4.3MechanicsStretch

Equilibrium

A rigid body is in equilibrium when it has no tendency to move or rotate. This requires the resultant force to be zero AND the resultant moment about any point to be zero — giving equations to solve.

26 min Video by Zeeshan Zamurred Moments

Edexcel A Level Maths: 4.3 Equilibrium (Moments, Resultant Force)Watch the full walkthrough before the notes below.

Open on YouTube

What you'll be able to do

State the conditions for equilibrium
Resolve forces to zero
Take moments to zero about a chosen point
Solve beam and plank problems

Two conditions

For equilibrium: (1) the resultant force is zero (resolve horizontally and vertically), and (2) the resultant moment about any point is zero.

\sum F = 0 and \sum M = 0

Both must hold.

Choosing a pivot

Take moments about a point where an unknown force acts — that force then has zero moment and drops out, simplifying the equation.

1Take moments about the OTHER support so its reaction vanishes.

2Solve for the wanted reaction.

AnswerMoments about the other support isolates the unknown.

Tip — Take moments about an unknown force to eliminate it from the equation.

Formula recap

\sum F = 0

No resultant force.

\sum M = 0

No resultant moment.

Common mistakes to avoid

Only checking forces, not moments.

Both ΣF = 0 and ΣM = 0 are required.

Forgetting the weight acts at the centre of a uniform beam.

A uniform beam’s weight acts at its midpoint.

Key takeaways

Equilibrium: ΣF = 0 and ΣM = 0.
Take moments about an unknown force to eliminate it.
A uniform beam’s weight acts at its midpoint.

Test yourself

Ready to lock in Equilibrium? Pick a mode and earn XP & Dobloons.