Slug (mass)

The slug is a derived unit of mass in the 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 weights or define a base weight and derive a mass unit.^[1] A slug is defined as the mass that is accelerated by 1 ft/s² when a force of one pound (lb_F) is exerted on it.

$1\,{\text{slug}}=1\,{\frac {{\text{lb}}_{F}\cdot {\text{s}}^{2}}{\text{ft}}}\qquad \Longleftrightarrow \qquad 1\,{\text{lb}}_{F}=1\,{\frac {{\text{slug}}\cdot {\text{ft}}}{{\text{s}}^{2}}}$

One slug has a mass of 32.174049 lb_m or 14.593903 kg based on standard gravity, the international foot, and the avoirdupois pound.^[2] At the surface of the Earth, an object with a mass of 1 slug exerts a force downward (the definition of weight) of approximately 32.2 lb_F 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 mass and force units^[7][8]

Base	force, length, time		weight, length, time		mass, length, time
Force (F)	F = m⋅a = w⋅a/g		F = m⋅a/gc = w⋅a/g		F = m⋅a = w⋅a/g
Weight (w)	w = m⋅g		w = m⋅g/gc ≙ m		w = m⋅g
System	BG	GM	EE	M	AE	CGS	MTS	SI
Acceleration (a)	ft/s^2	m/s^2	ft/s^2	m/s^2	ft/s^2	Gal	m/s^2	m/s^2
Mass (m)	slug	hyl	lbm	kg	lb	g	t	kg
Force (F)	lb	kp	lbF	kp	pdl	dyn	sn	N
Pressure (p)	lb/in^2	at	PSI	atm	pdl/ft^2	Ba	pz	Pa

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.

Similar units

The blob is the inch version of the slug (1 blob = 1 lb_f·s²/in = 12 slugs)^[2][9] or equivalent to 175.126 kg. This unit is also called slinch (a portmanteau of the words slug and inch).^[10][11] Similar terms include slugette,^[12] and a 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. . 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. Michael R. Lindeburg (2011). Civil Engineering Reference Manual for the Pe Exam. Professional Publications. ISBN 1591263417.
8. Wurbs, Ralph A, Fort Hood Review Sessions for Professional Engineering Exam (PDF), retrieved October 26, 2011
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.
14. Cardarelli, François (1999). Scientific Units, Weights and Measures. Springer. pp. 358, 377. ISBN 1-85233-682-X.

External links

• "What is a Slug?" on phy-astr.gsu.edu