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The momentum formula is p = mv: momentum (kg m/s) = mass (kg) × velocity (m/s). Free GCSE AQA Physics notes with key definitions and 14 questions answered.
Understanding Momentum is part of Momentum (HT only) in GCSE AQA Higher Physics.
5 min
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39
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GCSE AQA Higher
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The momentum formula is p = mv: momentum (kg m/s) = mass (kg) × velocity (m/s). Free GCSE AQA Physics notes with key definitions and 14 questions answered.
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Use this lesson to stay inside Momentum (HT only) while connecting the detail back to the wider Forces topic.
Read the core explanations from Understanding Momentum before testing yourself from memory.
Picture a lorry and a bicycle both travelling at 10 m/s. Which would be harder to stop? the lorry - but why exactly?
The answer lies in momentum. Both vehicles have the same speed, but the lorry has much more mass. This combination of mass and velocity gives the lorry far more momentum - making it much harder to stop.
Momentum is everywhere in physics. It explains why cricket balls hurt more than tennis balls at the same speed, why cars have crumple zones, and why rockets work in space. Understanding momentum is your key to solving collision problems and force calculations.
Here's the crucial point: momentum depends on both mass AND velocity. Double the mass, double the momentum. Double the velocity, double the momentum. But momentum is also a vector quantity - it has direction as well as size.
The momentum equation is beautifully simple, but don't let that fool you. This equation is the foundation for understanding collisions, explosions, and how forces change motion over time.
Notice we use velocity, not speed. This matters because velocity includes direction. A car travelling north at 20 m/s has different momentum from the same car travelling south at 20 m/s - they're in opposite directions.
The units work out perfectly: kg × m/s = kg m/s. Always include units in your calculations - examiners love to see them, and they help you spot mistakes.
You can rearrange this equation too. Need to find mass? Use $m = \frac{p}{v}$. Need velocity? Use $v = \frac{p}{m}$. These rearrangements are essential for exam success.
Let's tackle some real exam-style momentum calculations. The key is methodical working - write the formula, substitute values with units, then calculate. This approach gets you method marks even if your final answer is wrong.
Worked example: Basic Momentum Calculation
A 1200 kg car travels at 25 m/s. Calculate its momentum. [3 marks]
Answer: 30000 kg m/s (or 3.0 × 10⁴ kg m/s)
Notice how we kept units throughout? This prevents silly mistakes and shows the examiner you understand what you're calculating. The scientific notation version (3.0 × 10⁴) is often preferred for large numbers.
Worked example: Finding Mass from Momentum
A football has momentum 6.0 kg m/s when kicked at 15 m/s. Calculate the mass of the football. [3 marks]
Answer: 0.40 kg
That unit check in step 3 is crucial. If your units don't make sense, you've made an error somewhere. Mass should always come out in kg, velocity in m/s, and momentum in kg m/s.
Here's where momentum gets interesting - and where many students trip up. Momentum isn't just a number; it's a vector. This means direction matters as much as size.
Think about two identical cars approaching each other at the same speed. Car A travels east at 20 m/s, car B travels west at 20 m/s. They have the same mass and speed, but their momenta are opposite. If we call east positive, then car A has positive momentum and car B has negative momentum.
This vector nature becomes crucial when objects collide or when we're dealing with momentum conservation. The total momentum of a system considers both the size and direction of each object's momentum.
In exam questions, always establish a positive direction first. Usually, rightward or eastward is positive, but the question might specify. Once you've chosen, stick to it throughout your calculation.
Momentum isn't just an abstract physics concept - it shapes the world around us. Understanding momentum helps explain everything from car safety features to space travel.
Car manufacturers use momentum principles when designing crumple zones. A car hitting a wall has the same momentum change whether it stops instantly or over several seconds. But spreading that change over more time reduces the force - and that's what saves lives.
Sports players intuitively understand momentum too. A rugby player knows that a heavier player running at the same speed will be harder to tackle. Cricket batsmen know that timing matters more than brute force - it's about transferring momentum efficiently from bat to ball.
Even rockets in space rely on momentum conservation. When a rocket expels hot gases downward at high speed, the rocket gains momentum upward. No air needed - just Newton's laws and momentum conservation.
Momentum questions follow predictable patterns in GCSE exams. Master these techniques and you'll tackle any momentum problem with confidence.
Always start by writing p = mv, even for rearrangement questions. Examiners give method marks for showing the correct formula. Then substitute values with units - this gets you the second method mark even if your arithmetic goes wrong.
Watch out for the classic traps. Don't confuse momentum (kg m/s) with kinetic energy (J). Don't forget that momentum is a vector - include direction when asked. And remember that velocity can be negative if the object moves in the negative direction.
Remember the command words too. 'Calculate' means show your working step by step. 'State' means give a brief answer without explanation. 'Explain' means give reasons using scientific principles - perfect for discussing why momentum depends on both mass and velocity.
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Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
The momentum formula is p = mv: momentum (kg m/s) = mass (kg) × velocity (m/s). It rearranges to m = p/v to find mass and v = p/m to find velocity.
The unit of momentum is kg m/s, because momentum is mass in kg × velocity in m/s. Do not confuse momentum (kg m/s) with kinetic energy, which is measured in joules (J).
Momentum is the quantity of motion of a moving object, calculated as mass multiplied by velocity and measured in kg m/s. It depends on both mass and velocity, and it is a vector quantity, so it has direction as well as size.
To calculate momentum, multiply mass by velocity using p = mv. A 1200 kg car travelling at 25 m/s has a momentum of 1200 × 25 = 30000 kg m/s, or 3.0 × 10⁴ kg m/s.
Momentum is measured in kg m/s and is a vector, while kinetic energy is measured in joules (J). Confusing momentum with kinetic energy is a classic trap.
Rearrange p = mv to m = p/v. A football with momentum 6.0 kg m/s kicked at 15 m/s has a mass of 6.0 ÷ 15 = 0.40 kg; the m/s cancels, leaving kg.
Cricket balls hurt more than tennis balls at the same speed because a cricket ball has more mass, and so more momentum. Momentum is mass × velocity, so doubling the mass doubles the momentum.
Momentum uses velocity rather than speed because velocity includes direction. A car travelling north at 20 m/s has different momentum from the same car travelling south at 20 m/s.
Doubling the velocity doubles the momentum, and doubling the mass also doubles the momentum, because p = mv. Momentum depends on both mass and velocity, and it is a vector with direction as well as size.
Two identical cars approaching each other, car A east and car B west at 20 m/s, have the same size momentum but in opposite directions. Taking east as positive, car A has positive momentum and car B negative momentum.
A heavier rugby player running at the same speed is harder to tackle because they have more momentum: momentum depends on both mass and velocity.
A momentum of 30,000 kg m/s is 3.0 × 10⁴ kg m/s in scientific notation, which is often preferred for large numbers. A 1200 kg car at 25 m/s has this momentum.
A lorry has far more momentum than a bicycle when both travel at 10 m/s, because the lorry has much more mass and momentum = mass × velocity. This makes the lorry much harder to stop.
Units are checked so they make sense: mass in kg, velocity in m/s and momentum in kg m/s. Finding mass with m = p/v, the m/s cancels to leave kg, so 6.0 kg m/s ÷ 15 m/s = 0.40 kg.