In simple terms
A friendly intro before the formal notes — no formulas yet.
Linear momentum and its conservation
Cambridge 9702 Paper 2 — Linear momentum and its conservation (3.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.
- 1
Momentum (p) is the product of mass (m) and velocity (v).
- 2
The unit of momentum is the kilogram-metre per second (kg m/s).
- 3
As a vector, momentum's direction is the same as the velocity's direction.
- 4
It is a measure of an object's 'quantity of motion'.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 3.3.1
State the principle of conservation of momentum
- 3.3.2
Apply the principle of conservation of momentum to solve simple problems, including elastic and inelastic interactions between objects in both one and two dimensions (knowledge of the concept of coefficient of restitution is not required)
- 3.3.3
Recall that, for an elastic collision, total kinetic energy is conserved and the relative speed of approach is equal to the relative speed of separation
- 3.3.4
Understand that, while momentum of a system is always conserved in interactions between objects, some change in kinetic energy may take place
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Momentum p = mv is a vector
Momentum p = mv is a vector — direction matters.
23 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
23 simulations · 5 to start with
Start herein this order — each one shows a different piece of the topic
- 3JCN PhysicsStart here · 19702 3.3 · IB A.2
Elastic & Inelastic Collisions
Collide two carts with adjustable masses, speeds and elasticity; read momentum and KE before and after
Why this one: Slide elasticity from 1 to 0: momentum stays conserved while the kinetic energy after collapses.
Try this
- Set equal masses, one at rest, with full elasticity; read momentum and KE before and after.
- Set elasticity to zero and compare the KE after.
- Make one cart heavier and repeat.
Look for Momentum is conserved in every case; KE is conserved only when the collision is perfectly elastic.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- The Physics ClassroomStart here · 29702 3.3 · IB A.2
Exploding Carts
Two carts on a low-friction track push apart with a spring-loaded plunger; vary the relative mass and compare the speeds
Why this one: Explosions from rest: the carts gain equal and opposite momentum, so the lighter one moves faster.
Try this
- Set equal masses and fire the plunger.
- Double one mass and compare the two speeds.
- Compare the momentum of each cart.
Look for The carts gain equal and opposite momentum, so the lighter cart moves faster.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- The Physics ClassroomStart here · 39702 3.3 · IB A.2
The Cart and The Brick
A brick drops onto a moving cart; use the position-time data to find speeds before and after and compare the momentum totals
Why this one: Read speeds off position–time data and show m₁v₁ equals (m₁ + m₂)v after the brick lands.
Try this
- Read the cart's speed from the position-time data before the brick lands.
- Read the combined speed after.
- Compare total momentum before and after.
Look for Total momentum is the same before and after the brick lands.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- The Physics ClassroomStart here · 49702 3.3 · IB A.2
Two-Dimensional Collision Simulation
Collide objects in two dimensions and analyse momentum conservation in each direction
Why this one: Momentum is conserved along x and along y separately; check each component in a glancing hit.
Try this
- Set up an oblique collision and run it.
- Compare the x-momentum before and after.
- Compare the y-momentum before and after.
Look for Momentum is conserved separately along x and along y.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- 3JCN PhysicsStart here · 59702 3.3 · IB A.2
Perfect Elastic Collision Problem
Perfectly elastic collision problem with adjustable masses; check both momentum and KE conservation
Why this one: Equal masses swap velocities; compare the speeds of approach and separation in an elastic collision.
Try this
- Set equal masses and check momentum and KE before and after.
- Make one mass much heavier and compare the final velocities.
Look for In a perfectly elastic collision both momentum and KE are conserved, and equal masses exchange velocities.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
More simulations18 more on this topic — core ones first
- oPhysicsCore9702 3.3 · 9702 5.1 · IB A.2
Momentum & Energy: Elastic and Inelastic Collisions
1D collision of two masses: set masses, velocities and elasticity; compare momentum and KE before/after
Try this
- Set equal masses, one at rest, fully elastic; compare the velocities after.
