résultante

Résultante, in physics and engineering, denotes the vector sum of two or more quantities such as forces, velocities, or moments acting on a body. The resultant represents the net effect these quantities produce, and its magnitude and direction are found by vector addition of the individual contributions.

In statics, the system is in equilibrium when the resultant force is zero. For a body subjected to forces Fi, the resultant FR is FR = sum Fi; in components FRx = sum Fi,x, FRy = sum Fi,y (and FRz in three dimensions). The concept extends similarly to other vector quantities, such as velocity or torque, where the resultant is the net vector sum.

Graphical methods for determining the resultant include the parallelogram rule and the tip-to-tail method, which illustrate how the individual vectors combine to a single resultant.

Example: if F1 = (3 N, 0) and F2 = (0, 4 N), the resultant is FR = (3, 4) N, with magnitude |FR| = 5 N and direction arctan(4/3) ≈ 53.1° above the x-axis.

In rigid-body analysis, the effect of multiple forces is described by the resultant force and the resultant moment (torque) about a reference point. An equivalent single force can replace the original system if its line of action passes through the reference point; otherwise, the system also produces a net moment.

Etymology and usage: the term résulteante is French for the net effect; in English, resultant or resultant force is standard. The concept is central across statics, dynamics, and engineering disciplines.