kokonaismomentin

Kokonaismomentin is a term used in physics and engineering to denote the net or resultant moment produced by a system of forces acting on a rigid body about a chosen reference point or axis. Each force contributes a moment M_i = r_i × F_i, where r_i is the position vector from the reference point to the point of application, and F_i is the force. The overall or total moment is the vector sum of these contributions. In two dimensions, about the origin, the scalar moment is often written as M = Σ(x_i F_yi − y_i F_xi). The units are newton-meters (N·m). A common convention is that positive moments tend to produce counterclockwise rotation, while negative moments produce clockwise rotation.

The total moment determines the rotational effect of a force system. In statics, equilibrium requires that the sum of moments about any point is zero: ΣM = 0. In dynamics, the rotational analogue of Newton’s second law states that ΣM = Iα, where I is the moment of inertia about the chosen axis and α is the angular acceleration. The concept is also closely related to the idea of a pure couple, a system of forces that produces a finite moment independent of the line of action of the forces.

Applications of kokonaismomentin occur across engineering disciplines, including structural analysis, machine design, and robotics. Engineers compute the total moment about supports, joints, or axes to assess stability, balance, and performance. In practice, calculations may use convenient reference points, decomposition of forces into components, and the superposition principle to simplify the determination of the net moment.

Etymology: the term is Finnish, with kokonaismomentti or kokonaismomentin referring to the total or resultant moment of a force system; kokonaismomentin is the genitive form.