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It has been suggested that Couple (mechanics) be merged into this article or section. (Discuss)
For other uses, see Torque (disambiguation).

Relationship between force (F), torque (?), and momentum vectors (p and L) in a system which has rotation constrained in one plane only. (Forces and moments due to gravity and friction not shown.)
Torque is the tendency of a force to rotate an object about an axis (or fulcrum or pivot). Just as a force is a push or a pull, a torque can be thought of as a twist. The symbol for torque is ?, the Greek letter tau.
Torque is also called moment or moment of force. This should neither be confused with the various other definitions of "moment" in physics nor with "momentum". In the context of mechanical engineering, the terms "moment" and "torque" are not necessarily interchangeable; rather, one or the other may be preferred in a specific context. For example, "torque" is usually used to describe a rotational force down a shaft, for example a turning screw-driver, whereas "moment" is more often used to describe a bending force on a beam.[citation needed]
The magnitude of torque depends on three quantities: First, the force applied; second, the length of the lever arm connecting the axis to the point of force application; and third, the angle between the two. In symbols:


where
is the torque vector and is the magnitude of the torque,
is the lever arm vector (vector from the axis to the point of force application), and is the length (or magnitude) of the lever arm vector,
is the force vector, and is the magnitude of the force,
denotes the cross product,
is the angle between the force vector and the lever arm vector.
The length of the lever arm is particularly important; choosing this length appropriately lies behind the operation of levers, pulleys, gears, and most other simple machines involving a mechanical advantage.
The SI unit for torque is the newton meter (N). In Imperial and U.S. customary units, it is measured in foot pounds (ftbf) (also known as 'pound feet') and for smaller measurement of torque: inch pounds (inbf) or even inch ounces (inzf).
Contents
1 History
2 Explanation
2.1 Proof of the equivalence of definitions
3 Units
4 Extended units in relation with rotation angles
5 Special cases and other facts
5.1 Moment arm formula
5.2 Force at an angle
5.3 Static equilibrium
5.4 Torque as a function of time
6 Machine torque
7 Relationship between torque, power and energy
7.1 Conversion to other units
7.2 Derivation
8 Principle of Moments
9 See also
10 References
11 External links
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History
The concept of torque, also called moment or couple, originated with the studies of Archimedes on levers. The rotational analogues of force, mass, and acceleration are torque, moment of inertia, and angular acceleration, respectively.
Explanation
The force applied 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 meters from the fulcrum, for example, exerts the same torque as one newton applied six meters from the fulcrum. This assumes the force is in a direction at right angles to the straight lever. The direction of the torque can be determined by using the right hand grip rule: curl the fingers of your right hand to indicate the direction of rotation, and stick your thumb out so it is aligned with the axis of rotation. Your thumb points in the direction of the torque vector.
Mathematically, the torque on a particle (which has the position r in some reference frame) can be defined as the cross product:

where
r is the particle's position vector relative to the fulcrum
F is the force acting on the particle.
The torque on a body determines the rate of change of its angular momentum,

where
L is the angular momentum vector
t is time.
As can be seen from either of these relationships, torque is a vector, which points along the axis of the rotation it would tend to cause.
Proof of the equivalence of definitions
The definition of angular momentum for a single particle is:

where "" indicates the vector cross product and p is the particle's linear momentum. The time-derivative of this is:

This result can easily be proven by splitting the vectors into components and applying the product rule. Now using the definitions of velocity v = dr/dt, acceleration a = dv/dt and linear momentum p = mv, we can see that:

But the cross product of any vector with itself is zero, so the second term vanishes. Hence with the definition of force F = ma, (Newton's 2nd law) we obtain:

And by definition, torque ? = r.
Note that there is a hidden assumption that mass is constant this is quite valid in non-relativistic mechanics. Also, total (summed) forces and torques have been used it perhaps would have been more rigorous to write:

Units
Torque has dimensions of force times distance and the SI unit of torque is the "newton meter" (N m). Even though the order of "newton" and "meter" are mathematically interchangeable, the BIPM (Bureau International des Poids et Mesures) specifies that the order should be N m not m N. N is also acceptable. Because "mN" is the symbol for the "millinewton", it must not be used to refer to the newton meter. In applications that are not case-sensitive, it is also necessary to avoid "NM" and "nm", because "nm" is the symbol for the nanometer.
The joule, which is the SI unit for energy or work, is also defined as 1 N m, but this unit is not used for torque. Since energy can be thought of as the result of "force dot distance", energy is always a scalar whereas torque is "force cross distance" and so is a (pseudo) vector-valued quantity. The dimensional equivalence of these units, of course, is not simply a coincidence: a torque of 1 N m applied through a full revolution will require an energy of exactly 2? joules. Mathematically,

where
E is the energy
? is torque
? is the angle moved, in radians.
Other non-SI units of torque include "pound-force-feet" or "foot-pounds-force" or "inch-pounds-force" or "ounce-force-inches" or "meter-kilograms-force" or "kilogrammeter" (kgm). For all these units, the word "force" is often left out, for example abbreviating "pound-force-foot" to simply "pound-foot". (In this case, it would be implicit that the "pound" is pound-force and not pound-mass.)
Extended units in relation with rotation angles
This section may stray from the topic of the article. Please help improve this section or discuss this issue on the talk page.
As a consequence of the previous equation, if you introduce the radian (rad) as part of the dimensional units in the SI units system, the torque could be measured using "newton meters per radian" (Nm/rad), or "joules per radian" (J/rad), while the energy needed and spent to perform the rotation would be measured simply in "newton meters" or "joules".
In the strict SI system, angles are not given any dimensional unit, because they do not designate physical quantities, despite the fact that they are measurable indirectly simply by dividing two distances (the arc length and the radius): one way to conciliate the two systems would be to say that arc lengths are not measures of distances (given they are not measured over a straight line, and a full circle rotation returns to the same position, i.e. a null distance). So arc lengths should be measured in "radian meter" (rad), differently from straight segment lengths in "meters" (m). In such extended SI system, the...(and so on) To get More information , you can visit some products about ceramic coated cookware , ceramic piggy bank , dinnerware ceramic , ceramic capacitors , ceramic tile wholesale , glazed ceramic tile , manufacturers ceramic tile , ceramic transfer paper , ceramic tiling , ceramic hair straightening iron , .