Answer
a. $1100$ rad/min
b. 175 rev/min
Work Step by Step
Suppose a point moves along a circle of radius $r$
and the ray from the center of the circle to the point
traverses $\theta$ radians in time $t$.
Let $ s=r\theta$ be the distance the point travels in time $t$.
The angular speed of the point is $\omega=\theta/t$.
The linear speed of the point is $v=s/t$.
$ v=r\omega$.
1 revolution = $ 2\pi$ radians.
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a.
48 in = 4 ft,
1 mi = 5280 ft
1 h = 60 min
From $ v=r\omega$,
$\displaystyle \omega=\frac{v}{r}=\frac{50\ mi/h}{4\ ft}\cdot\frac{5280\ ft}{1\ mi}\cdot\frac{1\ h}{60\ min}$
$=1100$ rad/min
b.
$\displaystyle \frac{1100\ rad}{1\ min}\cdot\frac{1\ rev}{2\pi\ rad}\approx $175.070437401 rev/min
$\approx$ 175 rev/min
