Torque
Torque is the rotational analogue of linear force.
Torque, in physics and mechanics, is the rotational equivalent of linear force, often called the moment of force or simply the moment. While a linear force pushes or pulls a body, torque applies a twist to an object around a specific axis—for instance, a screwdriver twisting a screw to make it rotate. The terminology varies by region and field: "torque" is standard in physics, while "moment" is more common in engineering, and this article follows the US physics convention. The word "torque" comes from Latin for "to twist" and was reportedly suggested by James Thomson, first appearing in print in April 1884. That same year, Silvanus P. Thompson used it in his book *Dynamo-Electric Machinery*, describing it as a twist. In mechanical engineering in the UK and US, "moment of force" (often shortened to "moment") has been used since at least 1811, appearing in Siméon Denis Poisson’s work, with an English translation in 1842.
Mathematically, torque is represented by the lowercase Greek letter tau (τ). It is defined as the product of the perpendicular component of a force and the distance from the pivot point (lever arm). In three dimensions, torque is a pseudovector, calculated as the cross product of the displacement vector (from the pivot to the force application point) and the force vector. The right-hand grip rule determines its direction: curling fingers from lever arm to force direction gives the thumb pointing along the torque vector, which is perpendicular to both the position and force vectors. Forces parallel to the position vector produce no torque. The magnitude depends on the force applied, the lever arm length, and the angle between them. The SI unit is the newton-meter (N·m).
Torque relates directly to angular momentum: the net torque on a body equals the rate of change of its angular momentum. For a point particle, torque is the time derivative of angular momentum, analogous to Newton’s second law for rotation. This holds for any trajectory and can be extended to systems of particles or continuous masses. The derivative of torque with respect to time is called rotatum, from Latin for "to rotate," though this term is not universally recognized.
- field
- Physics and mechanics
- known_for
- Rotational correspondent of linear force; moment of force
- SI_unit
- Newton-meter (N⋅m)
- symbol
- Lowercase Greek letter tau (𝜏) or M for moment of force
- etymology
- From Latin torquēre, 'to twist'
Lore & Background
In physics and mechanics, torque is the rotational counterpart of linear force, often described as a twist applied to an object around a chosen axis. It is also called the moment of force or simply the moment. The term "torque" comes from Latin, meaning 'to twist,' and was suggested by James Thomson, appearing in print in April 1884. That same year, Silvanus P. Thompson used the term in the first edition of *Dynamo-Electric Machinery*, describing torque as that which produces or tends to produce torsion around an axis, arguing it is better to treat this action as a single definite entity rather than using terms like 'couple' and 'moment.' In US physics, torque is the preferred term, while in engineering, especially in the UK and US, it is generally referred to as moment of force, a usage traceable to at least 1811 in the work of Siméon Denis Poisson. Torque is mathematically represented by the lowercase Greek letter tau (𝜏). It is defined as the product of the magnitude of the perpendicular component of a force and the distance from the line of action of that force to the point of rotation. In three dimensions, torque is a pseudovector given by the cross product of the displacement vector and the force vector; its direction follows the right-hand grip rule. The SI unit for torque is the newton-meter (N⋅m). The net torque on a body determines the rate of change of its angular momentum, making it the rotational analogue of Newton's second law. The derivative of torque with respect to time is called rotatum, from the Latin for 'to rotate,' though this term is not universally recognized.
Reader's Guide
Torque is fundamental in physics and mechanics as the rotational counterpart of linear force. It is defined mathematically as the cross product of the displacement vector and the force vector: τ = r × F, with magnitude τ = rF sin θ, where r is the lever arm length, F is the force magnitude, and θ is the angle between them. The direction of torque is given by the right-hand grip rule. Torque determines the rate of change of angular momentum: net torque equals dL/dt. For a point particle, angular momentum L = Iω, where I = mr² is the moment of inertia and ω is the angular velocity. The SI unit is the newton-meter. Understanding torque is essential for analyzing rotational motion in engineering, from simple levers to complex machinery, and its historical terminology reflects a shift from describing forces in terms of couples to a unified concept of twist.
Did You Know?
- The SI unit for torque is the newton-meter (N⋅m).
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