5.1MechanicsCore

Resolving Forces

A force at an angle can be split into two perpendicular components. Resolving forces into horizontal and vertical (or other) directions lets you apply Newton’s laws one direction at a time.

24 min Video by Zeeshan Zamurred Forces and Friction

Edexcel A Level Maths: 5.1 Resolving ForcesWatch the full walkthrough before the notes below.

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What you'll be able to do

Resolve a force into components
Use F cos θ and F sin θ
Choose convenient directions
Combine components of several forces

Components of a force

A force $F$ at angle $θ$ to a direction has a component $F cos θ$ along that direction and $F sin θ$ perpendicular to it.

F_{x} = F cos θ, F_{y} = F sin θ

Resolving a force.

1Horizontal:

20 cos 30° \approx 17.3

2Vertical:

20 sin 30° = 10

AnswerH ≈ 17.3 N, V = 10 N.

Tip — The component ALONG the angle’s reference direction uses cos; the perpendicular one uses sin.

Formula recap

F_{x} = F cos θ

Along the reference direction.

F_{y} = F sin θ

Perpendicular component.

Common mistakes to avoid

Swapping sin and cos.

The component adjacent to θ uses cos; the opposite uses sin.

Forgetting to resolve every angled force.

Resolve all forces into the same two directions before combining.

Key takeaways

A force splits into F cos θ and F sin θ.
Resolve all forces into common directions.
Adjacent component uses cos; opposite uses sin.

Test yourself

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