Slug (unit)
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Slug Unit
slug
Unit systemBritish Gravitational system
Unit ofMass
Symbolslug
Conversions
BGS base units1 ft-1?lbf?s2
SI units14.59390 kg
US customary units32.17404 lb

The slug is a derived unit of mass in a weight-based system of measures, most notably within the British Imperial measurement system and the United States customary measures system. Systems of measure either define mass and derive a force unit or define a base force and derive a mass unit[1] (cf. poundal, a derived unit of force in a force-based system). A slug is defined as the mass that is accelerated by 1 ft/s2 when a net force of one pound (lbf) is exerted on it.[2]

${\displaystyle 1~{\text{slug}}=1~{\text{lbf}}{\cdot }{\frac {{\text{s}}^{2}}{\text{ft}}}\quad \Longleftrightarrow \quad 1~{\text{lbf}}=1~{\text{slug}}{\cdot }{\frac {\text{ft}}{{\text{s}}^{2}}}}$

One slug is a mass equal to 32.1740 lb (14.59390 kg) based on standard gravity, the international foot, and the avoirdupois pound.[3] At the Earth's surface, an object with a mass of 1 slug weighs approximately 32.2 lbf or 143 N.[4][5]

## History

The slug is part of a subset of units known as the gravitational FPS system, one of several such specialized systems of mechanical units developed in the late 19th and the 20th century. Geepound was another name for this unit in early literature.[6]

The name "slug" was coined before 1900 by British physicist Arthur Mason Worthington,[7] but it did not see any significant use until decades later.[8] It is derived from the meaning "solid block of metal", not from the slug mollusc.[9] A 1928 textbook says:

No name has yet been given to the unit of mass and, in fact, as we have developed the theory of dynamics no name is necessary. Whenever the mass, m, appears in our formulae, we substitute the ratio of the convenient force-acceleration pair (w/g), and measure the mass in lbs. per ft./sec.2 or in grams per cm./sec.2.

-- Noel Charlton Little, College Physics, Charles Scribner's Sons, 1928, p. 165.
Three approaches to units of mass and force or weight[10][11]
Base Force Weight Mass
2nd law of motion m = F/a F = Wa/g F = ma
System BG GM EE M AE CGS MTS SI
Acceleration (a) ft/s2 m/s2 ft/s2 m/s2 ft/s2 Gal m/s2 m/s2
Mass (m) slug hyl pound-mass kilogram pound gram tonne kilogram
Force (F),
weight (W)
pound kilopond pound-force kilopond poundal dyne sthène newton
Pressure (p) pound per square inch technical atmosphere pound-force per square inch standard atmosphere poundal per square foot barye pieze pascal

The slug is listed in the Regulations under the Weights and Measures (National Standards) Act, 1960. This regulation defines the units of weights and measures, both regular and metric, in Australia.

## Related units

The blob is the inch version of the slug (1blob is equal to 1 lbf?s2/in, or 12slugs)[3][12] or equivalent to 386.0886 pounds (175.1268 kg). This unit is also called slinch (a portmanteau of the words slug and inch).[13][14] Similar terms include slugette[15] and snail.[16]

Similar (but long-obsolete) metric units included the glug (980.665 g) in the centimetre-gram-second system,[17][18] and the mug, hyl, par, or TME (German: technische Masseneinheit, lit.'technical mass unit', 9.80665 kg) in the metre-kilogram-second system.[19]

## References

1. ^ See Elementary High School physics and chemistry text books/fundamentals.
2. ^ Collins, Danielle (May 2019). "How to convert between mass and force -- in metric and English units". Linear Motion Tips. Retrieved 2021.
3. ^ a b Shigley, Joseph E. and Mischke, Charles R. Mechanical Engineering Design, Sixth ed, pp. 31-33. McGraw Hill, 2001. ISBN 0-07-365939-8.
4. ^ Beckwith, Thomas G., Roy D. Marangoni, et al. Mechanical Measurements, Fifth ed, pp. 34-36. Addison-Wesley Publishing, 1993. ISBN 0-201-56947-7.
5. ^ Shevell, R.S. Fundamentals of Flight, Second ed, p. xix. Prentice-Hall, 1989.
6. ^ gee Archived 2018-01-27 at the Wayback Machine. unit2unit.eu
7. ^ Worthington, Arthur Mason (1900). Dynamics of Rotation: An Elementary Introduction to Rigid Dynamics (3rd ed.). Longmans, Green, and Co. p. 9.
8. ^ Gyllenbok, Jan (April 11, 2018). Encyclopaedia of Historical Metrology, Weights, and Measures: Volume 1. Birkhäuser. ISBN 9783319575988 – via Google Books.
9. ^ Society, Digital Equipment Computer Users (September 4, 1965). "Papers and Presentations" – via Google Books.
10. ^ Comings, E. W. (1940). "English Engineering Units and Their Dimensions". Industrial & Engineering Chemistry. 32 (7): 984-987. doi:10.1021/ie50367a028.
11. ^ Klinkenberg, Adrian (1969). "The American Engineering System of Units and Its Dimensional Constant gc". Industrial & Engineering Chemistry. 61 (4): 53-59. doi:10.1021/ie50712a010.
12. ^ Norton, Robert L. Cam Design and Manufacturing Handbook, p. 13. Industrial Press Inc., 2009. ISBN 0831133678.
13. ^ Slug Archived 2016-11-30 at the Wayback Machine. DiracDelta Science & Engineering Encyclopedia
14. ^ "1 blob". Wolfram Alpha Computational Knowledge Engine. Retrieved 2011.
15. ^ Celmer, Robert. Notes to Accompany Vibrations II. Version 2.2. 2009.
16. ^ Rowlett, Russ. "How Many? A Dictionary of Units of Measurement". unc.edu, September 1, 2004. Retrieved January 26, 2018.
17. ^ Cardarelli, François (1999). Encyclopaedia of Scientific Units, Weights and Measures. Springer. pp. 358, 377. ISBN 1-85233-682-X.
18. ^ David, A. (1958). "Beware of the "Glug," a New Unit of Mass!". Letters to the Editor. American Journal of Physics. 26 (1): 41. doi:10.1119/1.1934599.
19. ^ Cardarelli, François (1999). Encyclopaedia of Scientific Units, Weights and Measures. Springer. pp. 470, 497. ISBN 1-85233-682-X.