# Dictionary Definition

torque n : a twisting force [syn: torsion]

# User Contributed Dictionary

## English

### Pronunciation

- Rhymes: -ɔː(r)k

### Noun

- A rotational or twisting effect of a force; a moment of force. Torque is measured as an equivalent straight line force multiplied by the distance from the axis of rotation, hence the SI unit Newton-metre (Nm) or imperial unit foot-pound (ft.lbf).
- alternative spelling of torc

#### Derived terms

#### Related terms

#### Translations

a rotational or twisting force

- Chinese: 力矩 (lìjǔ)
- Czech: točivý moment
- Dutch: koppel
- Finnish: vääntömomentti
- French: couple
- German: Drehmoment
- Italian: coppia
- Japanese: トルク, toruku
- Norwegian: dreiemoment
- Spanish: par de torsión
- Swedish: vridmoment

#### See also

# Extensive Definition

A very useful special case, often given as the
definition of torque in fields other than physics, is as
follows:

- \tau = (\textrm) \cdot \textrm

The construction of the "moment arm" is shown in
the figure below, along with the vectors r and F mentioned above.
The problem with this definition is that it does not give the
direction of the torque but only the magnitude, and hence it is
difficult to use in three-dimensional cases. If the force is
perpendicular to the displacement vector r, the moment arm will be
equal to the distance to the centre, and torque will be a maximum
for the given force. The equation for the magnitude of a torque
arising from a perpendicular force:

- \tau = (\textrm) \cdot \textrm

For example, if a person places a force of
10 N on a spanner which is 0.5 m long, the torque will be
5 N m, assuming that the person pulls the spanner
by applying force perpendicular to the spanner.

### Force at an angle

If a force of magnitude F is at an angle θ from
the displacement arm of length r (and within the plane
perpendicular to the rotation axis), then from the definition of
cross product, the magnitude of the torque arising is:

- \tau=rF \sin\theta

### Static equilibrium

For an object to be in static equilibrium, not only must the sum of the forces be zero, but also the sum of the torques (moments) about any point. For a two-dimensional situation with horizontal and vertical forces, the sum of the forces requirement is two equations: ΣH = 0 and ΣV = 0, and the torque a third equation: Στ = 0. That is, to solve statically determinate equilibrium problems in two-dimensions, we use three equations.### Torque as a function of time

Torque is the time-derivative of angular momentum, just as force is the time derivative of linear momentum:- \boldsymbol = \,\!

where

- L is angular momentum.

Angular momentum on a rigid body can be written
in terms of its moment of
inertia \boldsymbol I \,\! and its angular
velocity \boldsymbol:

- \mathbf=I\,\boldsymbol \,\!

so if \boldsymbol I \,\! is constant,

- \boldsymbol=I=I\boldsymbol \,\!

where α is angular
acceleration, a quantity usually measured in radians per second squared.

## Machine torque

Torque is part of the basic specification of an engine: the power output of an engine is expressed as its torque multiplied by its rotational speed. Internal-combustion engines produce useful torque only over a limited range of rotational speeds (typically from around 1,000–6,000 rpm for a small car). The varying torque output over that range can be measured with a dynamometer, and shown as a torque curve. The peak of that torque curve usually occurs somewhat below the overall power peak. The torque peak cannot, by definition, appear at higher rpm than the power peak.Understanding the relationship between torque,
power and engine speed is vital in automotive
engineering, concerned as it is with transmitting
power
from the engine through the drive train to the wheels. Typically
power is a function of torque and engine speed. The gearing of the
drive train must be chosen appropriately to make the most of the
motor's torque characteristics.

Steam
engines and electric
motors tend to produce maximum torque close to zero rpm, with
the torque diminishing as rotational speed rises (due to increasing
friction and other constraints). Therefore, these types of engines
usually have quite different types of drivetrains from internal
combustion engines.

Torque is also the easiest way to explain
mechanical
advantage in just about every simple
machine.

## Relationship between torque, power and energy

If a force is allowed to act through a
distance, it is doing mechanical
work. Similarly, if torque is allowed to act through a
rotational distance, it is doing work. Power is
the work per unit time.
However, time and rotational distance are related by the angular
speed where each revolution results in the circumference of the
circle being travelled by the force that is generating the torque.
The power injected by the applied torque may be calculated
as:

- \mbox=\mbox \cdot \mbox \,

On the right hand side, this is a scalar
product of two vectors,
giving a scalar on the
left hand side of the equation. Mathematically, the equation may be
rearranged to compute torque for a given power output. Note that
the power injected by the torque depends only on the instantaneous
angular speed - not on whether the angular speed increases,
decreases, or remains constant while the torque is being applied
(this is equivalent to the linear case where the power injected by
a force depends only on the instantaneous speed - not on the
resulting acceleration, if any).

