Q. Two astronauts, 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. (Use any variable or symbol stated above as necessary.)

(a) Treating the astronauts as particles, calculate the magnitude of the angular momentum of the two-astronaut system.
Li = Your answer is correct.

(b) Calculate the rotational energy of the system.
K = Your answer is correct.

By pulling on the rope, one of the astronauts shortens the distance between them to d/7.
(c) What is the new angular momentum of the system?
Lf = Your answer is correct.

(d) What are the astronauts' new speeds?
vf = Your answer is incorrect.

(e) What is the new rotational energy of the system?
Kf = Your answer is incorrect.

(f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope?