A flywheel has a constant angular deceleration of 1.3 rad/s^2. Find the angle through which the flywheel turns as it comes to rest from an angular speed of 230 rad/s.
We can use the formula
\[ \omega^2 = \omega_0^2 + 2 \alpha \Delta \theta \]
where $\omega$ is the final angular velocity, $\omega_0$ is the initial angular velocity, $\alpha$ is the angular acceleration, and $\Delta \theta$ is the angle through which the flywheel turns.
In this case, $\omega = 0$ (since the flywheel comes to rest), $\omega_0 = 230 \, \text{rad/s}$, and $\alpha = -1.3 \, \text{rad/s}^2$. Plugging in these values gives us
\[ (0)^2 = (230)^2 + 2(-1.3) \Delta \theta . \]
Simplifying, we get
\[ 0 = 52900 - 2.6 \Delta \theta . \]
Solving for $\Delta \theta$, we find
\[ \Delta \theta = \frac{52900}{2.6} = \boxed{20346.15} \, \text{rad} . \]