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 = , 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} == Specific systems of units==