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 a of the end of the antenna at the instant when \(L=1.2 \mathrm{~m}\) and \(\beta=45^{\circ}\) if the rates \(\dot{\theta}=2 \mathrm{rad} / \mathrm{s}, \dot{\beta}=\frac{3}{2} \mathrm{rad} / \mathrm{s}\), and \(\dot{L}=0.9 \mathrm{~m} / \mathrm{s}\) are constant during the motion.

Transcribed Image Text:

z X L R 0