In engineering and physics, gc is a unit conversion factor used to convert mass to force or vice versa.[1] It is defined as

In unit systems where force is a derived unit, like in SI units, gc is equal to 1. In unit systems where force is a primary unit, like in imperial and US customary measurement systems, gc may or may not equal 1 depending on the units used, and value other than 1 may be required to obtain correct results.[2] For example, in the kinetic energy (KE) formula, if gc = 1 is used, then KE is expressed in foot-poundals; but if gc = 32.174 is used, then KE is expressed in foot-pounds.

Motivations

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According to Newton's second law, the force F is proportional to the product of mass m and acceleration a:

 

or

 

If F = 1 lbf, m = 1 lb, and a = 32.174 ft/s2, then

 

Leading to

 

gc is defined as the reciprocal of the constant K

 

or equivalently, as

 

Specific systems of units

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International System English System 1 English System 2
gc = 1 (kg·m)/(N·s2) gc = 32.174 (lb·ft)/(lbf·s2) gc = 1 (slug·ft)/(lbf·s2)

References

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  1. ^ Janna, William (2015). Introduction to Fluid Mechanics (5th ed.). CRC Press. p. 5. ISBN 9781482211610.
  2. ^ Cengel, Yunus; Boles, Michael (2014). Thermodynamics: An Engineering Approach (9th ed.). McGraw-Hill Education. p. 6. ISBN 9781259822674.