Torque
In physics and mechanics, torque is the rotational equivalent of linear force.[1] It is also referred to as the moment, moment of force, rotational force or turning effect, depending on the field of study. It represents the capability of a force to produce change in the rotational motion of the body. The concept originated with the studies by Archimedes of the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Torque is defined as the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. The symbol for torque is typically , the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.
Torque | |
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![]() 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 | , M |
SI unit | N⋅m |
Other units | pound-force-feet, lbf⋅inch, ozf⋅in |
In SI base units | kg⋅m2⋅s−2 |
Dimension | M L2T−2 |
Part of a series on |
Classical mechanics |
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In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector. The magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector[2] 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:
where
- is the torque vector and is the magnitude of the torque,
- is the position vector (a vector from the point about which the torque is being measured to the point where the force is applied),
- is the force vector,
- denotes the cross product, which produces a vector that is perpendicular to both r and F following the right-hand rule,
- 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.