In simple terms
A friendly intro before the formal notes — no formulas yet.
Momentum and Newton's laws of motion
Cambridge 9702 Paper 2 — Momentum and Newton's laws of motion (3.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.
- 1
Momentum () is a vector quantity with units kg m/s or Ns.
- 2
The direction of momentum is the same as the direction of velocity.
- 3
An object at rest has zero momentum.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 3.1.1
Understand that mass is the property of an object that resists change in motion
- 3.1.2
Recall and solve problems using it, understanding that acceleration and resultant force are always in the same direction
- 3.1.3
Define and use linear momentum as the product of mass and velocity
- 3.1.4
Define and use force as rate of change of momentum
- 3.1.5
State and apply each of Newton's laws of motion
- 3.1.6
Describe and use the concept of weight as the effect of a gravitational field on a mass and recall that the weight of an object is equal to the product of its mass and the acceleration of free fall
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.
Step 1
Momentum () is a vector quantity with units kg m/s or Ns.
26 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.
26 simulations · 5 to start with
Start herein this order — each one shows a different piece of the topic
- 3JCN PhysicsStart here · 19702 3.1 · IB A.2
Newton's Second Law
Adjust applied force and mass on a cart; read acceleration and compare with F = ma
Why this one: Double F and a doubles; double m and a halves: F = ma checked with your own numbers.
Try this
- Fix the mass and double the applied force; read the acceleration.
- Fix the applied force and double the mass; read the acceleration.
- Compare each reading with F = ma.
Look for Acceleration is proportional to the applied force and inversely proportional to the mass.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- The Physics ClassroomStart here · 29702 3.1 · IB A.2
Egg Drop
Explore which variables give a safe landing or a broken egg: drop height and the landing surface
Why this one: Same change in momentum, longer stopping time, smaller force: F = Δp/Δt decides whether the egg survives.
Try this
- Drop the egg from a low height and note the result.
- Raise the drop height until the egg breaks.
- Change the landing surface and repeat.
Look for A longer stopping time means a smaller force for the same change in momentum.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- PhETStart here · 39702 3.1
Collision Lab
Collide carts of chosen mass and velocity in 1D or 2D; read momenta before and after.
Why this one: Read p = mv for each cart before and after; the momentum arrows add to the same total every time.
Try this
- Set m₁ = 1 kg at +1 m/s into m₂ = 1 kg at rest, elasticity 100% — watch them swap.
- Change elasticity to 0% — the carts stick; compare total momentum before and after.
- Show “Momenta diagram” and check the arrows add up the same way each time.
Look for Total momentum is the same before and after whatever the elasticity.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- 3JCN PhysicsStart here · 49702 3.1 · IB A.2
Elevator
Ride an accelerating elevator and read apparent weight on the scale
Why this one: The scale reads m(g + a): more than your weight accelerating up, less accelerating down.
Try this
- Ride the elevator at constant speed and read the scale.
- Accelerate upward and compare the reading with the true weight.
- Accelerate downward and compare.
Look for The scale reads N = m(g + a): more than the weight accelerating up, less accelerating down.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- The Physics ClassroomStart here · 59702 3.1 · 9702 3.2 · IB A.2
Rocket Sledder
Vary the sledder's mass, the parachute size, the applied force and the friction; speed, acceleration and force values display as it moves
Why this one: Open the parachute and watch speed level off once drag plus friction equal the thrust: terminal velocity.
Try this
- Apply a force with no parachute and read the acceleration.
- Open the parachute and watch the speed level off.
- Increase the mass and compare the acceleration.
Look for Speed stops rising when air resistance plus friction equal the applied force.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
More simulations21 more on this topic — core ones first
- PhETCoreJava · best on a laptop9702 3.1–3.2 · IB A.2
Forces in 1 Dimension
Push a crate or fridge with a chosen applied force; read friction, net force, and the acceleration and velocity graphs.
Try this
- Apply a small force — the crate does not move; read the friction force matching it.
- Increase the force past the friction limit — acceleration appears on the graph.
- Hold the force steady — the velocity graph becomes a straight ramp.
Look for Static friction cancels small pushes; once moving, net force = ma and velocity grows linearly.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- PhETCoreJava · best on a laptop9702 3.1–3.2 · IB A.2
Forces and Motion
Push a crate or fridge across a surface with chosen friction; see the free-body diagram and the force, velocity and acceleration graphs.
Try this
- Push the crate with 100 N — compare applied force with friction on the free-body diagram.
