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.
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
1
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.
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
Horizontal equilibrium.
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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