Two astronauts (Fig P11.51), each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, orbiting their center of mass at speeds v. treating the astronauts as particles, calculate
(a) The magnitude of the angular momentum of the system and
(b) The rotational energy of the system. By pulling on the rope, one of the astronauts shortens the distance between them to d/2.
(c) What is the new angular momentum of the system?
(d) What are the astronauts’ new speeds?
(e) What is the new rotational energy of the system?
(f) How much work does the astronaut do in shortening the rope?