4.1.6—Equilibrium

A particle is in equilibrium when the resultant force is zero, so the sums of components along two independent axes both vanish.

Choose axes that simplify the geometry, include all applied forces and reactions, then solve simultaneously. A negative unknown indicates the assumed direction was opposite.

For a ring held by two strings, horizontal components cancel and vertical components add to the load; the ring remains at rest.

Equal forces are not required—different magnitudes can balance when their directions differ.