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