What you'll learn
Momentum explains why a fast, heavy object is so hard to stop, and why things recoil when they push off each other. For AQA GCSE Physics (higher tier) you need to be able to calculate momentum, apply the conservation of momentum to collisions and explosions, and use the idea of momentum to explain safety features that reduce the force in a crash. This guide covers the momentum equation, the principle of conservation of momentum, worked collision and explosion problems, and how changing the time of a collision changes the force. By the end you should be able to calculate momentum, solve conservation-of-momentum problems, and explain safety features in terms of momentum and force.
Key terms and definitions
Momentum — A measure of the motion of an object, equal to its mass multiplied by its velocity; measured in kg m/s.
Velocity — Speed in a particular direction; a vector quantity.
Conservation of momentum — In a closed system, the total momentum before an event equals the total momentum after it.
Closed system — A system where no external force acts, so total momentum is conserved.
Collision — An event where objects come together and interact.
Explosion — An event where objects that were together move apart.
Resultant force — The overall force acting on an object, equal to the rate of change of momentum.
Vector — A quantity with both size and direction.
Core concepts
Calculating momentum
Momentum is calculated using:
momentum = mass × velocity (p = m v)
Momentum is measured in kilograms metres per second (kg m/s). Because velocity has a direction, momentum is a vector — it has direction too. When working in one dimension, you must choose a positive direction (for example, to the right) and treat velocities in the opposite direction as negative.
The conservation of momentum
The principle of conservation of momentum states that, in a closed system, the total momentum before an event equals the total momentum after the event. A closed system is one where no external force acts. This principle applies to collisions and explosions, and it is the key to almost every calculation in this topic:
total momentum before = total momentum after
Collisions
In a collision, two objects come together. To solve a collision problem, work out the total momentum before the collision (adding the momentum of each object, taking direction into account), then set it equal to the total momentum after. If two objects join together and move as one after the collision, their combined mass moves with a single velocity.
Explosions
In an explosion, objects that were together move apart. Before an explosion, if the objects are stationary, the total momentum is zero. By conservation of momentum, the total momentum after must also be zero. This means the objects move apart in opposite directions with equal and opposite momenta — which is why a gun recoils backwards when a bullet is fired forwards.
Force and rate of change of momentum
A resultant force acting on an object changes its momentum. The force is equal to the rate of change of momentum:
force = change in momentum ÷ time taken
This is very important for safety. For a given change in momentum (for example, a car stopping in a crash), if the change happens over a longer time, the force is smaller. This is why safety features are designed to increase the time of a collision.
Explaining safety features
Many car safety features work by increasing the time taken for a person's momentum to change, which reduces the force on them:
- Crumple zones in a car crumple on impact, increasing the time the car takes to stop.
- Seat belts stretch slightly, increasing the time for the passenger to stop.
- Air bags cushion the impact, increasing the stopping time.
In each case, because the change in momentum happens over a longer time, the force on the person is smaller, reducing injury. This is a very common exam question and always uses force = change in momentum ÷ time.
Why momentum is conserved
Conservation of momentum follows from Newton's third law, which says that when two objects interact, they exert equal and opposite forces on each other. During a collision, each object pushes on the other with the same size of force for the same length of time, so each experiences an equal and opposite change in momentum. This means one object's gain in momentum is exactly matched by the other's loss, so the total momentum of the system does not change. Understanding this reasoning helps you see why the principle works, rather than just applying it as a rule.
Momentum in everyday and sporting situations
Momentum ideas appear in many real situations. A large ship is very hard to stop because it has a huge mass and therefore a large momentum even at low speed. In sport, "following through" when hitting a ball increases the time the force acts, increasing the change in momentum and so the speed given to the ball. Catching a fast ball, players draw their hands back to increase the stopping time and reduce the force on their hands. Recognising these examples helps you apply the equations to unfamiliar contexts in the exam, which is exactly what higher-mark questions test.
Worked examples
Example 1: Calculating momentum
Calculate the momentum of a 1200 kg car travelling at 15 m/s. Momentum = mass × velocity = 1200 × 15 = 18,000 kg m/s in the direction of travel.
Example 2: A collision where objects join
A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley and they join together. Find their combined velocity after the collision. Momentum before = (2 × 3) + (1 × 0) = 6 kg m/s. After, the combined mass is 3 kg moving at velocity v. By conservation: 6 = 3 × v, so v = 2 m/s in the original direction.
Example 3: An explosion
A stationary firework of mass 0.5 kg explodes into two equal 0.25 kg pieces. One piece moves left at 6 m/s. Find the velocity of the other. Total momentum before = 0 (stationary). After: (0.25 × −6) + (0.25 × v) = 0. So 0.25v = 1.5, giving v = +6 m/s (6 m/s to the right). The pieces move apart with equal and opposite momentum.
Example 4: Force in a crash
A passenger's momentum changes by 900 kg m/s when a car stops. Compare the force if this happens in 0.1 s versus 0.5 s. Force = change in momentum ÷ time. At 0.1 s: 900 ÷ 0.1 = 9000 N. At 0.5 s: 900 ÷ 0.5 = 1800 N. The longer time gives a much smaller force, which is why crumple zones and seat belts reduce injury.
Common mistakes and how to avoid them
The most common error is ignoring direction. Momentum is a vector, so in collisions and explosions you must make one direction positive and the opposite direction negative. Forgetting the negative sign gives the wrong answer, especially in explosions.
Students often forget that the total momentum before an explosion of a stationary object is zero. This is the whole basis of explosion calculations — the momenta must cancel afterwards.
Another mistake is using speed instead of velocity and not tracking direction. Always state the direction of your final answer.
When explaining safety features, do not just say they "absorb the impact". Explain that they increase the time over which the momentum changes, so the force is smaller (force = change in momentum ÷ time). That reasoning is what earns the marks.
Finally, check your units — momentum is in kg m/s, and force in newtons. Mixing up mass and weight, or using grams instead of kilograms, leads to errors.
Exam technique for "Momentum and conservation of momentum"
For calculations, always write "total momentum before = total momentum after", then substitute, keeping directions consistent. Show each object's momentum separately so your working is clear and earns method marks.
Safety-feature questions are essentially the same physics every time: a longer collision time means a smaller force for the same change in momentum. Learn the sentence and apply it to crumple zones, seat belts and air bags.
Explosion questions rely on the total momentum being zero at the start, so the pieces have equal and opposite momentum afterwards. Set the total after equal to zero and solve. Take care with positive and negative directions throughout, and state the direction in your final answer.
Quick revision summary
- momentum = mass × velocity (p = m v), measured in kg m/s; momentum is a vector.
- Conservation of momentum: in a closed system, total momentum before = total momentum after.
- In a collision, add the momenta before and set equal to after; joined objects move as one combined mass.
- In an explosion of a stationary object, total momentum stays zero, so pieces move apart with equal and opposite momentum.
- force = change in momentum ÷ time — a longer collision time means a smaller force.
- Crumple zones, seat belts and air bags increase the collision time, reducing the force and injury.