The mass and mean radius of the moon are \(m=7.35 \times 10^{22} \mathrm{~kg}\) and \(R=1.74 \times 10^{6} \mathrm{~m}\).

(a) From these parameters, along with Newton's constant of gravity \(G=6.674 \times 10^{-11} \mathrm{~m}^{3} \mathrm{~kg}^{-1} \mathrm{~s}^{-2}\), find the moon's escape velocity in \(\mathrm{m} / \mathrm{s}\).

(b) For a slingshot boom of length \(50 \mathrm{~m}\), what must be the minimum rotation frequency \(\omega\) to sling material off the moon, as described in Example 1.3? Take into account both the radial and tangential components of the payioad velocity when it comes off the end of the boom. Assume payloads are initially set upon the boom at radius \(r=3\) meters and with \(\dot{r}=0\).