Answer
a. 282.7 rad/min
b. 4524 in/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$.
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1 revolution = $ 2\pi$ radians.
a.
$\displaystyle \omega=\frac{45\cdot 2\pi}{1 \ min}=90\pi$ rad/min
$\approx$282.7 rad/min
b.
$ v=r\omega=16\cdot 90\pi=1440\pi$ in/min
$\approx 4524$ in/min
