Answer
$t = 8.6~s$
Work Step by Step
We can find an expression for the angular displacement of Disk A:
$\theta_A = (9.5~rad/s)~t$
We can find an expression for the angular displacement of Disk B:
$\theta_B = \frac{1}{2}(2.2~rad/s^2)~t^2 = (1.1~rad/s^2)~t^2$
We can find $t$ when $\theta_A = \theta_B$:
$\theta_A = \theta_B$
$9.5~t = 1.1~t^2$
$9.5 = 1.1~t$
$t = \frac{9.5}{1.1}$
$t = 8.6~s$
