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Torque has the dimension of force times distance, symbolically T −2 L 2 M and those fundamental dimensions are the same as that for energy or work. Official SI literature indicates newton-metre, is properly denoted N⋅m, as the unit for torque; although this is dimensionally equivalent to the joule, which is not used for torque.
The newton-metre or newton-meter (also non-hyphenated, newton metre or newton meter; symbol N⋅m [1] or N m [1]) [a] is the unit of torque (also called moment) in the International System of Units (SI). One newton-metre is equal to the torque resulting from a force of one newton applied perpendicularly to the end of a moment arm that is one ...
Both energy and torque can be expressed as a product of a force vector with a displacement vector (hence pounds and feet); energy is the scalar product of the two, and torque is the vector product. Although calling the torque unit "pound-foot" has been academically suggested, both are still commonly called "foot-pound" in colloquial usage.
Despite this, in practice torque units are commonly called the foot-pound (denoted as either lb-ft or ft-lb) or the inch-pound (denoted as in-lb). [4] [5] Practitioners depend on context and the hyphenated abbreviations to know that these refer to neither energy nor moment of mass (as the symbol ft-lb rather than lbf-ft would imply).
Cartesian y-axis basis unit vector unitless kinetic energy: joule (J) wave vector: radian per meter (m −1) Boltzmann constant: joule per kelvin (J/K) wavenumber: radian per meter (m −1) stiffness: newton per meter (N⋅m −1) ^ Cartesian z-axis basis unit vector
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The simplest kind of couple consists of two equal and opposite forces whose lines of action do not coincide. This is called a "simple couple". [1] The forces have a turning effect or moment called a torque about an axis which is normal (perpendicular) to the plane of the forces. The SI unit for the torque of the couple is newton metre.