The correct answer is $\boxed{\text{D}}$.
The angular acceleration is the rate of change of angular velocity. It is measured in radians per second squared (rad/s$^2$).
To calculate the angular acceleration, we need to know the initial angular velocity, the final angular velocity, and the time interval over which the change in angular velocity occurred. In this case, we are given that the initial angular velocity is 10 rpm, the final angular velocity is 20 rpm, and the time interval is 10 seconds.
To convert from rpm to rad/s, we use the following conversion factor:
1 rpm = $\frac{2\pi}{60}$ rad/s
Therefore, the initial angular velocity is:
$\omega_i = 10 \text{ rpm} \times \frac{2\pi}{60} \text{ rad/s} = \frac{\pi}{3}$ rad/s
The final angular velocity is:
$\omega_f = 20 \text{ rpm} \times \frac{2\pi}{60} \text{ rad/s} = \frac{2\pi}{3}$ rad/s
The angular acceleration is:
$\alpha = \frac{\omega_f – \omega_i}{t} = \frac{\frac{2\pi}{3} – \frac{\pi}{3}}{10 \text{ s}} = \frac{\pi}{30}$ rad/s$^2$
Therefore, the angular acceleration of the flywheel is $\frac{\pi}{30}$ rad/s$^2$. This means that the flywheel’s angular velocity is increasing at a rate of $\frac{\pi}{30}$ radians per second per second.
Option A is incorrect because it is the initial angular velocity of the flywheel. Option B is incorrect because it is the final angular velocity of the flywheel. Option C is incorrect because it is the angular acceleration of the flywheel multiplied by 10.