Torques

Torque, or moment of force, is a measure of the tendency of a force to rotate an object about a specific point or axis. If a force F acts at a position r from the origin, the torque is defined as the cross product τ = r × F. The magnitude is |τ| = r F sin θ, where θ is the angle between r and F. The direction of τ is given by the right-hand rule, pointing along the axis of rotation; torque is a pseudovector in three-dimensional space.

Torques about a chosen reference point depend on the location of the force application and the direction of the force relative to that point. The net effect of multiple forces is the sum of their torques about the same point. When considering rotation about a fixed axis, only the component of torque along that axis matters for rotational motion.

In dynamics, torque is related to angular momentum by τ = dL/dt. For a rigid body rotating about a fixed axis, the torque about that axis is τ = I α, where I is the moment of inertia and α is the angular acceleration.

A common special case is a pure couple, formed by two equal and opposite forces whose lines of action are parallel. Such a configuration produces a torque that causes rotation without a net translational force.

Units are newton-meters (N·m). Although the same units commonly describe work and energy, torque is conceptually distinct: torque depends on force, lever arm, and orientation, and it governs rotational motion rather than translational work.