A motor starts from rest and reaches an angular velocity of 1200 rpm in 10 seconds, and then speeds up to 4500 rpm in another 10 seconds. What is the total angular displacement in revolutions?

Initial angular velocity ($\omega_i$):

$$\omega_i = 1200 \text{ rpm} = \frac{1200 \text{ revolutions}}{60 \text{ seconds}} = 20 \text{ rps}$$

Final angular velocity ($\omega_f$):

$$\omega_f = 4500 \text{ rpm} = \frac{4500 \text{ revolutions}}{60 \text{ seconds}} = 75 \text{ rps}$$

The time taken ($t$) is $10 \text{ s}$.

For constant angular acceleration, the total angular displacement can be found using the formula:

$$\theta = \left(\frac{\omega_i + \omega_f}{2}\right) t$$

Substitute the values:

$$\theta = \left(\frac{20 \text{ rps} + 75 \text{ rps}}{2}\right) \times 10 \text{ s}$$ $$\theta = \left(\frac{95 \text{ rps}}{2}\right) \times 10 \text{ s}$$ $$\theta = 47.5 \text{ rps} \times 10 \text{ s}$$ $$\theta = 475 \text{ revolutions}$$

The number of revolutions is $\text{475}$.