Principle

Conditions for equilibrium

\sum F = 0, \sum τ = 0

Statement

The net force and the net torque about any axis must both vanish.

Symbols and units

$F$	each external force	N
$τ$	each external torque	N·m

When it applies

Static equilibrium — zero linear and zero angular acceleration.

Derivation

Direct consequence of Newton's second law and its rotational form, applied at zero acceleration:

m a = 0 and I α = 0 \Rightarrow \sum F = 0, \sum τ = 0

Worked examples

Force on a see-saw

A 30 kg child sits 2.0 m from the pivot; find where a 20 kg child must sit to balance:

(30) (9.8) (2.0) = (20) (9.8) d \Rightarrow d = 3.0 m

Watch out for

Zero net force alone is not sufficient — a pair of equal, opposite forces offset from each other produces zero net force but a non-zero net torque.

Connects to