Newton-metre

Template:Short description Template:For Template:Infobox unit The newton-metre or newton-meter (also non-hyphenated, newton metre or newton meter; symbol N⋅m<ref name="BIPM-SI-5.1">Template:Cite web</ref> or N m<ref name="BIPM-SI-5.1"/>)Template:Efn is the unit of torque (also called Template:Em) 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 metre long.

The unit is also used less commonly as a unit of work, or energy, in which case it is equivalent to the more common and standard SI unit of energy, the joule.<ref name=Eshbach>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-metre".</ref> In this usage the metre term represents the distance travelled or displacement in the direction of the force, and not the perpendicular distance from a fulcrum (i.e. the lever arm length) as it does when used to express torque. This usage is generally discouraged,<ref>Fundamentals of Physics, 9th edition by Halliday Resnick Walker, p. 309. "The SI unit of torque is the newton-meter. In our discussion of energy we called this combination the joule. But torque is not work and torque should be expressed in newton-meters, not joules. google books link</ref> since it can lead to confusion as to whether a given quantity expressed in newton-metres is a torque or a quantity of energy.<ref name=bipm222/> "Even though torque has the same dimension as energy (SI unit joule), the joule is never used for expressing torque".<ref name=bipm222>Template:Cite web</ref>

Newton-metres and joules are dimensionally equivalent in the sense that they have the same expression in SI base units,

<math>1 \, \text{N} {\cdot} \mathrm{m} = 1 \, \frac{\text{kg} {\cdot} \text{m}^2}{\text{s}^2} \quad , \quad 1 \, \mathrm{J} = 1 \, \frac{\mathrm{kg} {\cdot} \mathrm{m}^2}{\mathrm{s}^2}</math>

but are distinguished in terms of applicable kind of quantity, to avoid misunderstandings when a torque is mistaken for an energy or vice versa. Similar examples of dimensionally equivalent units include Pa versus J/m³, Bq versus Hz, and ohm versus ohm per square.

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