Newton-metre

SI unit of torque
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 or newton-meter (also non-hyphenated, newton metre or newton meter; symbol N⋅m[1] or N m[1])[a] is the unit of torque (also called moment) 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.[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,

1 N ⋅ m = 1 kg ⋅ m 2 s 2 , 1 J = 1 k g ⋅ m 2 s 2 {\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}}}}

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.

Conversion factors

  • 1 kilogram-force metre = 9.80665 N⋅m[5][6]
  • 1 newton-metre ≈ 0.73756215 pound-force-feet
  • 1 pound-foot ≡ 1 pound-force-foot ≈ 1.35581795 N⋅m
  • 1 ounce-inch ≡ 1 ounce-force-inch ≈ 7.06155181 mN⋅m (millinewton-metres)
  • 1 dyne-centimetre = 10−7 N⋅m

See also

Notes

  1. ^ The nonstandard notation "Nm" occurs in some fields.

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