In the circle below, $\overline{AB} \| \overline{CD}$. $\overline{AD}$ is a diameter of the circle, and $AD = 36^{\prime \prime}$. What is the number of inches in the length of $\widehat{AB}$? Express your answer in terms of $\pi$. [asy]
import markers;
import olympiad; size(150); import geometry; import graph; defaultpen(linewidth(0.8));
draw(Circle(origin,36));
pair A = 36*dir(130);
pair B = 36*dir(50);
pair D = 36*dir(-50);
pair C = 36*dir(-130);
draw(B--A--D--C);
label("$A$",A,W); label("$B$",B,E); label("$C$",C,W); label("$D$",D,E);
markangle("$50^{\circ}$",D,A,B,radius=10);
[/asy]
By symmetry, $\widehat{BD}=\widehat{CA}=100^\circ$.  Furthermore, $\widehat{AB}=\widehat{CD}$, so \[360^\circ=\widehat{AB}+\widehat{BD}+\widehat{DC}+\widehat{CA}=2\widehat{AB}+200^\circ.\] Therefore the arc $\widehat{AB}$ measures $80^\circ$.  Since the diameter of the circle is $36''$, the length of the arc is \[\frac{80}{360}(\pi\cdot36)=\boxed{8\pi}\text{~inches}.\]