# Slug (unit)

The slug is a derived unit of mass in a weight-based system of measures, most notably within the British Imperial measurement system and in 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 force of one pound (lbf) is exerted on it.

${\displaystyle 1\,{\text{slug}}=1\,{\frac {{\text{lbf}}{\cdot }{\text{s}}^{2}}{\text{ft}}}\quad \Longleftrightarrow \quad 1\,{\text{lbf}}=1\,{\frac {{\text{slug}}{\cdot }{\text{ft}}}{{\text{s}}^{2}}}}$
Slug
Unit systemBritish Gravitational system
Unit ofmass
Symbolslug
Conversions
1 slug in ...... is equal to ...
SI units   14.59390 kg
US customary units   32.1740 lb

One slug has a mass of 32.1740 lb (14.59390 kg) based on standard gravity, the international foot, and the avoirdupois pound.[2] At the Earth's surface, an object with a mass of 1 slug exerts a force downward of approximately 32.2 lbf or 143 N.[3][4]

## 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.[5]

The name "slug" was coined before 1900 by British physicist Arthur Mason Worthington,[6] but it did not see any significant use until decades later. 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[7][8]
Base Force Weight Mass
2nd law of motion m = F/a F = W a/g F = m a
System BGGM EEM AECGSMTSSI
Acceleration (a) ft/s2m/s2 ft/s2m/s2 ft/s2Galm/s2m/s2
Mass (m) slughyl pound-masskilogram poundgramtonnekilogram
Force (F),
weight (W)
poundkilopond pound-forcekilopond poundaldynesthènenewton
Pressure (p) pounds per square inchtechnical atmosphere pounds-force per square inchatmosphere poundals per square footbaryepiezepascal

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.

The blob is the inch version of the slug (1 blob is equal to 1 lbf⋅s2/in, or 12 slugs)[2][9] or equivalent to 386.0886 pounds (175.1268 kg). This unit is also called slinch (a portmanteau of the words slug and inch).[10][11] Similar terms include slugette[12] and snail.[13]

Similar metric units include the glug in the centimetre–gram–second system, and the mug, par, or MTE in the metre–kilogram–second system.[14]

## References

1. See Elementary High School physics and chemistry text books/fundamentals.
2. Shigley, Joseph E. and Mischke, Charles R. Mechanical Engineering Design, Sixth ed, pp. 31–33. McGraw Hill, 2001. ISBN 0-07-365939-8.
3. Beckwith, Thomas G., Roy D. Marangoni, et al. Mechanical Measurements, Fifth ed, pp. 34-36. Addison-Wesley Publishing, 1993. ISBN 0-201-56947-7.
4. Shevell, R.S. Fundamentals of Flight, Second ed, p. xix. Prentice-Hall, 1989.
5. gee. unit2unit.eu
6. Worthington, Arthur Mason (1900). Dynamics of Rotation: An Elementary Introduction to Rigid Dynamics (3rd ed.). Longmans, Green, and Co. p. 9.
7. Comings, E. W. (1940). "English Engineering Units and Their Dimensions". Industrial & Engineering Chemistry. 32 (7): 984–987. doi:10.1021/ie50367a028.
8. 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.
9. Norton, Robert L. Cam Design and Manufacturing Handbook, p. 13. Industrial Press Inc., 2009. ISBN 0831133678.
10. Slug. DiracDelta Science & Engineering Encyclopedia
11. "1 blob". Wolfram Alpha Computational Knowledge Engine. Retrieved 27 October 2011.
12. Celmer, Robert. Notes to Accompany Vibrations II. Version 2.2. 2009.
13. Rowlett, Russ. "How Many? A Dictionary of Units of Measurement". unc.edu, September 1, 2004. Retrieved January 26, 2018.
14. Cardarelli, François (1999). Scientific Units, Weights and Measures. Springer. pp. 358, 377. ISBN 1-85233-682-X.