Answer
a. 6283 rad/min
b. 52.4 ft/s
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.
$\displaystyle \omega=\frac{1000\cdot 2\pi}{1 min}=2000\pi$ rad/min
$\approx$6283 rad/min
b.
6 in =$\displaystyle \frac{6}{12}$ ft,
1 min =60 s
$v=r\displaystyle \omega=(6in)(\frac{1ft}{12in})(\frac{2000\pi}{1min})(\frac{1min}{60s})$
$\approx $52.4 ft/s
