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M10.1MechanicsCore

Force Diagrams

A force diagram shows every force acting on an object as an arrow. Drawing one correctly — weight, normal reaction, tension, friction — is the essential first step of almost every mechanics problem.

25 min Forces and Motion
Edexcel AS Level Maths: 10.1 Force DiagramsCurated by Kepler, not produced by us. Watch it before the notes below.
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What you'll be able to do

  • Identify the common forces
  • Draw a clear force diagram
  • Know the direction of each force
  • Recognise equilibrium
1

The common forces

The forces you meet are: weight\textbf{weight} (W=mgW = mg, always downward), the normal reaction\textbf{normal reaction} (RR, perpendicular to the surface), tension\textbf{tension} (along a string, pulling), thrust\textbf{thrust} (along a rod, pushing) and friction\textbf{friction} (along the surface, opposing motion).

W=mgW = mg
Weight = mass × gravity, acting straight down.
2

Drawing the diagram

Represent the object as a dot (particle) and draw each force as an arrow from\textbf{from} the object in the correct direction. Label every arrow. Only include forces actually acting on the object.

Tip — Always include weight (mg) — it’s the most commonly forgotten force.

3

Equilibrium

If an object is in equilibrium\textbf{equilibrium} (at rest or moving at constant velocity), the forces balance: they sum to zero. Resolving in perpendicular directions then gives equal-and-opposite force pairs.

equilibrium⇒resultant force=0\text{equilibrium} \Rightarrow \text{resultant force} = 0
Balanced forces ⟶ no acceleration.
Example 1A 2 kg book rests on a table (g = 9.8). Find the normal reaction.
1Equilibrium vertically: R=W=mg=2×9.8R = W = mg = 2 \times 9.8.
AnswerR=19.6R = 19.6 N

Formula recap

W=mgW = mg
Weight (downward).
R⊥surfaceR \perp \text{surface}
Normal reaction.
equilibrium⇒ΣF=0\text{equilibrium} \Rightarrow \Sigma F = 0
Balanced forces.

Common mistakes to avoid

Forgetting to include the weight on a force diagram.
Weight (mg) always acts — include it pointing straight down.
Drawing the normal reaction vertically on a slope.
The normal reaction is perpendicular to the SURFACE, not always vertical.

Key takeaways

  • Common forces: weight (mg, down), normal reaction (⟂ surface), tension, thrust, friction.
  • Draw each force as a labelled arrow from the particle.
  • Equilibrium means the forces sum to zero.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

Browse practice topics

Related lessons

All 6 lessons

Put the methods into practice: see how A-Level maths duels work. An account is required to play; the overview and sample are public.