Two astronauts of equal mass 76 kg are holding on to opposite ends of a straight rope in space. The length of the rope between them is 18meters. They are rotating about an axis that passes through the center of mass midway between the two astronauts with angular velocity1 radian/sec. One of the astronauts pulls on the rope, decreasing the distance separating them to 18/2 meters. (In the following, take the rope to be massless.)
a) What is the new angular velocity of the two astronauts?
b) How much work did the astronaut who pulled on the rope do?