static equilibrium

A body is in static equilibrium if it remains at rest and does not begin to rotate. For an extended body this requires two conditions to hold simultaneously: the net external force on it must be zero (so it does not translate), and the net external torque about any point must also be zero (so it does not rotate). Both are independent non-trivial constraints — a body with zero net force but nonzero torque will begin to spin; a body with zero net torque but nonzero force will start to slide.

The second condition is subtle: the torques in it are computed about some pivot point, but a useful mathematical fact is that once the net force is zero, the net torque is the same about every pivot. So for any body you believe to be in force equilibrium, you can check rotational equilibrium about whichever pivot simplifies the algebra most — often a point where an unknown force acts, so that force drops out.

Static equilibrium is the mathematical engine of structural engineering. A bridge, a ladder leaning against a wall, a crane lifting a load, a building, a human standing on one foot — in each case the designer works out the external forces and torques and insists both sums vanish. A body out of equilibrium accelerates; for a bridge this means it is collapsing, for a human it means they are falling. The condition is pedagogically useful in classical physics and decisively important in practical engineering.