- Make the collision fully inelastic with the same setup.
- Give one mass twice the other and run both elasticities.
Look for Momentum is the same before and after in every case; kinetic energy is conserved only when the collision is elastic.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 3.3 · IB A.2
Momentum & Energy: Explosive Collisions
Two boxes pushed apart by an explosive charge; set masses, initial velocity and explosion energy
Try this
- Set the initial velocity to zero and equal masses, then explode.
- Make one mass three times the other and explode again.
- Increase the explosion energy and compare the speeds.
Look for The boxes move apart with equal and opposite momenta, so the lighter box moves faster.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 3.3 · 9702 5.1 · IB A.2
The Ballistic Pendulum
Ballistic pendulum: set bullet/block masses and bullet speed; see inelastic collision then rise height
Try this
- Set a bullet speed and read the rise height.
- Double the bullet speed and compare the rise height.
- Increase the block mass with the same bullet speed.
Look for Momentum is conserved in the collision and energy afterwards, so the rise height grows with the square of the bullet speed.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 3.3 · 9702 5.1 · IB A.2
Ballistic Pendulum "Quiz"
Ballistic pendulum quiz: given masses and rise height, compute the bullet speed and check it
Try this
- Read the masses and rise height and compute the speed just after impact.
- Use momentum conservation to find the bullet speed and check it.
- Reset for a new set of values and repeat.
Look for The speed just after impact comes from the rise height, and the bullet speed from momentum conservation.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 3.3 · IB A.2
Center of Mass: Person on a Floating Raft
Person walks along a floating raft; adjust masses and watch raft recoil so the centre of mass stays fixed
Try this
- Walk the person from one end of the raft to the other.
- Make the raft much heavier than the person and walk again.
- Make the two masses equal and compare the raft’s movement.
Look for The raft moves opposite to the person so the centre of mass stays fixed; equal masses move equal distances.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCoreIB A.4 · 9702 3.3 · IB A.2
Shooting Bullets Vertically into Blocks
Two bullets fired upward into identical blocks, one at centre, one off-centre; compare heights reached
Try this
- Fire both bullets and compare the heights reached.
- Watch the off-centre block spin.
Look for Both blocks rise to the same height because linear momentum is the same; the off-centre block also rotates.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Full topic notes
Formal explanation with the rigour you need for the exam.
What is Linear Momentum?
Linear momentum, denoted by the symbol , is a measure of an object's 'quantity of motion'. It’s a vector quantity, which means it has both a magnitude and a specific direction. The direction of an object's momentum is always the same as the direction of its velocity. Think of a heavy lorry moving slowly versus a small car moving quickly – which has more 'oomph' or momentum?
Momentum (p) is the product of mass (m) and velocity (v).
The unit of momentum is the kilogram-metre per second (kg m/s).
As a vector, momentum's direction is the same as the velocity's direction.
It is a measure of an object's 'quantity of motion'.
Momentum, Force, and Impulse
Newton's Second Law can be expressed more fundamentally in terms of momentum. Force is the rate at which an object's linear momentum changes over time. This leads to the concept of impulse, which is the change in momentum itself. Impulse is also the product of the average force and the time over which it acts, a crucial idea for understanding impacts.
Impulse (J) is the change in momentum (Δp).
It is calculated as the product of average force and time duration (FΔt).
The unit of impulse is the Newton-second (Ns), which is equivalent to kg m/s.
The area under a force-time graph represents the impulse delivered.
Remember that (delta) signifies 'change in'. So, means final momentum minus initial momentum (). This formula highlights that a larger force causes a faster change in momentum, and a force applied for a longer time causes a larger change in momentum.
