Resolving forces and equilibrium

Higher tier: a single force at an angle can be split into two parts at right angles. When all the forces on an object balance, it is in equilibrium.

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Resolving a force

A force at an angle can be replaced by two components at right angles, usually horizontal and vertical.
By scale drawing: draw the force to scale, then draw horizontal and vertical lines from its ends to make a right-angled triangle, and measure the sides.
By calculation: horizontal component = F × cos θ; vertical component = F × sin θ (θ measured from the horizontal).
Example: 10 N at 30° above the horizontal: horizontal = 8.7 N, vertical = 5.0 N.

Free body diagrams and equilibrium

A free body diagram shows all the forces acting on one object, as arrows from the object, with length showing size.
An object is in equilibrium when the resultant force is zero. It stays still or moves at constant velocity.
In a scale drawing, the force arrows drawn tip to tail make a closed shape (for three forces, a closed triangle).

Using components

To check equilibrium, resolve every force into horizontal and vertical components.
The horizontal components must add to zero, and the vertical components must add to zero.
Example: a sledge pulled with 50 N at 30° to the ground at constant velocity: the friction must equal the horizontal component, 50 × cos 30° = 43.3 N.
Worked example

A rope pulls a box with a force of 20 N at 60° above the horizontal. Find the horizontal and vertical components.

  1. Horizontal = 20 × cos 60° = 20 × 0.5 = 10 N
  2. Vertical = 20 × sin 60° = 20 × 0.866 = 17.3 N

Answer: Horizontal 10 N; vertical 17.3 N

Key idea

A force can be resolved into two components at right angles by scale drawing or using F cos θ and F sin θ. In equilibrium the resultant force is zero, the components in each direction add to zero, and the force arrows drawn tip to tail form a closed shape.

Key words
Resultant force
The single force that has the same effect as all the forces acting on an object together.
Velocity
Speed in a stated direction. A vector.
Friction
A force that opposes motion between surfaces in contact.

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Extra practice

2 more questions

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  1. A box rests on a slope without moving. Which statement is true?

    1. Only weight acts on it
    2. The resultant force on it is zero
    3. There are no forces on it
    4. It must be accelerating
    Show the answer

    Answer: The resultant force on it is zero

    Equilibrium means forces balance: zero resultant.

  2. Three forces act on an object. Drawn tip to tail, they leave a gap. What does this show?

    1. One force is zero
    2. The object is in equilibrium
    3. The object is not in equilibrium
    4. The forces are all equal
    Show the answer

    Answer: The object is not in equilibrium

    The gap is the resultant force, so there is an overall force.

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Practise this lesson free (6 questions)All GCSE and International GCSE Physics lessons

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Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.

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