Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_58

3/58 The hollow tube assembly rotates about a vertical axis with angular velocity \(\omega = \dot{\theta} = 4 \text{ rad/s}\) and \(\dot{\omega} = \ddot{\theta} = -2 \text{ rad/s}^2\). A small 0.2-kg slider \(P\) moves inside the horizontal tube portion under the control of the string which passes out the bottom of the assembly. If \(r = 0.8 \text{ m}\), \(\dot{r} = -2 \text{ m/s}\), and \(\ddot{r} = 4 \text{ m/s}^2\), determine the tension \(T\) in the string and the horizontal force \(F_{\theta}\) exerted on the slider by the tube.