- Set friction to zero — the crate accelerates for as long as you push.
- Swap the crate for the fridge — the same push gives less acceleration.
Look for Net force, not applied force, sets acceleration: a = (F − friction)/m.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- PhETCoreJava · best on a laptop9702 5.1 · 3.1 · 4.2 · IB A.3 · A.2
The Ramp
Push objects up a ramp; vary the angle, friction and mass and read the work done, energy bar charts and force graphs.
Try this
- Push a crate to the top at 15° with friction off — read the work done and the GPE gained.
- Turn friction on and repeat — the extra work shows up as thermal energy.
- Steepen the ramp — more force per metre, but the same GPE at the top.
Look for Work done = gain in GPE + energy lost to friction; the ramp trades force for distance.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- oPhysicsCore9702 3.1 · 9702 4.2 · IB A.2
Friction: Pulling a Box on a Horizontal Surface
Pull a box with a rope at adjustable tension/angle; explore static vs kinetic friction and normal force
Try this
- Increase the rope tension slowly from zero until the box starts to move.
- Raise the rope angle and note the normal force.
- Compare friction just before and just after the box starts moving.
Look for Static friction grows to match the pull up to a limit, then drops to a smaller kinetic value; an upward rope angle reduces the normal force.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 3.1 · 9702 4.2 · IB A.2
Static and Kinetic Friction on an Inclined Plane
Vary incline angle (0-90) and friction coefficients; see weight, normal and friction vectors and the motion
Try this
- Raise the incline angle slowly until the block begins to slide.
- Change the static coefficient and find the new slipping angle.
- Set the incline near 90° and look at the normal force vector.
Look for The block slips when tan θ reaches the static coefficient, and the normal force shrinks to zero as the incline approaches vertical.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- oPhysicsCore9702 3.1 · IB A.2
Inclined Plane with Friction, Two Masses, and a Pulley
Atwood-style system: mass on a rough incline linked over a pulley to a hanging mass; run to see the motion
Try this
- Run with the hanging mass larger than the incline mass.
- Run again with the two masses equal.
- Adjust the masses until the system stays at rest.
Look for The system accelerates only when the net force along the string exceeds the limiting friction on the incline.
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
$Impulse = F_{avg} \Delta t = \Delta p$
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.
Momentum: The 'Quantity of Motion'
Momentum is a measure of an object's motion that considers both its mass and its velocity. It's a vector quantity, meaning it has both magnitude and direction. Think of it as how much 'oomph' an object has – a heavy, fast object has more momentum than a light, slow one.
Momentum () is a vector quantity with units kg m/s or Ns.
The direction of momentum is the same as the direction of velocity.
An object at rest has zero momentum.
Newton's Three Laws of Motion
Sir Isaac Newton's laws are foundational to physics, explaining how forces affect motion. They govern everything from everyday pushes and pulls to the orbits of planets. Understanding them is crucial for mastering mechanics.
Newton's First Law: Inertia
An object will remain at rest, or continue to move at a constant velocity, unless acted upon by a net external force. This law introduces the concept of inertia – an object's resistance to changes in its state of motion.
An object's state of motion (rest or constant velocity) only changes if a resultant force acts.
Inertia is the tendency of an object to resist changes in its motion.
If forces are balanced (net force is zero), velocity remains constant.
Newton's Second Law: Force and Acceleration
The net force acting on an object is directly proportional to its acceleration and inversely proportional to its mass. Crucially, the net force is also defined as the rate of change of the object's momentum. Force causes momentum to change.
Net force () causes acceleration () in the same direction.
Acceleration is proportional to the net force and inversely proportional to mass ().
The general form, , is always true, even if mass changes.
Impulse
Impulse is a concept directly derived from Newton's Second Law. It is defined as the product of the average net force and the time interval over which it acts. Impulse is also equal to the change in momentum of the object. This relationship is particularly useful for analysing situations involving large forces acting over short times, like collisions or impacts.
Impulse is a vector quantity, with the same direction as the average force.
The unit of impulse is the Newton-second (Ns), which is equivalent to the unit of momentum (kg m/s).
The area under a force-time graph represents the impulse, or the change in momentum.
Newton's Third Law: Action-Reaction Pairs
For every action force exerted by one object, there is an equal magnitude and opposite direction reaction force exerted by a second object. It's critical to remember these forces always act on different bodies, meaning they never cancel each other out on a single object.
Forces always occur in pairs: action and reaction.
These pairs are equal in magnitude and opposite in direction.
