Thermionic emission: Difference between revisions
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[[File:Torque force equivalence at one meter leverage.png|right|300px]] | |||
A '''newton metre''' is a [[Physical unit|unit]] of [[torque]] (also called "[[moment (physics)|moment]]") in the [[International System of Units|SI]] system. The symbolic form is '''N m''' or '''N·m'''.<ref>[http://www.bipm.org/en/si/si_brochure/chapter5/5-1.html BIPM - unit symbols]</ref> One newton metre, sometimes hyphenated ''newton-metre'', is equal to the torque resulting from a [[force]] of one [[newton (unit)|newton]] applied perpendicularly to a [[moment arm]] which is one [[metre]] long. | |||
It 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 very different 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 discouraged by the [[BIPM|SI authority]], since it can lead to confusion as to whether a given quantity expressed in newton-metres is a torque or a quantity of energy. 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>[http://www.bipm.org/en/si/si_brochure/chapter2/2-2/2-2-2.html BIPM - special names]</ref> | |||
Newton metres and joules are "dimensionally equivalent" in the sense that they have the same expression in [[SI base unit]]s: | |||
::<math>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}</math> | |||
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 [[Becquerel]] versus [[Hertz]], and [[ohm]]s versus [[ohms per square]]. | |||
{{clear}} | |||
==Conversion factors== | |||
*1 newton metre = 0.7375621 [[pound-foot (torque)|pound-foot]] (often "foot-pound") | |||
*1 [[kilogram-force]] metre = 9.80665 Nm<ref>[http://books.google.com/books?id=hAFRfIZMzrwC&pg=PA6 ''Mechanical Engineering Formulas Pocket Guide'', p6]</ref><ref>[http://books.google.com/books?id=0g9QjxsbqmUC&pg=PA621 ''Concise encyclopedia of plastics'', by Donald V. Rosato, Marlene G. Rosato, Dominick V. Rosato, p621]</ref> | |||
*1 [[pound-foot (torque)|pound-foot]] (often "foot-pound") = 1 [[pound force]] foot ˜ 1.3558 Nm | |||
*1 inch [[ounce-force]] = 7.0615518 mNm | |||
*1 [[dyne]] centimetre = 10<sup>−7</sup> Nm | |||
*1 [[joule]] = 1 Nm | |||
==See also== | |||
*[[Bending moment]] | |||
*[[Spring scale]] | |||
*[[Torque tester]] | |||
==References== | |||
{{reflist}} | |||
[[Category:Units of torque]] | |||
[[Category:SI derived units]] | |||
Revision as of 21:36, 22 January 2014
A 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 discouraged by the SI authority, since it can lead to confusion as to whether a given quantity expressed in newton-metres is a torque or a quantity of energy. However, since torque represents energy transferred or expended per angle of revolution, one newton metre of torque is equivalent to one joule per radian.[3]
Newton metres and joules are "dimensionally equivalent" in the sense that they have the same expression in SI base units:
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 Becquerel versus Hertz, and ohms versus ohms per square.
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Conversion factors
- 1 newton metre = 0.7375621 pound-foot (often "foot-pound")
- 1 kilogram-force metre = 9.80665 Nm[4][5]
- 1 pound-foot (often "foot-pound") = 1 pound force foot ˜ 1.3558 Nm
- 1 inch ounce-force = 7.0615518 mNm
- 1 dyne centimetre = 10−7 Nm
- 1 joule = 1 Nm
See also
References
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- ↑ 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".
- ↑ BIPM - special names
- ↑ Mechanical Engineering Formulas Pocket Guide, p6
- ↑ Concise encyclopedia of plastics, by Donald V. Rosato, Marlene G. Rosato, Dominick V. Rosato, p621