on the system, so total momentum is conserved. That one sentence is often worth a mark.
Elastic, inelastic and totally inelastic: how to classify
| Type | Momentum | Kinetic energy | Typical clue in the question |
|---|---|---|---|
| Elastic | Conserved | Conserved | Bounce apart, “perfectly elastic”, air-track gliders with springs |
| Inelastic | Conserved | Some lost to thermal energy, sound or deformation | Objects deform, then separate |
| Totally inelastic | Conserved | Maximum loss for the situation | Objects stick together and move with one velocity |
The test is simple. Work out total kinetic energy before and after. If the numbers match, it is elastic. If the final value is smaller, it is inelastic. A final value larger than the initial one, with no energy source, means you have made an error.
For elastic collisions in one dimension, the relative speed of approach equals the relative speed of separation. This shortcut often saves a quadratic equation.
Worked example 1: objects that stick together
A 2.0 kg trolley moving at 3.0 m/s hits a stationary 1.0 kg trolley. They stick together. Find the common velocity and the kinetic energy lost.
- Momentum before: 2.0 × 3.0 = 6.0 kg·m/s.
- Momentum after: (2.0 + 1.0)v = 3.0v.
- So v = 2.0 m/s in the original direction.
- Kinetic energy before: ½ × 2.0 × 3.0² = 9.0 J.
- Kinetic energy after: ½ × 3.0 × 2.0² = 6.0 J.
- Energy lost: 3.0 J.
So the collision is totally inelastic. Note that the 3.0 J is not destroyed. It becomes thermal energy, sound and deformation.
Worked example 2: an elastic collision
The same 2.0 kg trolley at 3.0 m/s now hits the stationary 1.0 kg trolley elastically.
Momentum: 6.0 = 2.0v₁ + 1.0v₂.
Relative speeds: approach speed is 3.0 m/s, so v₂ − v₁ = 3.0.
Substitute v₂ = v₁ + 3.0 into the momentum equation: 6.0 = 2.0v₁ + v₁ + 3.0, so v₁ = 1.0 m/s and v₂ = 4.0 m/s.
Check the energy: before, 9.0 J. After, ½ × 2.0 × 1.0² + ½ × 1.0 × 4.0² = 1.0 + 8.0 = 9.0 J. It matches, so the answer is consistent.
This check is a habit worth building. It takes ten seconds and catches sign errors before the examiner does.
Collisions in two dimensions and explosions
Momentum is conserved separately in each perpendicular direction. Resolve every velocity into components, write one equation for x and one for y, then recombine the answer with Pythagoras and an inverse tangent.
Explosions are collisions run backwards. A system starts with zero total momentum (say, a stationary cannon and shell), so the pieces must leave with momenta that sum to zero. Kinetic energy increases here, because stored chemical or elastic energy is released.
Mistakes that cost marks
- Ignoring direction. A trolley moving left has negative momentum if right is positive. Write your sign convention down.
- Conserving kinetic energy by default. Only do this when the question says elastic, or when you have shown it.
- Mixing units. Convert grams to kilograms and km/h to m/s before you start.
- Mixing up impulse and force. Impulse is a change in momentum, in N·s or kg·m/s. Average force is impulse divided by time.
- Forgetting Newton’s third law. During a collision the forces on the two objects are equal and opposite, even when the masses differ. A truck and a car feel the same force magnitude, but the car suffers the larger acceleration.
Our perspective: practise with the exam in mind
We build Tiber Tutor with IB examiners, and we see the same pattern: students who understand momentum still lose marks through setup. They skip the conservation statement, drop a sign, or fail to link a kinetic energy comparison to a conclusion. Reading a clean set of notes is not enough. You need to attempt questions, compare your reasoning to an examiner mark scheme, and notice which step keeps going wrong.
That is why our resources are linked. A question points you to the matching notes, definitions and flashcards. A topic test shows whether the fix worked. Your progress tracking then shows whether collisions are still a weak spot before the mock exams. You do not need to guess where to spend the next hour, and that brings confidence as well as marks.
— Oliver
A study plan for momentum and collisions
- Learn the language. Revise the key terms with the IB Physics definitions and read the IB Physics notes.
- Memorise the essentials. Use flashcards for the formulas and the classification test, and keep a cram sheet for the final week.
- Practise by topic. Work through the IB Physics questions, then take a topic test.
- Build your own drill. The custom test builder lets you set a paper that is all momentum and impulse.
- Test under exam conditions. Finish with full mock exams.
If you want to see how the exam papers are laid out, the IB publishes specimen papers 1A, 1B and 2 for both levels.
Getting started with Tiber Tutor
Tiber Tutor offers a free 7-day trial. After that, the Per-Subject Plan is $9 per month and the All-Access Plan is $19 per month. Every question comes with content written by actual IB examiners, alongside animated videos, examiner mark schemes, student-led answer review and performance analytics that show which topics need work. For the range of examiner-written material and tracking you get, we believe it is the best value for money in IB science revision. See the plans and pricing, or look at the student page. Parents can start with the parents page.
FAQ
Is momentum conserved in an inelastic collision?
Yes. Total momentum is conserved in every collision where no external resultant force acts on the system. Only the kinetic energy changes in an inelastic collision, because some becomes thermal energy, sound or deformation.
How do I know if a collision is elastic?
Calculate the total kinetic energy before and after. If the two values are equal, the collision is elastic. In one dimension, you can also check whether the relative speed of approach equals the relative speed of separation.
What is the difference between impulse and momentum?
Momentum is a property of a moving object, mass times velocity. Impulse is the change in momentum, equal to force multiplied by the time it acts. They share the unit kg·m/s, which is equivalent to N·s.
Do SL and HL students both study collisions?
Both levels meet momentum, impulse and conservation in the forces and momentum topic. HL goes further in the course overall, so check your teacher’s course outline for the extra depth expected in your class. The IB’s SL and HL overview explains how the two levels differ.
Sources
- IB physics subject brief (PDF)
- Physics in the DP, International Baccalaureate
- OpenStax University Physics: Impulse and Collisions
- OpenStax University Physics: Types of Collisions
- IB physics specimen papers 1A, 1B and 2 (PDF)
- IB SL and HL brief (PDF)