Chapter 12 - Kinematics of a Particle - Section 12.8 - Curvilinear Motion: Cylindrical Components - Problems - Page 84: 187

$\dot{\theta}=0.0178$ rad/s

$r=2000 \csc \theta$ $\dot{r}=-2000\csc\theta \cot \dot{\theta}$ At $r=3000$ ft, $\theta = 41.8103$ $\dot{r}=-3354.102 \dot{\theta}$ $v=\sqrt{(\dot{r})^2+(r\dot{\theta})^2}$ $80^2=[(-3354.102)^2+(3000)^2](\dot{\theta})^2$ $\dot{\theta}=0.0178$ rad/s