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Forces and Newton's laws: A Level Maths knowledge organiser

Everything to know about forces and newton's laws on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Resultant force
The single force with the same effect as all the forces acting.
Newton's second law
F = ma: resultant force = mass × acceleration.
Normal reaction
The force from a surface, at right angles to it.
Friction
Opposes motion; F ≤ μR, with F = μR when the object is moving or about to move.

Key formulas

Forces\(F=ma,\) \(W=mg,\) \(F\le\mu R\ (\text{limiting: }F=\mu R)\)
Slope at \(\theta\): weight component \(mg\sin\theta\) down the slope; \(R=mg\cos\theta\) if nothing else acts perpendicular to it

Worked example

A 5 kg box is pulled along a rough horizontal floor by a horizontal force of 30 N. μ = 0.4 and g = 9.8 m s⁻². Find the acceleration.

  1. R = mg = 5 × 9.8 = 49 N
  2. Friction F = μR = 0.4 × 49 = 19.6 N
  3. 30 − 19.6 = 5a

Answer: a = 2.08 m s⁻²

Common mistakes

  • G positive when up is positive
  • Weight given as m
  • Normal reaction missing from the diagram
  • Resultant set to zero in a dynamics question

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

  • Draw clear force diagrams showing weight, tension, normal reaction and thrust, and find the resultant of forces acting in one or two dimensions.
  • Use Newton's third law to analyse connected particles such as a car towing a trailer, finding the acceleration and the tension or thrust in the connection.
  • Resolve forces into perpendicular components, find the resultant of several forces and its direction, and use the components to solve equilibrium problems.
  • Solve problems with friction on inclined planes, deciding the direction of friction and whether a particle stays at rest or slides.
  • Model static situations such as objects hanging from strings, stating assumptions and finding unknown tensions and angles.
  • Solve problems with connected particles, including one on an inclined plane and one hanging over a pulley, with friction where it applies.

The printable sheet

Forces and Newton's laws knowledge organiser for A Level Maths: one A4 page of key definitions, formulas, a worked example and common mistakes
Forces and Newton's laws knowledge organiser (A Level Maths), A4. Download the PDF.

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