torque

Torque is force applied with leverage. For a force F applied at position r from a pivot, the torque about that pivot is τ = r × F, with magnitude |τ| = r·F·sin θ, where θ is the angle between them. Its units are newton-metres. It is a vector along the pivot axis, with direction given by the right-hand rule.

Torque stands to angular momentum exactly as force stands to linear momentum: τ = dL/dt. If the net external torque on a system is zero, its angular momentum is conserved. If the net torque is nonzero, the angular momentum changes at a rate equal to the torque — a direct consequence of Newton's laws applied to rotational motion.

In engineering, torque is the practically useful number for anything rotating: the output of a car engine is quoted in torque as well as power; a wrench's usefulness depends on its length (longer → more torque for the same hand force); a torque wrench on a tight bolt is how mechanics know they've tightened it properly. In biology, the skeletal muscles and bones together form a system of levers that generate torques about joints; where muscles insert, how long the bones are, and the angles involved together determine the torques available for motion.