Answer
The turbine rotates through 19000 revolutions as it coasts to a stop.
Work Step by Step
The turbine coasts to a stop from 3800 rpm. During this time, the average angular speed is $\frac{3800~rpm+0}{2}$ which is 1900 rpm. We can find the number of revolutions the turbine rotates through as it stops;
$\theta = (1900~rpm)(10~min) = 19000~rev$
The turbine rotates through 19000 revolutions as it coasts to a stop.
