Definition and Properties of Torque
- Term 'torque' suggested by James Thomson in 1884
- Silvanus P. Thompson used the term in the first edition of Dynamo-Electric Machinery in the same year
- Torque defined as that which produces or tends to produce torsion
- Originated from Archimedes' studies on levers
- Different vocabulary used for torque depending on geographical location and field of study
- Torque is the rotational analogue of linear force
- Torque is the product of the magnitude of the perpendicular component of the force and the distance from the point around which it is determined
- Torque is defined as the cross product of the displacement vector and the force vector
- Torque is perpendicular to both the position and force vectors
- The net torque on a body determines the rate of change of the body's angular momentum
- Torque is a vector quantity with both magnitude and direction
- Torque can be positive or negative, indicating the direction of rotation
- Torque can be measured using a torque wrench or torque sensor

Units and Conversion of Torque
- The SI unit for torque is the newton-metre (N⋅m)
- Torque can also be expressed in other units such as pound-feet (lb-ft) or kilogram-force metre (kgf⋅m)
- Torque has the dimension of force times distance
- Official SI literature suggests using the unit newton-metre (N⋅m) and never the joule
- The traditional imperial and U.S. customary units for torque are the pound foot (lbf-ft) and pound inch (lbf-in)
- Practitioners depend on context and the hyphen in the abbreviation to know that these refer to torque and not to energy or moment of mass
- Conversion factor may be necessary when using different units of power or torque
- Rotational speed (unit: revolution per minute or second) can be converted to angular speed (unit: radian per second) by multiplying by 2π radians per revolution

Applications of Torque
- Torque is used in various applications such as engines, motors, and machines
- Torque is essential for rotational motion and the operation of mechanical systems
- Torque is used in the design and analysis of gears, pulleys, and levers
- Torque is a key concept in robotics and automation
- Understanding torque is crucial for the efficient and safe operation of machinery and equipment
- Torque forms part of the basic specification of an engine
- The power output of an engine is expressed as its torque multiplied by the angular speed of the drive shaft

Equilibrium and Torque
- For an object to be in static equilibrium, the sum of the forces and torques must be zero
- In a two-dimensional situation, three equations are used to solve statically determinate equilibrium problems
- The sum of the forces requirement is two equations: ΣF = 0 and ΣF = 0
- The torque requirement is a third equation: Στ = 0
- These equations ensure that the object is balanced and not moving
- The principle of moments, also known as Varignon's theorem, states that the resultant torques due to several forces applied to a point is equal to the sum of the contributing torques
- The balance of torques is achieved when the sum of the torques resulting from two forces acting around a pivot on an object is zero
- The principle of moments is used to analyze the equilibrium of objects subjected to multiple torques
- The principle of moments is based on the vector cross product of the position vector and the force vector

Relationship between Torque, Power, and Energy
- Torque and angular displacement can do mechanical work
- The work done by torque can be expressed as the integral of torque with respect to angular displacement
- The change in rotational kinetic energy is equal to the work done by torque
- Power is the work done per unit time
- The relationship between torque, power, and angular velocity can be observed in bicycles

Torque (Wikipedia)

For other uses, see Torque (disambiguation).

In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). It describes the rate of change of angular momentum that would be imparted to an isolated body.

Torque
Relationship between force F, torque τ, linear momentum p, and angular momentum L in a system which has rotation constrained to only one plane (forces and moments due to gravity and friction not considered).
Common symbols	${\displaystyle \tau }$, M
SI unit	N⋅m
Other units	pound-force-feet, lbf⋅inch, ozf⋅in
In SI base units	kg⋅m2⋅s−2
Dimension	M L2 T−2

The concept originated with the studies by Archimedes of the usage of levers, which is reflected in his famous quote: "Give me a lever and a place to stand and I will move the Earth". Just as a linear force is a push or a pull applied to a body, a torque can be thought of as a twist applied to an object with respect to a chosen point. Torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined. The law of conservation of energy can also be used to understand torque. The symbol for torque is typically ${\displaystyle {\boldsymbol {\tau }}}$, the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.

In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the displacement vector and the force vector. The magnitude of torque applied to a rigid body depends on three quantities: the force applied, the lever arm vector connecting the point about which the torque is being measured to the point of force application, and the angle between the force and lever arm vectors. In symbols:

$${\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} }$$

$${\displaystyle \tau =rF\sin \theta ,}$$

where

• ${\displaystyle {\boldsymbol {\tau }}}$ is the torque vector and ${\displaystyle \tau }$ is the magnitude of the torque,
• ${\displaystyle \mathbf {r} }$ is the position vector (a vector from the point about which the torque is being measured to the point where the force is applied), and r is the magnitude of the position vector,
• ${\displaystyle \mathbf {F} }$ is the force vector, and F is the magnitude of the force vector,
• ${\displaystyle \times }$ denotes the cross product, which produces a vector that is perpendicular both to r and to F following the right-hand rule,
• ${\displaystyle \theta }$ is the angle between the force vector and the lever arm vector.

The SI unit for torque is the newton-metre (N⋅m). For more on the units of torque, see § Units.