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and physics, ''g''_c is a unit conversion of units#Conversion factors, conversion factor used to convert mass to force or vice versa. It is defined as :

g_\text = \frac

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

Motivations

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

F \propto ma

or :

F = K ma

If ''F'' = 1 pound-force, lbf, ''m'' = 1 pound mass, lb, and ''a'' = , then :

1~\text = K \cdot 1~\text \cdot 32.174~\frac

Leading to :

K = \frac = 0.03108~\frac

''g''_c is defined as the multiplicative inverse, reciprocal of the constant ''K'' :

g_\text = \frac = 32.174~\frac

or equivalently, as :

g_\text = \frac

Specific systems of units

References

{{Reflist Equations