Newton-metre: Difference between revisions
Content deleted Content added
ClueBot NG (talk | contribs) m Reverting possible vandalism by 109.93.195.172 to version by RacoonyRE. Report False Positive? Thanks, ClueBot NG. (3932055) (Bot) |
m Footnote typo |
||
| (26 intermediate revisions by 17 users not shown) | |||
| Line 5: | Line 5: | ||
| 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 |
| standard = [[SI]] |
||
| quantity = [[torque]] |
| quantity = [[torque]] |
||
| symbol = N⋅m |
| symbol = N⋅m |
||
| symbol2 = N m |
| symbol2 = N m |
||
| units1 = [[Foot–pound–second system|FPS system]] |
| units1 = [[Foot–pound–second system|FPS system]] |
||
| inunits1 = 0.73756215 [[pound-foot (torque)|lbf |
| inunits1 = 0.73756215 [[pound-foot (torque)|lbf.ft]] |
||
| units2 = inch⋅pound-force |
| units2 = inch⋅pound-force |
||
| inunits2 = 8.8507 in lbf |
| inunits2 = 8.8507 in lbf |
||
| Line 16: | Line 16: | ||
| inunits3 = 141.6 in oz |
| inunits3 = 141.6 in oz |
||
}} |
}} |
||
The '''newton-metre''' (also '''newton metre''' or '''newton meter'''; symbol '''N⋅m'''<ref name="BIPM-SI-5.1">[http://www.bipm.org/en/publications/si-brochure/section5-1.html BIPM – unit symbols]</ref> or '''N m'''<ref name="BIPM-SI-5.1"/>) |
The '''newton-metre''' or '''newton-meter''' (also non-hyphenated, '''newton metre''' or '''newton meter'''; symbol '''N⋅m'''<ref name="BIPM-SI-5.1">[http://www.bipm.org/en/publications/si-brochure/section5-1.html BIPM – unit symbols]</ref> or '''N m'''<ref name="BIPM-SI-5.1"/>){{efn|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 -->}} is the unit of [[torque]] (also called {{em|[[moment (physics)|moment]]}}) in the [[International System of Units]] (SI). 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 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 |
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 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. [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/> "Even though torque has the same dimension as energy (SI unit joule), the joule is never used for expressing torque".<ref name=bipm222>[http://www.bipm.org/en/publications/si-brochure/section2-2-2.html BIPM - special names]</ref> |
||
Newton-metres and joules are [[dimensional analysis|dimensionally]] equivalent in the sense that they have the same expression in [[SI base unit]]s, |
Newton-metres and joules are [[dimensional analysis|dimensionally]] equivalent in the sense that they have the same expression in [[SI base unit]]s, |
||
| Line 24: | Line 24: | ||
::<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> |
::<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 to avoid misunderstandings when a torque is mistaken for an energy or vice versa. Similar examples of dimensionally equivalent units include [[Pascal (unit)|Pa]] versus J/m<sup>3</sup>, [[Becquerel|Bq]] versus [[Hertz|Hz]], and [[ohm]] versus [[Sheet resistance|ohm per square]]. |
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 [[Pascal (unit)|Pa]] versus J/m<sup>3</sup>, [[Becquerel|Bq]] versus [[Hertz|Hz]], and [[ohm]] versus [[Sheet resistance#Units|ohm per square]]. |
||
{{clear}} |
{{clear}} |
||
| Line 37: | Line 37: | ||
==See also== |
==See also== |
||
*[[Bending moment]] |
*[[Bending moment]] |
||
*[[Spring scale]] |
*[[Spring scale]] |
||
*[[Torque tester]] |
*[[Torque tester]] |
||
*[[Newton-second]], the derived [[SI]] unit of [[impulse (physics)|impulse]] |
*[[Newton-second]], the derived [[SI]] unit of [[impulse (physics)|impulse]] |
||
==Notes== |
|||
{{notelist}} |
|||
==References== |
==References== |
||
Latest revision as of 22:00, 8 November 2024
| 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 system | SI |
| Unit of | torque |
| Symbol | N⋅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] "Even though torque has the same dimension as energy (SI unit joule), the joule is never used for expressing torque".[4]
Newton-metres and joules are dimensionally equivalent in the sense that they have the same expression in SI base units,
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
[edit]- 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
[edit]- Bending moment
- Spring scale
- Torque tester
- Newton-second, the derived SI unit of impulse
Notes
[edit]- ^ The nonstandard notation "Nm" occurs in some fields.
References
[edit]- ^ a b BIPM – unit symbols
- ^ 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".
- ^ 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
- ^ a b BIPM - special names
- ^ Mechanical Engineering Formulas Pocket Guide, p6
- ^ Concise encyclopedia of plastics, by Donald V. Rosato, Marlene G. Rosato, Dominick V. Rosato, p621
