Answer
It would take 9 revolutions for the blade to come to rest.
Work Step by Step
$\omega^2-\omega_1^2 = 2\alpha ~\theta_1$
$\theta_1 = \frac{0-\omega_1^2}{2\alpha}=\frac{-\omega_1^2}{2\alpha}$
$\omega^2-\omega_3^2 = 2\alpha ~\theta_3$
$\theta_3 = \frac{0-\omega_3^2}{2\alpha}=\frac{-\omega_3^2}{2\alpha}$
$\theta_3 = \frac{-(3~\omega_1)^2}{2\alpha}=9\times \frac{-\omega_1^2}{2\alpha}$
$\theta_3 = 9\times \theta_1$
It would take 9 revolutions for the blade to come to rest.
