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# Newton metre

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### Newton metre

The newton metre is a unit of torque (also called "moment") in the SI system. The symbolic form is N m or N·m.[1] One newton metre, sometimes hyphenated 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.

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 very different 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:

1 \, \mathrm{N} \! \cdot \! \mathrm{m} = 1 \frac{\mathrm{kg} \, \mathrm{m}^2}{\mathrm{s}^2} \quad , \quad 1 \, \mathrm{J} = 1 \frac{\mathrm{kg} \, \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 ohms versus ohms 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. ^ , p6Mechanical Engineering Formulas Pocket Guide
6. ^ , by Donald V. Rosato, Marlene G. Rosato, Dominick V. Rosato, p621Concise encyclopedia of plastics
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