Answer
After 8 revolutions, the angular speed is $1rev/s$
Work Step by Step
The blades' initial angular speed $\omega_0=0$, final speed is $\omega=0.5rev/s$, and $\theta=2rev$
The blades' angular acceleration is $$\alpha=\frac{\omega^2-\omega_0^2}{2\theta}=0.0625rev/s^2$$
After 8 revolutions, or $\theta=8rev$, the angular speed is $$\omega^2=\omega_0^2+2\alpha\theta=1$$ $$\omega=1rev/s$$
