gc (engineering)

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

$g_{\text{c}}={\frac {ma}{F}}$

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

$F=Kma$

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

$1~{\text{lbf}}=K\cdot 1~{\text{lb}}\cdot 32.174~{\frac {\text{ft}}{{\text{s}}^{2}}}$

Leading to

$K={\frac {1~{\text{lbf}}}{1~{\text{lb}}\cdot 32.174~{\frac {\text{ft}}{{\text{s}}^{2}}}}}=0.03108~{\frac {{\text{lbf}}\cdot {\text{s}}^{2}}{{\text{lb}}\cdot {\text{ft}}}}$

g_c is defined as the reciprocal of the constant K

$g_{\text{c}}={\frac {1}{K}}=32.174~{\frac {{\text{lb}}\cdot {\text{ft}}}{{\text{lbf}}\cdot {\text{s}}^{2}}}$

or equivalently, as

$g_{\text{c}}={\frac {ma}{F}}$

Specific systems of units

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)