For a rigid body on the point of slipping, set up three scalar conditions: resolve along two convenient directions and take moments about a well-chosen point (one that kills an unknown reaction). At every rough contact that is on the point of slipping, replace friction by its limiting value F=μN directed to oppose impending motion; smooth contacts give a normal reaction only. The unknowns are exactly the reactions and the required relation between μ and the geometry.
Trigger: "limiting equilibrium", "on the point of slipping", "least coefficient of friction", a ladder/rod/disc resting against walls, pegs or other bodies.
Instances:
(i) ladder or rod against a wall and floor, two limiting contacts;
(ii) a rod resting on two bars/pegs, friction at each support;
(iii) stacked discs or cylinders, friction at the body-body and body-ground contacts.
