GCSE · Physics · Edexcel · Spec 1PH0

Momentum equation p = mv

A 40-tonne lorry is parked at the kerb. A football flies past it. Which has more momentum? Most people pick the lorry — hold that thought.

Lift the dot: make the trolley heavier

Mass 2 kg

Mass: 2 kg. Momentum at 3 m/s: 6.0 kg m/s

The dot is the trolley rolling right at 3 m/s. Lift it to add mass: same velocity, more momentum. Now look at 0 m/s — every line goes through it, however heavy the trolley. No velocity, no momentum. Left of 0 the trolley rolls the other way, and its momentum is negative: same size, opposite direction.

Back to the lorry

Who has the most momentum?

A 40 000 kg lorry is parked at the kerb. Two identical 0.4 kg footballs fly past it at 20 m/s — one heading east, one heading west.

Which is closest to what you think?

The lorry has by far the most momentum. It's thousands of times heavier than a football.Momentum is just another word for speed. Each ball has 20 of it, and the lorry has none.The lorry has none, and the two balls have exactly the same momentum: 8 kg m/s each.The lorry has none. Each ball has 8 kg m/s, but in opposite directions: +8 and −8 kg m/s.

How sure are you?

I'm sureI think soI'm guessing

The lorry has by far the most momentum. It's thousands of times heavier than a football.

This is a common misconception

Mass is only half the story. Momentum is mass × velocity, and the parked lorry's velocity is zero: 40 000 kg × 0 m/s = 0. However heavy it is, standing still means no momentum at all. Each football has 0.4 kg × 20 m/s = 8 kg m/s, so both balls beat the lorry.

Momentum is just another word for speed. Each ball has 20 of it, and the lorry has none.

This is a common misconception

Close, but momentum isn't speed — speed leaves out the mass. Each ball has 0.4 kg × 20 m/s = 8 kg m/s, not 20. And mass can matter hugely: if the lorry crept forward at just 1 m/s it would have 40 000 kg m/s — 5000 times a ball's momentum, while moving 20 times slower.

The lorry has none, and the two balls have exactly the same momentum: 8 kg m/s each.

This is a common misconception

Right size, wrong sign. Momentum is a vector — it points the same way as the velocity. Take east as positive: the eastbound ball has +8 kg m/s and the westbound ball has −8 kg m/s. Same size, opposite signs, because they're moving in opposite directions.

The lorry has none. Each ball has 8 kg m/s, but in opposite directions: +8 and −8 kg m/s.

This matches the evidence

Exactly. The lorry's momentum is 40 000 × 0 = 0 because it isn't moving. Each ball has 0.4 × 20 = 8 kg m/s, and because momentum takes the direction of the velocity, one is +8 kg m/s and the other −8 kg m/s (taking east as positive).

Momentum needs mass AND velocity — no velocity, no momentum — and it points wherever the object is heading, so opposite directions mean opposite signs.

The momentum triangle

Cover the quantity you want to find. Side by side means multiply; one above the other means divide.

Tap the quantity you want to find. The triangle shows you the formula.

Cover momentum, mass or velocity to reveal its rearranged formula, then plug in numbers to solve.

Finding a velocity

Problem

A 450 g football has a momentum of 9 kg m/s. Calculate its velocity.

Your turn to check

Find the line where it goes wrong

A 60 g tennis ball is hit at 25 m/s. Calculate its momentum.

A student's answer — which line goes wrong?

p = m × v
m = 60 g, v = 25 m/s
p = 60 × 25
p = 1500
p = 1500 kg m/s

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Mass on the move — and it has a direction. Anything standing still has none at all.

What you need to know

Momentum = mass × velocity. In symbols p = m × v, with p in kg m/s, m in kg and v in m/s.
It takes mass AND velocity. No velocity means no momentum, however heavy the object is.
Momentum points the way the object moves. Pick one direction as positive, and anything moving the other way has negative momentum.

The big picture

Momentum is mass on the move: momentum = mass × velocity, or p = m × v, measured in kg m/s. It's a vector, pointing the same way as the velocity, so objects moving in opposite directions have momenta of opposite sign. Anything standing still has zero momentum, however heavy. At the same velocity, more mass means more momentum; at the same mass, more velocity means more momentum. To find a mass or a velocity, rearrange to m = p ÷ v or v = p ÷ m, with the mass in kilograms and the velocity in m/s.

Key points

1Momentum = mass × velocity: p = m × v, measured in kg m/s.

2An object at rest has zero momentum, however massive it is.

3At the same velocity, a bigger mass has more momentum. At the same mass, a bigger velocity gives more momentum.

4Momentum is a vector: it has size and direction, and it points the same way as the velocity. So objects moving in opposite directions have momenta of opposite sign.

5Rearranged: m = p ÷ v and v = p ÷ m.

6Use kilograms and metres per second. Convert grams to kilograms by dividing by 1000.

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Worked example

Problem

A cyclist and their bike are moving west at 8 m/s. Taking east as positive, their momentum is −720 kg m/s. Calculate the total mass of the cyclist and bike.

⚠ Watch out

Putting a mass in grams straight into p = m × v. The equation needs kilograms, so divide by 1000 first. Otherwise a momentum comes out 1000 times too big — and a velocity found with v = p ÷ m comes out 1000 times too small.

🧠

Memory hook

Momentum is Mass on the moVe: p = m × v. No move, no momentum — and it always points the way the move goes.

✓

Check yourself

Cover the page. A 5 kg bowling ball rolls left at 2 m/s. Taking right as positive, what is its momentum? And what is its momentum once it has stopped?

Flashcards

(12)

What is momentum?

The product of an object's mass and its velocity: momentum = mass × velocity.

Write the momentum equation in symbols.

p = m × v

What is the unit of momentum?

Kilogram metres per second: kg m/s.

In p = m × v, what units must mass and velocity be in?

Mass in kilograms (kg), velocity in metres per second (m/s).

What is the momentum of an object that isn't moving?

Zero — its velocity is zero, so m × 0 = 0, however heavy it is.

Is momentum a scalar or a vector?

A vector: it has size and direction, and its direction is the same as the velocity's.

Two identical objects move at the same speed in opposite directions. How do their momenta compare?

Same size, opposite signs — one positive, one negative.

Two objects move at the same velocity. Which has more momentum?

The one with more mass.

An object's mass stays the same but its velocity increases. What happens to its momentum?

It increases — for the same mass, a larger velocity gives more momentum.

Rearrange p = m × v to find mass.

m = p ÷ v

Rearrange p = m × v to find velocity.

v = p ÷ m

How do you convert a mass in grams to kilograms?

Divide by 1000. For example, 250 g = 0.25 kg.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Lift the dot: make the trolley heavier

Who has the most momentum?

Find the line where it goes wrong

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