Static Equilibrium

Definition

The state of an object that is completely at rest, with all forces and all torques balanced to zero.

∑F⃗=0,∑τ⃗=0\sum \vec{F} = 0,\quad \sum \vec{\tau} = 0

Technical definition

Two conditions must hold simultaneously: ΣF = 0 (translational equilibrium — no net force) and Στ = 0 (rotational equilibrium — no net torque). Both are required; zero net force alone does not prevent spinning.

Example

A bridge holds still because the upward forces from its supports exactly cancel gravity's downward pull, and the torques about any point also cancel — otherwise it would rotate or collapse.

Common confusion

An object with zero net force is not necessarily in static equilibrium — it could be spinning. And ‘equilibrium’ does not always mean ‘at rest’: dynamic equilibrium (like a car cruising at constant velocity) also has ΣF = 0.