Torque is a measure of the rotational effect produced by a force about a specified point or axis. It is commonly represented by the symbol tau and is calculated from the vector cross product of position relative to the reference point and force. Its magnitude depends on the applied force, the perpendicular distance from the axis to the force line of action and the angle between the position vector and force. Torque is measured in newton metres. Although its SI unit has the same dimensions as joules, torque and energy are physically different quantities because torque is associated with rotational action while energy represents an amount of transferred or stored energy.
The magnitude of torque can be expressed as force multiplied by perpendicular lever arm distance. A force applied farther from a pivot therefore produces greater torque for the same force magnitude. The angle of application also matters because only the component of force perpendicular to the position vector contributes to the torque magnitude. A force directed directly toward or away from the axis has zero torque about that axis even if the force itself is large. This principle explains the mechanical advantage of long handles and the effectiveness of applying forces tangentially to rotating objects.
Torque is a vector quantity in three dimensional mechanics and its direction is determined by the cross product of the position vector and force vector. The right hand rule is commonly used to determine its direction. For planar rotation, torque is often represented using a sign convention in which clockwise and anticlockwise directions have opposite signs. The net torque about an axis determines angular acceleration according to the rotational analogue of Newtons second law. For a rigid body with constant moment of inertia, net torque equals moment of inertia multiplied by angular acceleration.
Torque plays a central role in rotational equilibrium. An object can have zero net force while simultaneously experiencing nonzero torques, producing angular acceleration. Conversely, an object can have zero net torque while experiencing forces that produce translational acceleration. Static equilibrium requires both the resultant force and resultant torque to satisfy the appropriate equilibrium conditions. The choice of reference point can simplify torque calculations, especially when several forces act on a rigid body. When a force passes through the selected pivot, its torque about that pivot is zero.
Torque is closely related to angular momentum and rotational power but should not be confused with either. Torque is the rate of change of angular momentum, while power in rotational motion describes the rate of energy transfer and is related to torque multiplied by angular velocity. Angular momentum depends on mass distribution and motion, whereas torque describes an external or internal rotational interaction. A rotating object can possess angular momentum even when the instantaneous external torque is zero. Similarly, torque can be present when angular velocity is zero, such as when a stationary object is being twisted before rotation begins.
In machines, torque determines the turning capability of shafts, gears, wheels and actuators. Engines and electric motors are commonly characterised by torque as a function of rotational speed. Gear systems can exchange rotational speed for torque while approximately conserving mechanical power apart from losses. A reduction gear can increase output torque while reducing output angular velocity. Clutches transmit torque between rotating components, while shafts must be designed to withstand torsional stresses caused by transmitted torque. These applications make torque a central quantity in mechanical design.
Torque also occurs in less obvious situations. Gravitational forces can produce torque about a pivot when an objects centre of mass is displaced from the vertical line through the pivot. Magnetic moments experience torque in magnetic fields, while electric dipoles can experience torque in electric fields. Fluid forces can create torque on turbines and propellers. Internal torques can arise in rotating machinery and deformable bodies even when the total external torque has particular values. The physical meaning always depends on the reference axis or point and the interaction producing the rotational tendency.
Common misconceptions include treating torque as simply force or assuming that greater force always means greater torque. The lever arm and direction are equally important. Another misconception is that torque and joules are interchangeable because newton metres is the unit expression for both. Their dimensions coincide but their physical roles differ. Torque is also not inherently a measure of how fast something rotates. Angular velocity describes rotational speed, angular acceleration describes how rotational speed changes and torque describes the rotational interaction responsible for angular momentum change.
