7.1MechanicsStretch

Static Particles

A particle in static equilibrium has no resultant force. By resolving forces in two perpendicular directions and setting each sum to zero, you get equations to find unknown forces.

24 min Video by Zeeshan Zamurred Applications of Forces

Edexcel A Level Maths: 7.1-7.2 Statics and ModellingWatch the full walkthrough before the notes below.

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What you'll be able to do

Apply equilibrium to a particle
Resolve forces in two directions
Set each resultant to zero
Solve for unknown forces

Equilibrium of a particle

A static particle has zero resultant force. Resolve all forces horizontally and vertically (or in any two perpendicular directions) and set each component sum to zero.

\sum F_{x} = 0, \sum F_{y} = 0

Equilibrium conditions for a particle.

1Resolve horizontally: ΣFₓ = 0.

2Resolve vertically: ΣF_y = 0.

3Solve the two simultaneous equations.

AnswerTwo equations from resolving in two directions.

Tip — For a particle (not a rigid body) you only need ΣF = 0 — moments are not required.

Formula recap

\sum F_{x} = 0

Horizontal equilibrium.

\sum F_{y} = 0

Vertical equilibrium.

Common mistakes to avoid

Taking moments for a particle.

A particle only needs ΣF = 0; moments are for rigid bodies.

Resolving in only one direction.

Resolve in two perpendicular directions for two equations.

Key takeaways

Static particle: zero resultant force.
Resolve in two perpendicular directions, each summing to zero.
No moments needed for a particle.

Test yourself

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