GCSE · Physics · Edexcel · Spec 1PH0

Recall vector and scalar quantities (list)

"The treasure is 20 steps away" is no help at all. "20 steps north" and you're digging. Some quantities need a direction to be complete. Today you'll learn which.

Physics · Vectors and scalars

Sort the ten quantities

For each quantity, ask one question: is it complete without saying which way? If it is, it's a scalar. If it needs a direction, it's a vector.

Still to sort

Vector: size and direction (0)

Only half an answer until you say which way.

Where the line is: A vector needs a direction to be complete. If the number and unit already tell the whole story, it isn't a vector.

Scalar: size only (0)

A number and a unit tell the whole story.

Where the line is: A scalar is complete with just its size. Adding 'to the left' to it would make no sense.

10 of 10 still to sort.

Pick a quantity, then pick its column. Commit first, then read why.

Same trip, two ways of describing it

Scalar (size only)vsVector (size and direction)

You jog 300 m east to the park gate at a steady 2 m/s, then straight back home at the same steady pace. Each row puts a scalar next to its vector partner.

Focus

Back home at the end

Scalar (size only)

Distance: 600 m

Vector (size and direction)

Displacement: 0 m

The insight

You covered 600 m of ground, but you finished exactly where you started. Distance counts every step; displacement only cares where you ended up compared with the start.

Standing at the park gate

Scalar (size only)

Distance: 300 m

Vector (size and direction)

Displacement: 300 m east

What each one measures

Scalar (size only)

Distance: total ground covered along the path

Vector (size and direction)

Displacement: straight-line gap from the start, plus a direction

Jogging out to the gate

Scalar (size only)

Speed: 2 m/s

Vector (size and direction)

Velocity: 2 m/s east

Jogging back home

Scalar (size only)

Speed: 2 m/s

Vector (size and direction)

Velocity: 2 m/s west

The odd pair out

?

Reason it through

Why is weight a vector when mass is a scalar?

Link 1 of 4

First link · your turn

Start with what weight actually is. Is it the amount of stuff in you, or something that happens to that stuff?

2
Locked — reveal the link above first
3
Locked — reveal the link above first
4
Locked — reveal the link above first

The ones without partners

Acceleration, force, momentum and energy

Four quantities on the list don't come in a pair: acceleration, force, momentum and energy. They're where most sorting mistakes happen.

Which of these is closest to what you think right now?
How sure are you?

Rebuild the list

The seven lines, from memory

Here's the list as seven lines: three pairs and four single quantities. For each line, tick every box that's true, then check your grid.

Distance / displacement
Speed / velocity
Acceleration
Force
Weight / mass
Momentum
Energy

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Ten quantities, one test: does it make sense without a direction?

What you need to know

  • A scalar quantity has size (magnitude) only. A vector quantity has size and direction.
  • Vectors in the list: displacement, velocity, acceleration, force, weight and momentum.
  • Scalars in the list: distance, speed, mass and energy.
  • In each pair, the vector is displacement (not distance), velocity (not speed) and weight (not mass).

The big picture

Some quantities are complete as a number and a unit: those are scalars. Others make no sense until you say which way: those are vectors. In the list you need to know, displacement, velocity, acceleration, force, weight and momentum are vectors; distance, speed, mass and energy are scalars.

Key points

1One test sorts every quantity: is it complete without saying which way? If not, it's a vector.
2Distance/displacement and speed/velocity are true partners: the same measurement and the same unit, without and with a direction.
3Weight and mass are not partners in that way. Weight is a force (in newtons) acting downwards; mass is an amount of matter (in kilograms).
4Acceleration, force and momentum are vectors. Energy is a scalar, even though it moves from place to place.

Worked example

Problem

A report on a skydiver reads: 'Mass 70 kg. Weight 700 N. Falling at 50 m/s. Kinetic energy 87 500 J.' Which of these four values are vectors, and how should each vector be written so it is complete?

⚠ Watch out

Treating weight and mass as the same thing. Weight is a force, so it is a vector measured in newtons that acts downwards. Mass is the amount of matter in an object, a scalar measured in kilograms.

🧠

Memory hook

Sat-nav or price tag? '300 metres' from a sat-nav is useless until it says which way: that's a vector. '£5' on a price tag is complete on its own: that's a scalar. For any quantity, ask which one it's like.

✓

Check yourself

Cover the page. Name the vector in each pair (distance/displacement, speed/velocity, weight/mass), then say which of acceleration, force, momentum and energy is the only scalar. Answer: displacement, velocity and weight; energy.

Flashcards

(10)
What is a scalar quantity?
A quantity with size (magnitude) only, no direction. Example: a mass of 5 kg.
What is a vector quantity?
A quantity with size AND direction. Example: a force of 20 N to the left.
Distance or displacement: which is the vector?
Displacement: how far from the start, and which way. Distance (total ground covered) is the scalar. Both are in metres.
Speed or velocity: which is the vector?
Velocity: speed in a stated direction. Speed is the scalar. Both are in m/s.
Is acceleration a vector or a scalar?
A vector. It is how quickly velocity changes, and that change has a direction.
Is force a vector or a scalar?
A vector. Every push or pull acts in a direction. Measured in newtons (N).
Weight or mass: which is the vector?
Weight. It is a force (gravity pulling downwards), in newtons. Mass is a scalar: the amount of matter, in kg.
Is momentum a vector or a scalar?
A vector. It depends on velocity, so it points the way the object is moving.
Is energy a vector or a scalar?
A scalar: an amount in joules. Being transferred from place to place doesn't give it a direction.
What single question tells you if a quantity is a vector?
Does it make sense without saying which way? If not, it's a vector.

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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