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 Forces and Friction

Edexcel A Level Maths: 5.1 Resolving ForcesCurated by Kepler, not produced by us. Watch it 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 $\theta$ to a direction has a component $F\cos\theta$ along that direction and $F\sin\theta$ perpendicular to it.

F_x = F\cos\theta, \quad F_y = F\sin\theta

Resolving a force.

Example 1Resolve a 20 N force at 30° above the horizontal.

1Horizontal:

20\cos 30° \approx 17.3

2Vertical:

20\sin 30° = 10

Answer

H ≈ 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\theta

Along the reference direction.

F_y = F\sin\theta

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

Answer a few questions, then review anything you missed.

Prefer paper? Open the written self-check

Answer each question before opening its answer. This self-check does not record a quiz score.

The component of F along the reference direction is:
- $F\cos\theta$
- $F\sin\theta$
- $F\tan\theta$
- $F$
Show answer and explanation
Answer: $F\cos\theta$
Adjacent uses cos.
The perpendicular component is:
- $F\sin\theta$
- $F\cos\theta$
- $F$
- $F\tan\theta$
Show answer and explanation
Answer: $F\sin\theta$
Opposite uses sin.
A 20 N force at 30° has horizontal component:
- $\approx 17.3$ N
- $10$ N
- $20$ N
- $\approx 11.5$ N
Show answer and explanation
Answer: $\approx 17.3$ N
20cos30°.
Its vertical component is:
- $10$ N
- $17.3$ N
- $20$ N
- $5$ N
Show answer and explanation
Answer: $10$ N
20sin30°.
Why resolve forces?
- to apply Newton’s laws per direction
- to make them bigger
- to remove them
- to rotate them
Show answer and explanation
Answer: to apply Newton’s laws per direction
One direction at a time.

Next step

Keep practising

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

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Related lessons

All 3 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.