Answer
$a = 0.73~m/s^2$
Work Step by Step
We can express the angular speed in units of $rad/s$:
$\omega = (33\frac{1}{3}~rev/min)(\frac{2\pi~rad}{1~rev})(\frac{1~min}{60~s}) = 3.49~rad/s$
We can find the centripetal acceleration:
$a = \omega^2~r$
$a = (3.49~rad/s)^2~(0.060~m)$
$a = 0.73~m/s^2$
