Calculate the average angular acceleration and number of revolutions turned through in this time.

We use the conversion factor: $1 \text{ rev/min} = \frac{2\pi \text{ rad}}{60 \text{ s}} = \frac{\pi}{30} \text{ rad/s}$.

$$\omega_0 = 1430 \text{ rev/min} \times \frac{\pi \text{ rad/s}}{30 \text{ rev/min}} = \frac{143\pi}{3} \text{ rad/s}$$ $$\omega_f = 1490 \text{ rev/min} \times \frac{\pi \text{ rad/s}}{30 \text{ rev/min}} = \frac{149\pi}{3} \text{ rad/s}$$

The formula for average angular acceleration is $\alpha_{avg} = \frac{\omega_f - \omega_0}{\Delta t}$.

$$\alpha_{avg} = \frac{\frac{149\pi}{3} \text{ rad/s} - \frac{143\pi}{3} \text{ rad/s}}{0.5 \text{ s}}$$ $$\alpha_{avg} = \frac{\frac{(149-143)\pi}{3} \text{ rad/s}}{0.5 \text{ s}}$$ $$\alpha_{avg} = \frac{\frac{6\pi}{3} \text{ rad/s}}{0.5 \text{ s}} = \frac{2\pi \text{ rad/s}}{0.5 \text{ s}}$$ $$\alpha_{avg} = 4\pi \text{ rad/s}^2 \approx 12.57 \text{ rad/s}^2$$

The average angular acceleration is $\boxed{4\pi \text{ rad/s}^2}$ or approximately $\boxed{12.57 \text{ rad/s}^2}$.

For uniform angular acceleration, the angular displacement can be found using $\Delta \theta = \frac{(\omega_0 + \omega_f)}{2} \Delta t$.

$$\Delta \theta = \frac{\left(\frac{143\pi}{3} \text{ rad/s} + \frac{149\pi}{3} \text{ rad/s}\right)}{2} \times 0.5 \text{ s}$$ $$\Delta \theta = \frac{\left(\frac{292\pi}{3} \text{ rad/s}\right)}{2} \times 0.5 \text{ s}$$ $$\Delta \theta = \frac{146\pi}{3} \text{ rad/s} \times 0.5 \text{ s}$$ $$\Delta \theta = \frac{73\pi}{3} \text{ rad} \approx 76.45 \text{ rad}$$

We use the conversion factor: $1 \text{ revolution} = 2\pi \text{ radians}$.

$$\text{Number of revolutions} = \frac{\Delta \theta}{2\pi}$$ $$\text{Number of revolutions} = \frac{\frac{73\pi}{3} \text{ rad}}{2\pi \text{ rad/rev}}$$ $$\text{Number of revolutions} = \frac{73}{6} \text{ revolutions} \approx 12.17 \text{ revolutions}$$

The number of revolutions turned through is $\boxed{\frac{73}{6} \text{ revolutions}}$ or approximately $\boxed{12.17 \text{ revolutions}}$.