Momentum Calculations Revision Notes | GCSE AQA Higher Physics

1. What is Momentum?

Picture a massive lorry and a small car both travelling at 30 mph. Which would be harder to stop? Your instinct says the lorry - and physics agrees. The lorry has more momentum.

Momentum captures this idea perfectly. It combines both mass and velocity into one quantity that tells us how much 'oomph' a moving object has. A heavy object moving slowly can have the same momentum as a light object moving fast.

2. The Momentum Equation

The momentum equation is beautifully simple, but don't let that fool you. It's one of the most powerful tools in physics.

Notice that momentum is a vector quantity - it has both magnitude and direction. If two identical cars travel at the same speed but in opposite directions, their momenta cancel out when added together.

You can rearrange this equation to find any unknown quantity. Need to find mass? Use $m = \frac{p}{v}$. Need velocity? Use $v = \frac{p}{m}$.

Worked example: Calculating Momentum

A 1200 kg car travels at 25 m/s. Calculate its momentum. [2 marks]

1. $p = mv$ — [M1] for correct formula
2. $p = 1200 \times 25$ — Mass in kg, velocity in m/s
3. $p = 30,000$ kg m/s — [A1] for correct answer with units

Answer: 30,000 kg m/s

3. Conservation of Momentum

Here's where momentum gets really interesting. When objects collide, something remarkable happens - the total momentum stays exactly the same before and after the collision.

This works because of Newton's third law. When object A pushes on object B during a collision, object B pushes back with an equal and opposite force. The momentum lost by A exactly equals the momentum gained by B.

The conservation equation looks like this: momentum before = momentum after, or $m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$, where u represents initial velocities and v represents final velocities.

4. Collision Calculations

Real collision problems can look intimidating, but there's a systematic approach that works every time. The key is to be methodical about directions and signs.

Choose a positive direction (usually right or the direction of initial motion). Any object moving in this direction has positive velocity; any object moving opposite has negative velocity.

Worked example: Two-Object Collision

A 3 kg trolley moving at 4 m/s collides with a stationary 2 kg trolley. After collision, the 3 kg trolley moves at 1 m/s in the same direction. Find the velocity of the 2 kg trolley. [4 marks]

1. $m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$ — [M1] for conservation of momentum
2. $(3 \times 4) + (2 \times 0) = (3 \times 1) + (2 \times v_2)$ — Second trolley initially at rest, so $u_2 = 0$
3. $12 + 0 = 3 + 2v_2$ $12 = 3 + 2v_2$ — [M1] for correct substitution
4. $2v_2 = 12 - 3 = 9$ $v_2 = 4.5$ m/s — [A1] for correct final answer with units

Answer: 4.5 m/s in the positive direction

Notice how the momentum was redistributed. The 3 kg trolley slowed down from 4 m/s to 1 m/s, losing momentum. The 2 kg trolley gained exactly this amount, accelerating from rest to 4.5 m/s.

5. Real-World Applications

Momentum conservation isn't just a physics curiosity - it governs everything from car safety to space travel. Understanding it helps explain why certain safety features work and others don't.

Car crumple zones work by extending collision time. The momentum change is the same, but spreading it over longer time reduces the force ($F = \frac{\Delta p}{\Delta t}$). This is why modern cars are designed to deform in crashes.

Rockets work by conservation of momentum too. They throw hot gases backwards at high speed, and by Newton's third law, the rocket gains momentum forwards. No air is needed - rockets work perfectly in space.

Even walking relies on momentum conservation. You push backwards on the ground, and the ground pushes forwards on you. The Earth gains a tiny amount of momentum backwards, but its enormous mass means its velocity change is negligible.

6. Exam Technique and Common Mistakes

Momentum questions are mark-winners if you know the technique, but they're full of traps for the unwary. Here's how to avoid the common pitfalls and secure full marks.

Always define your positive direction clearly at the start. Write something like 'taking rightward as positive' so the examiner knows your sign convention. This prevents confusion with negative velocities.

Show every step of your working. Even if you make an arithmetic error, you can still get method marks for using the correct formula and approach. Never skip the formula step - it's usually worth a mark.

For 6-mark questions, structure your answer clearly: state the principle (conservation of momentum), write the equation, substitute values, solve algebraically, then calculate numerically. This methodical approach maximises your mark potential.