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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 ...
By contrast, torque is a vector – the cross product of a force vector and a distance vector. Torque and energy are related to one another by the equation [citation needed] =, where E is energy, τ is (the vector magnitude of) torque, and θ is the angle swept (in radians). Since plane angles are dimensionless, it follows that torque and ...
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.
The SI unit of power, defined as energy per unit of time, is the watt, which is a joule per second. Thus, one joule is one watt-second, and 3600 joules equal one watt-hour. The CGS energy unit is the erg and the imperial and US customary unit is the foot pound.
Torque is a pretty easy measurement to understand once it's explained, but horsepower can be a trickier beast. We lay out the meaning of the two ratings.
The moment of force, or torque, is a first moment: =, or, more generally, .; Similarly, angular momentum is the 1st moment of momentum: =.Momentum itself is not a moment.; The electric dipole moment is also a 1st moment: = for two opposite point charges or () for a distributed charge with charge density ().
The SI units for the torque constant are newton meters per ampere (N·m/A). Since 1 N·m = 1 J, and 1 A = 1 C/s, then 1 N·m/A = 1 J·s/C = 1 V·s (same units as back EMF constant). The relationship between K T {\displaystyle K_{\text{T}}} and K v {\displaystyle K_{\text{v}}} is not intuitive, to the point that many people simply assert that ...