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.
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
1
Components of a force
A force at angle to a direction has a component along that direction and perpendicular to it.
Resolving a force.
1Horizontal: N.
2Vertical: N.
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
Along the reference direction.
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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