# Angular-motion equations

The four motion equations combine the properties (angular position/length $\theta$, angular speed $\omega$, initial angular speed $\omega_0$, angular acceleration $\alpha$, time $t$) of angular motion in a curved turn.

$$\omega= \omega_0+\alpha t\\ \theta=\theta_0+v_0t+\frac12 \alpha t^2\\ \omega^2= \omega_0^2+2\alpha (\theta-\theta_0)\\ \theta=\theta_0+\frac12 ( \omega + \omega_0)t$$