# Newton metre

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The newton metre (also newton-metre, symbol N m or N·m)[1] is a unit of torque (also called "moment") in the SI system. 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.

It 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.[2] 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 as it does when used to express torque. This usage is generally discouraged,[3] since it can lead to confusion as to whether a given quantity expressed in newton metres is a torque or a quantity of energy.[4] However, since torque represents energy transferred or expended per angle of revolution, one newton metre of torque is equivalent to one joule per radian.[4]

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

${\displaystyle 1\,{\text{N}}{\cdot }\mathrm {m} =1{\frac {{\text{kg}}{\cdot }{\text{m}}^{2}}{{\text{s}}^{2}}}\quad ,\quad 1\,\mathrm {J} =1{\frac {\mathrm {kg} {\cdot }\mathrm {m} ^{2}}{\mathrm {s} ^{2}}}}$

Again, N⋅m and J are distinguished in order to avoid misunderstandings where 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.

## References

1. ^ BIPM – unit symbols
2. ^ 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".
3. ^ Fundamentals of Physics, 9th edition by Halliday Resnick Ralker, p309. "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
4. ^ a b BIPM - special names
5. ^ Mechanical Engineering Formulas Pocket Guide, p6
6. ^ Concise encyclopedia of plastics, by Donald V. Rosato, Marlene G. Rosato, Dominick V. Rosato, p621

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