Question

# A motorcycle is traveling at 42 miles per hour on tires that measure 1.2 feet in diameter. Find the approximate angular speed of the tires in radians

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A motorcycle is traveling at 42 miles per hour on tires that measure 1.2 feet in diameter. Find the approximate angular speed of the tires in radians per minute.

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