Newton metre Information & Newton metre Links at HealthHaven.com

Newton metre is a unit of torque (also called "moment") in the SI system.^[1] Less commonly, it is used as a unit of energy, in which case it is synonymous with the more common and standard SI unit of energy, the joule.^[2] The symbolic form is N m or N·m,^[3] and sometimes hyphenated newton-metre. One newton metre is equal to the torque resulting from a force of one newton applied perpendicularly to a moment arm which is one metre long.

A newton metre is dimensionally equal to a joule, the SI unit of energy and work. However, it is not appropriate to express a torque in joules — the units are helpful to distinguish a torque quantity from an energy quantity.^[4] The two quantities, torque and energy, are physically quite different despite being dimensionally equivalent. For example, energy is a scalar while torque is a vector (in fact, a pseudovector). Also, a given force applied to an object can contribute torque but not work, or work but not torque, or both, or neither.

Conversely, Newton metre is sometimes used as a unit of energy, instead of joule.^[2] As above, this practice is discouraged by the SI authority, since it can lead to confusion as to whether a given quantity expressed in newton metres is a torque or an energy.^[5]

On the other hand, there are relations between torque and energy that shed light on their dimensional relationship. In particular, a torque can contribute to rotational energy; the work done in this process (measured in J) is equal to the torque (measured in N m) times the angle through which the body rotates in the direction of the torque.^[6] This accounts for the use of an alternative unit for torque, Joule per radian (J/rad)

[edit] Conversion factors

1 joule = 1 N·m
1 newton metre = 0.7375621 foot-pound force (often "foot-pound")
1 metre kilogram-force = 9.80665 N·m
1 centimetre kilogram-force = 98.0665 mN·m
1 foot-pound force (often "foot-pounds") = 1 pound-force foot (often "pound-feet") ≈ 1.3558 N·m
1 inch ounce-force = 7.0615518 mN·m
1 dyne centimetre = 10⁻⁷ N·m

[edit] See also

[edit] References

^ From the official SI website: "...For example, the quantity torque may be thought of as the cross product of force and distance, suggesting the unit newton metre, or it may be thought of as energy per angle, suggesting the unit joule per radian."
^ ^a ^b For example: Eshbach's handbook of engineering fundamentals - 10.4 Engineering Thermodynamics and Heat Transfer "In SI units the basic unit of energy is Newton-Meter".
^ BIPM - unit symbols
^ From the official SI website: "A derived unit can often be expressed in different ways by combining base units with derived units having special names. Joule, for example, may formally be written newton metre, or kilogram metre squared per second squared. This, however, is an algebraic freedom to be governed by common sense physical considerations; in a given situation some forms may be more helpful than others. In practice, with certain quantities, preference is given to the use of certain special unit names, or combinations of unit names, to facilitate the distinction between different quantities having the same dimension."
^ BIPM - special names
^ $U_{1 \to 2} = \left| \int_{\theta_1}^{\theta_2} \tau d\theta \right|$
Ferdinand Beer et al., Vector Mechanics for Engineers page 1084.

[BIPM-0] From the official SI website: "...For example, the quantity torque may be thought of as the cross product of force and distance, suggesting the unit newton metre, or it may be thought of as energy per angle, suggesting the unit joule per radian."

[Eshbach-1] For example: Eshbach's handbook of engineering fundamentals - 10.4 Engineering Thermodynamics and Heat Transfer "In SI units the basic unit of energy is Newton-Meter".

[2] BIPM - unit symbols

[BIPM2-3] From the official SI website: "A derived unit can often be expressed in different ways by combining base units with derived units having special names. Joule, for example, may formally be written newton metre, or kilogram metre squared per second squared. This, however, is an algebraic freedom to be governed by common sense physical considerations; in a given situation some forms may be more helpful than others. In practice, with certain quantities, preference is given to the use of certain special unit names, or combinations of unit names, to facilitate the distinction between different quantities having the same dimension."

[4] BIPM - special names

[5] $U_{1 \to 2} = \left| \int_{\theta_1}^{\theta_2} \tau d\theta \right|$
Ferdinand Beer et al., Vector Mechanics for Engineers page 1084.

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