Answer
$a=8.66$ m/s$^2$
Work Step by Step
$\dot{\theta}=5$
$\ddot{\theta}=0$
$r=100(2-\cos \theta)$
$\dot{r}=100\dot{\theta} \sin \theta = 500\sin \theta$
$\ddot{r}=500 \dot{\theta} \cos \theta = 2500 \cos \theta$
At $\theta=120$
$a_r=\ddot{r}-r\dot{\theta}^2=2500\cos \theta - 100(2-\cos\theta)(5)^2=5000(\cos 120 - 1)=-7500 mm/s^2$
$a_s=r\ddot{\theta}+2\dot{r}\dot{\theta}=0+2(500\sin \theta)(5)=5000\sin 120 = 4330.1$ mm/s$^2$
$a=\sqrt{(-7500)^2+(4330.1)^2}=8660.3$ mm/s$^2 = 8.66$ m/s$^2$