The Principle of Conservation of Momentum
This principle is one of the most fundamental laws in physics. It states that for a closed system, where no net external forces act, the total linear momentum of the system remains constant. This means the total momentum before an event, such as a collision or an explosion, will be exactly equal to the total momentum after the event. The individual momenta of objects within the system might change, but their vector sum stays the same.
Total momentum of a closed system remains constant.
Applies when no net external forces act on the system.
Total momentum before = Total momentum after (as a vector sum).
Crucial for analysing collisions and explosions.
Elastic vs. Inelastic Collisions
While linear momentum is always conserved in a closed system, the total kinetic energy of the system might not be. This difference allows us to classify collisions into two main types: elastic and inelastic. It's crucial for understanding the energy transformations that occur during impacts.
Elastic Collision: Total kinetic energy (KE) of the system IS conserved.
Elastic Collision: Relative speed of approach equals relative speed of separation.
Inelastic Collision: Total kinetic energy (KE) of the system is NOT conserved.
Perfectly Inelastic Collision: A specific type where objects stick together after impact, resulting in the maximum possible loss of KE.
Momentum: Is always conserved in BOTH types of collisions (in a closed system).
A common misconception is that kinetic energy is always conserved if momentum is. Remember, only in perfectly elastic collisions is kinetic energy conserved. In all inelastic collisions, momentum is conserved, but kinetic energy is not.
Explosions and Recoil
The principle of conservation of momentum is also perfectly demonstrated in explosions or recoil scenarios. Here, an object initially at rest breaks apart into two or more pieces. Since the initial momentum of the system is zero, the vector sum of the momenta of all the pieces after the explosion must also be zero. This means the pieces will fly off in opposite directions (in a two-body explosion) to keep the total momentum conserved.
Initial Momentum = 0 Final Momentum =
For a two-body explosion from rest, , which means . The negative sign indicates that the velocities are in opposite directions. This is the principle behind rocket propulsion and the recoil of a gun.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A trolley of mass 2.0 kg moving at 3.0 m/s collides head-on with a stationary trolley of mass 4.0 kg. If the two trolleys stick together after the collision, what is their common final velocity?
- 1
Identify initial conditions:
A ball of mass 0.50 kg moving at 4.0 m/s collides head-on with a stationary ball of mass 0.30 kg. The collision is perfectly elastic. Calculate the final velocities of both balls.
- 1
Define variables & initial conditions:
How it all connects
The big idea sits in the middle — tap a linked idea to explore the link.
Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Key terms for this topic — skim now; the Check step will test them.
- impulse
This leads to the concept of impulse, which is the change in momentum itself.
- Momentum formula
Linear momentum () is calculated as the product of mass () and velocity (), so .
- Scalar or vector?
Linear momentum is a vector quantity, meaning it has both magnitude and direction.
- Force & momentum
Force is defined as the rate of change of an object's linear momentum ().
- Conservation conditions
The total momentum of a closed system is conserved if no net external forces act upon it.
- Elastic vs inelastic
In an elastic collision, total kinetic energy is conserved, while in an inelastic collision, total kinetic energy is not conserved.
- KE in inelastic
The 'lost' kinetic energy is converted into other forms, such as heat, sound, or energy for deformation.
- In a perfectly elastic
The relative speed at which objects approach each other before impact equals their relative speed of separation after impact.
- Closed system
A closed system means no mass or energy enters or leaves, and importantly, no net external forces act on the system.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
If you can explain it simply, you own it — gaps here are marks you’d lose.
Teach it back
Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.
Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
Momentum (p) is the product of mass (m) and velocity (v).
The unit of momentum is the kilogram-metre per second (kg m/s).
As a vector, momentum's direction is the same as the velocity's direction.
It is a measure of an object's 'quantity of motion'.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
State the principle of conservation of momentum.
Calculate the change in momentum of the ball during the collision with the ground.
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
One marked question is worth ten re-reads — close the loop before you move on.
Reading it isn’t knowing it — prove it.
Before you move on: do 9702/23 · Q2(a) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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