on geographical location and field of study. This article follows the definition used in US physics in its usage of the word torque. In the UK and in US mechanical engineering, torque is referred to as moment of force, usually shortened to moment. This terminology can be traced back to at least 1811 in Siméon Denis Poisson's Traité de mécanique. An English translation of Poisson's work appears in 1842. Definition and relation to angular momentum A force applied perpendicularly to a lever multiplied by its distance from the lever's fulcrum (the length of the lever arm) is its torque. A force of three newtons applied two metres from the fulcrum, for example, exerts the same torque as a force of one newton applied six metres from the fulcrum. The direction of the torque can be determined by using the right hand grip rule: if the fingers of the right hand are curled from the direction of the lever arm to the direction of the force, then the thumb points in the direction of the torque. More generally, the torque on a point particle (which has the position r in some reference frame) can be defined as the cross product: where F is the force acting on the particle. The magnitude τ of the torque is given by where F is the magnitude of the force applied, and θ is the angle between the position and force vectors. Alternatively, where F⊥ is the amount of force directed perpendicularly to the position of the particle. Any force directed parallel to the particle's position vector does not produce a torque. It follows from the properties of the cross product that the torque vector is perpendicular to both the position and force vectors. Conversely, the torque vector defines the plane in which the position and force vectors lie. The resulting torque vector direction is determined by the right-hand rule. The net torque on a body determines the rate of change of the body's angular momentum, where L is the angular momentum vector and t is time. For the motion of a point particle, where is the moment of inertia and ω is the orbital angular velocity pseudovector. It follows that where α is the angular acceleration of the particle, and p|| is the radial component of its linear momentum. This equation is the rotational analogue of Newton's second law for point particles, and is