Answer
The time it takes the wheel to reach the operating speed is $8s$
Work Step by Step
We have initial velocity $\omega_0=0$ and final velocity $\omega=0.24rad/s$. The angular acceleration $\overline\alpha=0.03rad/s^2$
The time it takes the wheel to reach $\omega$ is $$\Delta t=\frac{\omega-\omega_0}{\overline\alpha}=8s$$
