Introduction to Momentum Conservation Revision Notes | GCSE AQA Higher Physics

1. What Is Momentum?

Picture a massive lorry rolling slowly down a hill and a tennis ball flying through the air at high speed. Which would be harder to stop? Your instinct says the lorry, even though the tennis ball is moving faster.

This is because the lorry has more momentum. Momentum depends on both mass and velocity - it's not enough to be heavy or fast alone. A stationary lorry has zero momentum, no matter how massive it is.

Momentum is a vector quantity, which means it has both size and direction. A car travelling north at 20 m/s has different momentum from the same car travelling south at 20 m/s - the magnitudes are equal but the directions are opposite.

2. The Conservation Principle

Here's where momentum gets really powerful. In any collision, explosion, or interaction, something remarkable happens: the total momentum stays exactly the same. This isn't just a useful approximation - it's one of the fundamental laws of physics.

Think about two snooker balls colliding. Before the collision, Ball A might have lots of momentum and Ball B might be stationary. After the collision, both balls are moving in different directions with different speeds.

The individual momenta have changed completely, but when you add up all the momentum vectors, the total is identical to what you started with. This is conservation of momentum in action.

The key phrase here is 'closed system'. This means no external forces are acting on the objects. In reality, friction and air resistance are always present, but for most collisions these effects are tiny compared to the forces between the colliding objects.

3. Momentum in Collisions

Let's see how this works in practice. When objects collide, they exert equal and opposite forces on each other (Newton's third law). These forces act for the same time, so the changes in momentum are equal and opposite too.

If Object A gains 50 kg m/s of momentum to the right, then Object B must lose exactly 50 kg m/s of momentum to the right (or gain 50 kg m/s to the left). The total momentum of the system remains constant.

Worked example: Collision Calculation

A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley. After collision, they stick together. Find their combined velocity.

1. Before: $p_1 = 2 \times 3 = 6$ kg m/s, $p_2 = 1 \times 0 = 0$ kg m/s — Only the moving trolley has momentum initially
2. Total momentum before = $6 + 0 = 6$ kg m/s — This must equal the momentum after collision
3. After collision: combined mass = $2 + 1 = 3$ kg — They stick together, so we have one object of mass 3 kg
4. $6 = 3 \times v$, so $v = 2$ m/s — Using momentum = mass × velocity

Answer: The combined trolleys move at 2 m/s

Notice how the final velocity is less than the initial velocity of the moving trolley. This makes sense - the same momentum is now shared between a larger total mass, so the velocity must decrease.

4. Explosions and Momentum

Explosions are just collisions in reverse. Instead of two moving objects coming together, we start with one object that splits into two or more pieces. The same conservation principle applies.

Before the explosion, the total momentum is usually zero (if the object was at rest). After the explosion, the pieces fly apart, but their momenta must still add up to zero. This means they move in opposite directions.

Think of a cannon firing a cannonball. The cannon recoils backwards with momentum equal and opposite to the cannonball's forward momentum. The total momentum of the cannon-cannonball system remains zero.

Worked example: Explosion Calculation

A 1000 kg cannon fires a 5 kg cannonball at 200 m/s. Find the recoil velocity of the cannon.

1. Before firing: total momentum = 0 kg m/s — Both cannon and cannonball are initially at rest
2. Cannonball: $p = 5 \times 200 = 1000$ kg m/s forward — Taking forward as positive direction
3. Total momentum after = 0, so cannon momentum = -1000 kg m/s — Cannon momentum must be equal and opposite
4. $-1000 = 1000 \times v$, so $v = -1$ m/s — Negative means backwards (recoil direction)

Answer: The cannon recoils at 1 m/s backwards

5. Real-World Applications

Momentum conservation isn't just a physics classroom curiosity - it's everywhere in the real world. Car safety features, sports techniques, and space travel all rely on understanding momentum.

Crumple zones in cars work by extending the collision time. The momentum change is the same, but spreading it over a longer time reduces the force on passengers. Airbags work on the same principle - they increase the time taken for your body to stop.

In sports, momentum explains why follow-through matters in tennis or golf. The racket or club continues moving after hitting the ball, transferring maximum momentum. It also explains why heavier boxing gloves reduce injury - they increase the contact time and reduce the peak force.

Rockets in space use momentum conservation to change direction. They eject hot gases in one direction, gaining momentum in the opposite direction. Without anything to 'push against', this is the only way to manoeuvre in the vacuum of space.

6. Exam Technique and Common Mistakes

Momentum questions in exams follow predictable patterns. You'll typically need to calculate momentum before and after an event, then apply conservation. The key is being systematic about directions and units.

Always define a positive direction at the start - usually the direction of initial motion. Objects moving in the opposite direction have negative velocity and momentum. This prevents sign errors that lose marks.

Watch out for the units trap. Momentum is always in kg m/s, but velocities might be given in km/h or other units. Convert everything to standard SI units before calculating. Also remember that momentum is a vector - direction matters as much as magnitude.

The most common mistake is forgetting that momentum is conserved for the whole system, not individual objects. Individual momenta change dramatically in collisions, but the total always stays the same in a closed system.