Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_143

2/143 In a design test of the actuating mechanism for a telescoping antenna on a spacecraft, the supporting shaft rotates about the fixed \(z\)-axis with an angular rate \(\dot{\theta}\). Determine the \(R\)-, \(\theta\)-, and \(\phi\)-components of the acceleration \(\mathbf{a}\) of the end of the antenna at the instant when \(L = 1.2\text{ m}\) and \(\beta = 45^\circ\) if the rates \(\dot{\theta} = 2\text{ rad/s}\), \(\dot{\beta} = \frac{3}{2}\text{ rad/s}\), and \(\dot{L} = 0.9\text{ m/s}\) are constant during the motion.