Answer
The coin will not slide off the turntable as long as the coin is placed within $8.05~cm$ from the center of the turntable.
Work Step by Step
The angular speed is $(33.3~rpm)(2\pi~rad/rev)(1~min/60~s) = 3.49~rad/s$
For a given angular speed, the force of friction can provide the required centripetal force to keep the coin moving in a circle as long as the radius of rotation is small enough. We can find the radius when the force of static friction reaches its maximum possible value:
$F_f = m~a_r$
$mg~\mu_s = m~\omega^2~r$
$r = \frac{g~\mu_s}{\omega^2}$
$r = \frac{(9.80~m/s^2)(0.10)}{(3.49~rad/s)^2}$
$r = 0.0805~m$
$r = 8.05~cm$
The coin will not slide off the turntable as long as the coin is placed within $8.05~cm$ from the center of the turntable.
