moment

A moment is the rotational effect produced when a force acts at a distance from a pivot point or axis. It is calculated as force multiplied by the perpendicular distance from the line of action of that force to the pivot, measured in newton-metres (N·m) or foot-pounds (ft·lbf). A small force applied far from the pivot can produce the same moment as a large force applied close to it, which is why a long wrench makes a tight bolt easier to turn than a short one.

The direction of a moment follows the right-hand rule: curl your fingers in the direction of rotation and your thumb points along the axis of the moment. Moments are either clockwise or counterclockwise when viewed from a given angle. In systems with multiple forces, moments can add or cancel depending on their directions. A seesaw is balanced when the clockwise moment from one child equals the counterclockwise moment from the other, regardless of their weights if their distances from the fulcrum differ.

Moments in structural and machine analysis

Beams, shafts, and frames must resist moments. A simply supported beam experiences a bending moment along its length when loaded perpendicular to its axis; the maximum moment typically occurs near midspan. Design calculations must ensure the material's bending strength exceeds the applied moment. Torsional moments twist shafts in rotating machinery; power transmission shafts are sized to handle both the torque (moment about the shaft axis) and any bending moments from belt or gear forces acting sideways.

Unbalanced moments cause problems. If a rotating assembly has mass distributed unevenly around its axis, it creates an unbalanced moment that grows with speed, producing vibration, bearing wear, and noise. Balancing machines measure and correct this by adding or removing material. In structures, wind or seismic forces create large moments at bases and connections, and these must be resisted by stiff frames or guy wires, not just strength.

The term moment comes from Latin and originally meant importance or weight; it entered mechanics through the idea that a force's significance depends on where it acts. Today the word is almost always shortened from the full phrase moment of force, and in rotational contexts is often called torque when referring specifically to the moment that causes rotation about an axis.