Crucially, action and reaction forces act on different objects.
Mass vs. Weight: A Crucial Distinction
Often confused, mass and weight are distinct concepts. Mass is a scalar quantity measuring the amount of matter in an object and its inertia. Weight is a vector quantity representing the gravitational force exerted on an object. Your mass is constant, but your weight changes with gravitational field strength.
Mass () is a scalar measure of an object's inertia.
Weight () is the gravitational force acting on an object (a vector).
is the acceleration due to gravity (or gravitational field strength).
Conservation of Momentum: Collisions and Interactions
The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external resultant force acts on it. In simpler terms, the total momentum before an interaction, like a collision, will always equal the total momentum after.
Total momentum of a closed system stays constant.
This applies only if no external resultant force acts on the system.
Total momentum before collision = Total momentum after collision.
Types of Collisions
Collisions are classified by whether kinetic energy is conserved during the interaction, while momentum is always conserved in a closed system.
Elastic Collisions: Both total momentum and total kinetic energy are conserved.
In perfectly elastic collisions, relative speed of approach equals relative speed of separation.
Inelastic Collisions: Total momentum is conserved, but total kinetic energy is not conserved.
Lost kinetic energy in inelastic collisions is converted to heat, sound, or deformation.
Terminal Velocity: The Limit of Speed
When an object falls through a fluid (like air), it experiences resistive forces (e.g., air resistance or drag). As speed increases, these forces grow. Terminal velocity is reached when the downward driving forces (like weight) are perfectly balanced by the upward resistive forces, leading to zero net force and constant maximum speed.
Maximum constant speed achieved by an object falling through a fluid.
Occurs when resistive forces (drag) balance driving forces (weight).
At terminal velocity, the net force on the object is zero, and acceleration is zero.
Always remember that momentum is a vector quantity. Pay close attention to directions when solving problems, especially in collisions. Define a positive direction at the start and stick to it! Also, clearly state when you are applying the conservation of momentum.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A football of mass 0.45 kg is moving horizontally towards a player at 20 m/s. The player kicks the ball, causing it to move in the opposite direction with a speed of 30 m/s. If the player's boot is in contact with the ball for 0.050 s, what is the average force exerted on the ball by the player?
- 1
Define a positive direction and list knowns. Let the final direction of the ball be positive.
A 2.0 kg trolley moving at 3.0 m/s collides head-on with a stationary 1.0 kg trolley. After the collision, the 2.0 kg trolley continues in its original direction at 1.0 m/s. Calculate the velocity of the 1.0 kg trolley after the collision.
- 1
Identify knowns:
How it all connects
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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.
- inertia
An object's resistance to changes in its state of motion.
- Weight
Often confused, mass and weight are distinct concepts. Mass is a scalar quantity measuring the amount of matter in an object and its inertia. Weight is a vector quantity representing the gravitational force exerted on an object.
- principle of conservation of momentum
The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external resultant force acts on it.
- Momentum formula
Momentum () is the product of an object's mass () and its velocity (); .
- Newton's Third Law
For every action, there is an equal and opposite reaction force, with these forces always acting on different objects.
- Elastic vs inelastic
In elastic collisions, kinetic energy is conserved; in inelastic collisions, it is not (some is converted to other forms).
- Force & momentum
The net force is equal to the rate of change of momentum ().
- Terminal velocity
The net force acting on the object must be zero, meaning all downward driving forces are balanced by upward resistive forces.
- Newton's First Law
The Law of Inertia.
- Momentum units
Kilogram-metre per second (kg m/s) or Newton-second (Ns).
- Conservation principle
For a closed system, the total momentum before an interaction equals the total momentum after, if no external resultant force acts.
- Mass vs weight
Mass is a scalar measure of inertia; weight is the gravitational force (W=mg), a vector, acting on an object.
- Elastic collision
The relative speed of approach before impact equals the relative speed of separation after impact.
- Closed system
A closed system is one where no matter is exchanged with the surroundings and no external resultant force acts upon it. This is the condition required for the total momentum of the system to be conserved.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
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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 () is a vector quantity with units kg m/s or Ns.
The direction of momentum is the same as the direction of velocity.
An object at rest has zero momentum.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Calculate the mass of the sphere.
The parachute is fully open at time t₂. At a later time t₃ the skydiver reaches a constant velocity of 5.7 ms¯¹.
Describe and explain the variation with time of the magnitude of her acceleration between time t₂ and time t₃.
Extra simulations & links
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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 · Q1(d)(ii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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