the astronauts as particles, calculate each of the following.

$($a$)$ the magnitude of the angular momentum of the system

$kg*\frac{m^2}{s}$

$($b$)$ the rotational energy of the system

$kJ$

By pulling on the rope, the astronauts shorten the distance between them to $5\mathrm{.}00m.$

$($c$)$ What is the new angular momentum of the system?

$kg*\frac{m^2}{s}$

$($d$)$ What are their new speeds?

$\frac{m}{s}$

$($e$)$ What is the new rotational energy of the system?

$kJ$

$($f$)$ How much work is done by the astronauts in shortening the rope?