Serway & Jewett — Angular Momentum: Problem 40

Two astronauts (Fig. P11.39), 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 two-astronaut 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 potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope?