Gc (engineering)

In engineering and physics, gc 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, 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. 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
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 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
 * $$K = \frac{1~\text{lbf}}{1~\text{lb} \cdot 32.174~\frac{\text{ft}}{\text{s}^2}} = 0.03108~\frac{\text{lbf} \cdot \text{s}^2}{\text{lb} \cdot \text{ft}} $$

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