Answer
The slope of the plot of $a$ versus the radial distance $r$ is $~~43,900$
Work Step by Step
We can express the angular speed in units of $rad/s$:
$\omega = (2000~rev/min)(\frac{2\pi~rad}{1~rev})(\frac{1~min}{60~s}) = 209.44~rad/s$
We can find the slope of the plot of $a$ versus the radial distance $r$:
$a = \omega^2~r$
$\frac{a}{r} = \omega^2$
$\frac{a}{r} = (209.44)^2$
$\frac{a}{r} = 43,900$
The slope of the plot of $a$ versus the radial distance $r$ is $~~43,900$
