1. Stating the problem: A disc accelerates uniformly from rest to an angular velocity of 20 revolutions per second over a time period of 10 seconds. We need to find its angular acceleration in rad/s$^2$. 2. Convert angular velocity from revolutions per second to radians per second. Since 1 revolution = $2\pi$ radians, the final angular velocity $\omega_f$ is $$\omega_f = 20 \times 2\pi = 40\pi \text{ rad/s}.$$ 3. The initial angular velocity $\omega_i$ is 0 rad/s because the disc starts from rest. 4. Using the formula for angular acceleration $\alpha$ when acceleration is uniform: $$\alpha = \frac{\omega_f - \omega_i}{t},$$ where $t=10$ seconds. 5. Substitute values: $$\alpha = \frac{40\pi - 0}{10} = 4\pi \text{ rad/s}^2.$$ 6. Approximate numerical value: $$4\pi \approx 12.57 \text{ rad/s}^2.$$ Answer: The angular acceleration of the flywheel is $4\pi$ rad/s$^2$ or approximately 12.57 rad/s$^2$.