GCSE Physics resources

AQA GCSE Forces

Scalars, Vectors and Free-Body Diagrams

Scalars have magnitude only; vectors have magnitude and direction. A free-body diagram should show all relevant forces acting on one object, with arrows in the correct directions and labels that identify the interaction.

AQA 8463AQA 8464 GCSE PhysicsCombined Science: Trilogy FoundationHigher

Start here

The revision snapshot

Scalars have magnitude only; vectors have magnitude and direction. A free-body diagram should show all relevant forces acting on one object, with arrows in the correct directions and labels that identify the interaction.

By the end, you should be able to:

  • Make the forces visible.
  • Apply the forces model, evidence or method to an unfamiliar exam context.
  • Recognise and correct this wrong turn: Adding Newton-third-law pairs to one free-body diagram.

Before you revise

Diagnostic question

Choose an answer from memory. Your result tells you what to watch for in the guide.

Which statement correctly summarises scalars, vectors and free-body diagrams?

Core revision guide

Learn the model, then use it

Scalars, Vectors and Free-Body Diagrams questions become manageable when the central model, evidence and exam method are kept together. Read the explanation, test the misconception and then apply the idea without looking back.

Make the forces visible

Scalars have magnitude only; vectors have magnitude and direction. A free-body diagram should show all relevant forces acting on one object, with arrows in the correct directions and labels that identify the interaction.

Build the physics picture

A force diagram represents one object, not the whole situation. Each arrow must be an interaction force with a clear direction: for example weight, normal contact force, thrust or drag. Motion arrows and pairs of Newton-third-law forces do not belong on the same free-body diagram.

The relationship for this guide

Weight: W = mg (N, kg, N/kg). Choose each relationship from the physical change described, convert quantities into compatible units and keep the unit beside the final answer.

A trolley has weight, normal contact force, driving force and resistive force arrows from a common point.
Interaction forces are labelled on the isolated object; the separate resultant arrow shows the direction of acceleration.Open the full-size exam diagram
WeightW = mgN, kg, N/kg

Misconception clinic

Replace the tempting answer

Read each belief, say what is wrong with it, then compare your correction.

Tempting idea: Adding Newton-third-law pairs to one free-body diagram.

Use instead: Scalars have magnitude only; vectors have magnitude and direction. A free-body diagram should show all relevant forces acting on one object, with arrows in the correct directions and labels that identify the interaction.

Tempting idea: Calling speed a vector.

Use instead: A force diagram represents one object, not the whole situation. Each arrow must be an interaction force with a clear direction: for example weight, normal contact force, thrust or drag. Motion arrows and pairs of Newton-third-law forces do not belong on the same free-body diagram.

Tempting idea: Leaving force arrows unlabelled.

Use instead: Choose the object, draw one arrow per force and then compare opposite directions to find the resultant.

Retrieval practice

Quick checks

1. Which exam method is most reliable for scalars, vectors and free-body diagrams?

2. Which statement correctly applies scalars, vectors and free-body diagrams to a question?

3. A pupil writes: “Adding Newton-third-law pairs to one free-body diagram.” Which replacement is accurate?

Worked examples

See the method being built

These examples expose the difference between a secure make the forces visible method and the common error “Adding Newton-third-law pairs to one free-body diagram.”.

Example 1 · Classify quantities

Classify mass, velocity, distance and force as scalar or vector.

  1. Look for direction as well as size.
  2. Mass and distance have magnitude only.
  3. Velocity and force need direction.
Show the answer

Mass and distance are scalars; velocity and force are vectors.

Example 2 · Free-body diagram

A book rests on a table. Describe its free-body diagram.

  1. Choose the book only.
  2. Add weight down.
  3. Add normal contact force up.
Show the answer

Draw equal arrows: weight downward and normal contact force upward. Do not draw forces acting on the table.

Example 3 · Resultant force

A 12 N force acts right and an 8 N force acts left. Find resultant.

  1. Choose a positive direction.
  2. Subtract opposing forces.
  3. State direction.
Show the answer

Resultant force = 4 N to the right.

Exam precision

Exam technique: Make the forces visible

Do this: Choose the object, draw one arrow per force and then compare opposite directions to find the resultant.

Independent practice

Exam-style questions

Write an answer before opening the marking guidance. Then edit the exact phrase or step that would gain the next mark.

1. State one scalar quantity.

[1 mark]
Show marking guidance and model answer

Marking guidance: Award one mark for the precise statement shown in the model answer.

Model answer: For example, mass, distance, time or speed.

2. State one vector quantity.

[1 mark]
Show marking guidance and model answer

Marking guidance: Award one mark for the precise statement shown in the model answer.

Model answer: For example, force, velocity, displacement or acceleration.

3. Explain why a free-body diagram includes only one object.

[3 marks]
Show marking guidance and model answer

Marking guidance: Award up to 3 marks for distinct physics points joined into a clear cause-and-effect chain.

Model answer: It shows the forces acting on that chosen object, avoiding action-reaction forces on other objects.

4. A car has 500 N thrust and 500 N resistive force. State the resultant.

[2 marks]
Show marking guidance and model answer

Marking guidance: 2 marks are available for relevant, linked physics points that match the model answer.

Model answer: Zero newtons.

5. State the direction of weight near Earth’s surface.

[1 mark]
Show marking guidance and model answer

Marking guidance: Award one mark for the precise statement shown in the model answer.

Model answer: Vertically downward, towards the centre of Earth.

6. Explain what a zero resultant force means for a moving object.

[3 marks]
Show marking guidance and model answer

Marking guidance: Award up to 3 marks for distinct physics points joined into a clear cause-and-effect chain.

Model answer: It continues at constant velocity in a straight line.

Questions pupils ask

Scalars, Vectors and Free-Body Diagrams FAQs

What is the main idea in Scalars, Vectors and Free-Body Diagrams?

Scalars have magnitude only; vectors have magnitude and direction. A free-body diagram should show all relevant forces acting on one object, with arrows in the correct directions and labels that identify the interaction.

What mistake should I avoid in Scalars, Vectors and Free-Body Diagrams?

Adding Newton-third-law pairs to one free-body diagram. A force diagram represents one object, not the whole situation. Each arrow must be an interaction force with a clear direction: for example weight, normal contact force, thrust or drag. Motion arrows and pairs of Newton-third-law forces do not belong on the same free-body diagram.

Useful next steps

Connect this guide to your next task

Acceleration Required PracticalUse a trolley and light gates or video timing to measure speed and acceleration. Reduce friction where possible, repeat readings and keep the mass or force controlled according to the variable being investigated.Motion Graphs, Speed and AccelerationUse graph gradient and area carefully. A curved distance–time graph shows changing speed; a horizontal velocity–time line shows constant velocity; a negative velocity can still have a positive speed.How to Answer GCSE Physics Six-Mark QuestionsLonger answers are easier when you turn the question into a chain: claim, physics reason, consequence and context. Use the command word to decide what the answer must contain. More free PhysicsUK resourcesBrowse revision, practical and exam-support resources. Try AQA GCSE Physics in PhysicsUK Exam StudioApply your knowledge to marked exam-style work.