1. Given

   • The flywheel starts from rest, so initial angular velocity is $\omega_0 = 0$
   • It is accelerated uniformly, so angular acceleration $\alpha$ is constant.
   • Angular displacement in the first second is $\theta_1 = 5\ \text{rad}$

2. Use rotational kinematics For angular displacement in time $t$, $\theta = \omega_0 t + \frac{1}{2}\alpha t^2$

   In the first second, $t=1$ s: $5 = 0 + \frac{1}{2}\alpha(1)^2$ $\frac{\alpha}{2} = 5$ $\alpha = 10\ \text{rad/s}^2$

3. Find total angle in 2 seconds $\theta(2) = \omega_0(2) + \frac{1}{2}\alpha(2)^2$ $\theta(2) = 0 + \frac{1}{2}(10)(4) = 20\ \text{rad}$

4. Angle rotated in the next second This means displacement from $t=1$ s to $t=2$ s: $\theta_{\text{next second}} = \theta(2) - \theta(1)$ $= 20 - 5 = 15\ \text{rad}$

5. Check options

   • A: $7.5$ rad ❌
   • B: $15$ rad ✅
   • C: $20$ rad ❌
   • D: $30$ rad ❌

Therefore, the correct answer is: $\boxed{15\ \text{rad}}$