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