In simple terms
A friendly intro before the formal notes — no formulas yet.
The Rules of Crashing
Momentum is simply 'mass in motion' and has a direction. In any interaction like a collision, the total amount of this 'mass in motion' before and after is the same, provided no external forces interfere.
Imagine two roller-skaters on a smooth, flat rink. One is heavy and moving slowly, the other is light and moving fast. Before they collide, they have a certain combined 'push'. If they grab onto each other after colliding, this combined 'push' is conserved—they will move off together with a new velocity that keeps the total 'push' the same as it was initially. The total momentum of the skater system is conserved.
- 1
Momentum, , is a vector quantity. In a closed system with no external forces, total momentum is always conserved.
- 2
Impulse is the change in momentum, . It's also the area under a force-time graph.
- 3
In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, only momentum is conserved; some KE is lost.
- 4
In explosions from rest, the system's initial momentum is zero. By conservation, the total momentum of all fragments must also be zero.
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
Momentum p = mv — vector quantity conserved in closed system.
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.
Defining Linear Momentum
Momentum is a measure of an object's motion, often described as 'mass in motion'. It's not just about speed; a slow-moving lorry has a lot more momentum than a fast-moving tennis ball. Because it depends on velocity, momentum is a vector quantity, meaning it has both magnitude and direction. This is a critical detail in all calculations.
Momentum () = mass () × velocity () \
Units: kg m s⁻¹.
Vector Quantity: Direction is crucial. Always define a positive direction for one-dimensional problems.
A stationary object () has zero momentum.
The Principle of Conservation of Momentum
This is one of the most important principles in mechanics. It states that in a closed system (one with no external resultant forces), the total momentum before an interaction is equal to the total momentum after the interaction. The momentum of individual objects may change, but the total for the system remains constant.
Total Initial Momentum = Total Final Momentum \
Impulse
When a force acts on an object for a period of time, it causes a change in the object's momentum. This 'change in momentum' is called impulse. Newton's Second Law can be expressed as Force = rate of change of momentum, which leads directly to the impulse-momentum relationship. Impulse is also a vector quantity, acting in the same direction as the force that causes it.
Impulse () = Change in Momentum () \
In questions involving a force that varies with time, the impulse is the area under the force-time graph. Be careful with signs when calculating the change in momentum, especially if an object rebounds. If a ball hits a wall at velocity and rebounds with velocity , the change in momentum is (assuming initial direction is positive).
Collisions and Explosions
Collisions are classified based on what happens to the kinetic energy of the system. In a perfectly elastic collision, kinetic energy is conserved. In an inelastic collision, some kinetic energy is lost, usually as heat or sound. Explosions can be thought of as 'reverse collisions', where internal energy (e.g., chemical) is converted into kinetic energy, but momentum is still conserved.
All Collisions/Explosions: Linear momentum is conserved.
Elastic Collisions: Kinetic energy is also conserved.
Inelastic Collisions: Kinetic energy is lost. The total KE after is less than the total KE before.
Explosions from rest: Initial momentum is zero, so the vector sum of the final momenta is also zero.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A particle A of mass 0.5 kg moving at 4 m s⁻¹ on a smooth horizontal surface collides directly with a particle B of mass 0.3 kg which is moving at 2 m s⁻¹ in the opposite direction. After the collision, the particles coalesce to form a single particle C. Find the velocity of C after the collision.
- 1
First, define a positive direction. Let's take the initial direction of particle A as positive. \ \ 1. State initial velocities with correct signs: \ Velocity of A, m s⁻¹ \ Velocity of B, m s⁻¹ \ \ 2. Apply the Principle of Conservation of Momentum: \ Total momentum before = Total momentum after \ \ \ 3. Substitute values and solve for : \ \ \ \ m s⁻¹ \ \ Since the result is positive, the combined particle C moves at 1.75 m s⁻¹ in the original direction of particle A.
A shell of mass 3 kg is at rest on a smooth horizontal floor. It explodes into two fragments, P and Q. Fragment P has a mass of 1 kg and moves with a speed of 6 m s⁻¹. Fragment Q has a mass of 2 kg. Find the speed of fragment Q and the total kinetic energy generated in the explosion.
- 1
The shell is initially at rest, so the total initial momentum is 0. \ \ 1. Apply Conservation of Momentum: \ Total initial momentum = Total final momentum \ \ \ 2. Substitute values and solve for : \ Let the direction of P be positive, so m s⁻¹. \ \ \ \ m s⁻¹ \ The speed of Q is the magnitude of its velocity, which is 3 m s⁻¹. The negative sign indicates it moves in the opposite direction to P. \ \ 3. Calculate Kinetic Energy Generated: \ The KE generated is the total final KE, since the initial KE was zero. \ \ \ \ \ J \ The explosion generated 27 Joules of kinetic energy.
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
Try to recall each definition before you reveal it.
Quick check
Answer in your head first — then tap to check. No pressure.
Revision flashcards
Flip the card. Test yourself before the exam.
What is the definition of linear momentum?
Linear momentum is the product of an object's mass and its velocity. It is a vector quantity.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
- ✓
Units: kg m s⁻¹.
- ✓
Vector Quantity: Direction is crucial. Always define a positive direction for one-dimensional problems.
- ✓
A stationary object () has zero momentum.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Test Your Understanding with Exam-Style Questions
Test Your Understanding with Exam-Style Questions
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 Test Your Understanding with Exam-Style Questions on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.