Answer
The difference is $~~59,200~m/s^2$
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 magnitude of the centripetal acceleration when $r = 1.50~m$:
$a = \omega^2~r$
$a = (209.44~rad/s)^2(1.50~m)$
$a = 65,798~m/s^2$
We can find the magnitude of the centripetal acceleration when $r = 0.150~m$:
$a = \omega^2~r$
$a = (209.44~rad/s)^2(0.150~m)$
$a = 6580~m/s^2$
We can find the difference:
$65,798~m/s^2 - 6580~m/s^2 = 59,200~m/s^2$
The difference is $~~59,200~m/s^2$
