The formula:

\(v=rw\)

First, convert to ft/min:

\(\displaystyle{v}=\frac{{{9.55}{m}{i}}}{{{h}{r}}}\times\frac{{{5280}{f}{t}}}{{{1}{m}{i}}}\times\frac{{{1}{h}{r}}}{{{60}\min}}={840.4}\) ft per min

Substitute \(\displaystyle{r}=\frac{{d}}{{2}}{\quad\text{and}\quad}{v}={840.4}:\)

\(\displaystyle{840.4}={\left(\frac{{8.5}}{{2}}\right)}{w}\)

\(\displaystyle{w}=\frac{{840.2}}{{4.25}}\) rad per min

Convert to rev per min:

\(\displaystyle{w}=\frac{{840.2}}{{4.25}}\times\frac{{1}}{{{2}\pi}}\)

\(\displaystyle{w}\approx{31.5}\) rev per min