Scalars, Vectors & Forces

GCSE Physics cheat sheet · ForcesThis is a free GCSE Physics cheat sheet on scalars, vectors & forces, covering the key ideas in forces on a single page. Read it below, download it as a PNG or PDF, or print it out for your wall.

cheat sheet

The Scalars, Vectors & Forces cheat sheet: a one-page GCSE Physics summary of forces.

Scalars, Vectors & Forces

Scalars vs vectors, contact and non-contact forces, free-body diagrams, resultant force, and the relationship between weight, mass and gravitational field strength.

Illustrated by Cognito Art Team · Reviewed by Emily

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Everything on the GCSE Physics Scalars, Vectors & Forces poster is written out below, section by section. Use it to search the sheet, copy parts into your own notes, or check a fact quickly.

Scalars and Vectors

Scalars

A scalar is a quantity defined solely by its magnitude (size).

Examples: distance, speed, mass, temperature, time, energy.

Vectors

A vector is a quantity defined by both magnitude and direction.

Examples: displacement, velocity, acceleration, force, weight, momentum.

Representing vectors

Vectors are drawn as arrows:

  • Length shows size.
  • Direction shows direction.

Two perpendicular vectors can be added by scale drawing (tip-to-tail) or by Pythagoras to find the resultant.

Contact and Non-Contact Forces

A force is a push or a pull on an object caused by it interacting with something.

Contact forces

  • Friction – opposes motion between surfaces in contact.
  • Air resistance – opposes motion through air.
  • Tension – pull in a rope, cable or string.
  • Normal contact force – push from a surface (for example a table supporting a book).

Non-contact forces

  • Gravitational – attraction between masses.
  • Electrostatic – between charged objects.
  • Magnetic – between magnetic materials or moving charges.

Free-Body Diagrams and Resultant Force

A free-body diagram shows every force acting on one object as labelled arrows.

  • Arrow length shows relative size.
  • Arrow direction shows the direction of the force.

The resultant force is the single force that has the same effect as all the others combined.

For each direction, add forces in the same direction and subtract forces in the opposite direction.

Example: A truck has 1200 N to the right, 1000 N to the left, 1500 N up and 1500 N down.

  • Horizontal: 1200 − 1000 = 200 N to the right
  • Vertical: 1500 − 1500 = 0 N
  • Net resultant = 200 N to the right

Weight, Mass and Centre of Mass

W=m×g

  • W = weight (N)
  • m = mass (kg)
  • g = gravitational field strength (N/kg)

g varies with location

Locationg (N/kg)
Earth~9.8
Moon~1.6
Jupiter~25

Weight changes between planets; mass stays the same.

  • Mass (kg) – the amount of matter in an object (same everywhere).
  • Weight (N) – the gravitational pull on that mass.

Centre of mass

Weight acts at the centre of mass – the single point where the whole weight can be treated as acting. For a uniform regular shape, this is its geometric centre.

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