In practice, this relationship can be observed in
power stations which are connected to a large electrical power
grid. In such an
arrangement, the generator's
angular speed is fixed by the grid's frequency, and the power
output of the plant is determined by the torque applied to the
generator's axis of rotation.

Consistent units must be used. For metric SI
units power is watts,
torque is newton
meters and angular speed is radians per second (not rpm and
not revolutions per second).

Also, the unit newton meter is dimensionally
equivalent to the joule, which is the unit of
energy. However, in the case of torque, the unit is assigned to a
vector,
whereas for energy, it is
assigned to a scalar.

### Conversion to other units

For different units of power, torque, or angular speed, a conversion factor must be inserted into the equation. Also, if rotational speed (revolutions per time) is used in place of angular speed (radians per time), a conversion factor of 2 \pi must be added because there are 2 \pi radians in a revolution:- \mbox = \mbox \times 2 \pi \times \mbox \,,

where rotational speed is in revolutions per unit
time.

Useful formula in SI units:

- \mbox = \frac

where 60,000 comes from 60 seconds per minute
times 1000 watts per kilowatt.

Some people (e.g. American automotive engineers)
use horsepower
(imperial mechanical) for power, foot-pounds (lbf·ft) for torque
and rpm (revolutions per minute) for angular speed. This results in
the formula changing to:

- \mbox \approx \frac.

This conversion factor is approximate because the
transcendental number π
appears in it; a more precise value is
5252.113 122 032 55... It comes from
33,000 (ft·lbf./min) / 2π (radians/revolution). It also changes
with the definition of the horsepower, of course; for example,
using the metric horsepower, it becomes ~5180.

Use of other units (e.g. BTU/h for power) would
require a different custom conversion factor.

### Derivation

For a rotating object, the linear distance covered at the circumference in a radian of rotation is the product of the radius with the angular speed. That is: linear speed = radius x angular speed. By definition, linear distance=linear speed x time=radius x angular speed x time.By the definition of torque: torque=force x
radius. We can rearrange this to determine force=torque/radius.
These two values can be substituted into the definition of power:

- \mbox = \frac=\frac = \mbox \times \mbox

The radius r and time t have dropped out of the
equation. However angular speed must be in radians, by the assumed
direct relationship between linear speed and angular speed at the
beginning of the derivation. If the rotational speed is measured in
revolutions per unit of time, the linear speed and distance are
increased proportionately by 2 \pi in the above derivation to
give:

- \mbox=\mbox \times 2 \pi \times \mbox \,

If torque is in lbf·ft and rotational speed in
revolutions per minute, the above equation gives power in
ft·lbf/min. The horsepower form of the equation is then derived by
applying the conversion factor 33,000 ft·lbf/min per
horsepower:

- \mbox = \mbox \times\ 2 \pi\ \times \mbox \cdot \frac \times \frac \approx \frac

because 5252.113555... = \frac \,.

## See also

## References

## External links

- Power and Torque Explained A clear explanation of the relationship between Power and Torque, and how they relate to engine performance.
- "Horsepower and Torque" An article showing how power, torque, and gearing affect a vehicle's performance.
- "Torque vs. Horsepower: Yet Another Argument" An automotive perspective
- a discussion of torque and angular momentum in an online textbook
- Torque and Angular Momentum in Circular Motion on Project PHYSNET.
- An interactive simulation of torque

torque in Arabic: عزم الدوران

torque in Bosnian: Moment

torque in Catalan: Moment de força

torque in Czech: Kroutící moment

torque in Danish: Drejningsmoment

torque in German: Drehmoment

torque in Estonian: Jõumoment

torque in Spanish: Par de giro

torque in French: Couple (mécanique)

torque in Galician: Torque (magnitude)

torque in Korean: 돌림힘

torque in Croatian: Moment

torque in Ido: Momento

torque in Indonesian: Torsi

torque in Italian: Momento torcente

torque in Hebrew: מומנט כוח

torque in Latvian: Spēka moments

torque in Hungarian: Nyomaték

torque in Malay (macrolanguage): Tork

torque in Dutch: Koppel (natuurkunde)

torque in Japanese: トルク

torque in Norwegian Nynorsk: Dreiemoment

torque in Norwegian: Dreiemoment

torque in Polish: Moment siły

torque in Portuguese: Torque

torque in Russian: Момент силы

torque in Simple English: Torque

torque in Slovenian: Navor

torque in Serbian: Момент силе

torque in Finnish: Vääntömomentti

torque in Swedish: Vridmoment

torque in Ukrainian: Момент сили

torque in Vietnamese: Mô men lực

torque in Turkish: Tork

torque in Yiddish: טוירק

torque in Chinese: 力矩

torque in Tamil: கோண விசை