The particle P is released at time t = 0 from the position r = r0 inside the smooth tube with no velocity relative to the tube, which is driven at the constant angular velocity ω0 about a vertical axis. Determine the radial velocity vr, the radial position r, and the transverse velocity vθ as functions of time t. Explain why the radial velocity increases with time in the absence of radial forces. Plot the absolute path of the particle during the time it is inside the tube for r0 = 0.19 m, l = 1.4 m, and ω0 = 1.29 rad/s. Then answer the questions using the given numbers.