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| image = Newton-metre.png
| image = Newton-metre.png
| caption = One newton-metre is the torque resulting from a force of one newton applied perpendicularly to the end of a moment arm that is one metre long.
| caption = One newton-metre is the torque resulting from a force of one newton applied perpendicularly to the end of a moment arm that is one metre long.
| standard = [[SI derived unit]]
| standard = [[SI]]
| quantity = [[torque]]
| quantity = [[torque]]
| symbol = N⋅m
| symbol = N⋅m
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| inunits3 = 141.6 in oz
| inunits3 = 141.6 in oz
}}
}}
The '''newton-metre''' (also '''newton metre''' or '''newton meter'''; symbol '''N&sdot;m'''<ref name="BIPM-SI-5.1">[http://www.bipm.org/en/publications/si-brochure/section5-1.html BIPM – unit symbols]</ref> or '''N&nbsp;m'''<ref name="BIPM-SI-5.1"/>) is a [[Physical unit|unit]] of [[torque]] (also called {{em|[[moment (physics)|moment]]}}) in the [[International System of Units|SI]] system. One newton-metre is equal to the torque resulting from a [[force]] of one [[newton (unit)|newton]] applied perpendicularly to the end of a [[moment arm]] that is one [[metre]] long. The nonstandard notation ''Nm'' occurs in some fields.<!-- The medical literature contains a lot of "Nm" with reference to biophysical torque in orthopedic and prosthodontic contexts, but SI requires either multi-dot or space in such symbol combinations -->
The '''newton-metre''' (also '''newton metre''' or '''newton meter'''; symbol '''N&sdot;m'''<ref name="BIPM-SI-5.1">[http://www.bipm.org/en/publications/si-brochure/section5-1.html BIPM – unit symbols]</ref> or '''N&nbsp;m'''<ref name="BIPM-SI-5.1"/>) is the [[SI derived unit]] of [[torque]] (also called {{em|[[moment (physics)|moment]]}}). One newton-metre is equal to the torque resulting from a [[force]] of one [[newton (unit)|newton]] applied perpendicularly to the end of a [[moment arm]] that is one [[metre]] long. The nonstandard notation ''Nm'' occurs in some fields.<!-- The medical literature contains a lot of "Nm" with reference to biophysical torque in orthopedic and prosthodontic contexts, but SI requires either multi-dot or space in such symbol combinations -->


The unit is also used less commonly as a unit of [[work (physics)|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 [[Dot product#Physics|in the direction]] of the force, and not the [[Cross product#Mechanics|perpendicular distance]] from a fulcrum as it does when used to express torque. This usage is generally discouraged,<ref>Fundamentals of Physics, 9th edition by Halliday Resnick Ralker, p.&nbsp;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. [https://books.google.com/books?id=nQZyAgAAQBAJ&pg=PA309 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/> However, since torque represents energy transferred or expended per angle of revolution, one newton-metre of torque is equivalent to one joule per [[radian]].<ref name=bipm222>[http://www.bipm.org/en/publications/si-brochure/section2-2-2.html BIPM - special names]</ref>
The unit is also used less commonly as a unit of [[work (physics)|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 [[Dot product#Physics|in the direction]] of the force, and not the [[Cross product#Mechanics|perpendicular distance]] from a fulcrum as it does when used to express torque. This usage is generally discouraged,<ref>Fundamentals of Physics, 9th edition by Halliday Resnick Ralker, p.&nbsp;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. [https://books.google.com/books?id=nQZyAgAAQBAJ&pg=PA309 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/> However, since torque represents energy transferred or expended per angle of revolution, one newton-metre of torque is equivalent to one joule per [[radian]].<ref name=bipm222>[http://www.bipm.org/en/publications/si-brochure/section2-2-2.html BIPM - special names]</ref>

Revision as of 12:36, 19 August 2022

For the instrument that measures forces in newtons, see Spring scale.
Newton-metre
One newton-metre is the torque resulting from a force of one newton applied perpendicularly to the end of a moment arm that is one metre long.
General information
Unit systemSI
Unit oftorque
SymbolN⋅m, N m
Conversions
1 N⋅m in ...... is equal to ...
   FPS system   0.73756215 lbf.ft
   inch⋅pound-force   8.8507 in lbf
   inch⋅ounce-force   141.6 in oz

The newton-metre (also newton metre or newton meter; symbol N⋅m[1] or N m[1]) is the SI derived unit of torque (also called moment). 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 nonstandard notation Nm occurs in some fields.

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.[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,

but are distinguished 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.

Conversion factors

See also

References

  1. ^ a b 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, 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
  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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