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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asked 2021-06-02
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.

Answers (1)

2021-06-03
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
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