Answer
The coin will start to slide $2.4~seconds$ after the turntable is turned on.
Work Step by Step
At low angular speeds, the force of static friction can provide the required centripetal force to keep the coin moving in a circle. We can find the angular speed when the force of static friction reaches its maximum possible value:
$F_f = m~a_r$
$mg~\mu_s = m~\omega^2~r$
$\omega = \sqrt{\frac{g~\mu_s}{r}}$
$\omega = \sqrt{\frac{(9.80~m/s^2)(0.110)}{0.130~m}}$
$\omega = 2.88~rad/s$
We can find the time $t$ when the turntable reaches this angular speed:
$\omega_f = \omega_0+\alpha~t$
$t = \frac{\omega_f - \omega_0}{\alpha}$
$t = \frac{2.88~rad/s - 0}{1.20~rad/s^2}$
$t = 2.4~s$
The coin will start to slide $2.4~seconds$ after the turntable is turned on.
