Two identical twins hold on to a rope, one at each end, on a smooth, frictionless ice surface. They skate in a circle about the center of the rope (the center of mass of the two-body system) and perpendicular to the ice. The mass of each twin is
79.0 kg. The rope of negligible mass is 4.5 m long and they move at a speed of 5.40 m/s.
center of mass
(a) What is the magnitude, in kg \cdot m^2/s, of the angular momentum of the system comprised of the two twins?
kg \cdot m^2/s
(b) They now pull on the rope and move closer to each other so that the rope between them is now half as long. Determine the speed, in m/s, with which they move now.
m/s
(c) The two twins have to do work in order to move closer to each other. How much work, in joules, did they do?