Use the formula relating the linear speed v and angular speed ω:

v=ωr

where r is the radius. Convert 42 miles per hour to feet per minute: \(\displaystyle{\left({42}{m}{i}\le\frac{{s}}{{h}}{r}\right)}\cdot{\left({1}{h}\frac{{r}}{{60}}\min\right)}\cdot{\left({5280}{f}\frac{{t}}{{1}}{m}{i}\le\right)}={3696}{f}\frac{{t}}{\min}\)

Substitute v=3696 ft/min and \(\displaystyle{r}=\frac{{1.2}}{{2}}={0.6}\) then find ω: 3696=ω(0.6)

\(\displaystyle\frac{{3696}}{{0.6}}={w}\)

ω=6160 radians per minute

v=ωr

where r is the radius. Convert 42 miles per hour to feet per minute: \(\displaystyle{\left({42}{m}{i}\le\frac{{s}}{{h}}{r}\right)}\cdot{\left({1}{h}\frac{{r}}{{60}}\min\right)}\cdot{\left({5280}{f}\frac{{t}}{{1}}{m}{i}\le\right)}={3696}{f}\frac{{t}}{\min}\)

Substitute v=3696 ft/min and \(\displaystyle{r}=\frac{{1.2}}{{2}}={0.6}\) then find ω: 3696=ω(0.6)

\(\displaystyle\frac{{3696}}{{0.6}}={w}\)

ω=6160 radians per minute