#### 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.