Picture a large ring floating in space. It is rotating with angular momentum L. However, its radius is so large that it has essentially no tangential velocity or momentum and therefore no kinetic energy. The total energy is mc^2, with m being the invariant mass. It then begins to draw itself in by applying a force over a distance along its circumference. (picture strong stretched springs being allowed to pull in) Being a ring, the net force is inwards towards its center. As it reduces its radius the tangential momentum increases to conserve angular momentum, like a figure skater. It now seems to have kinetic energy, but this is a closed system. The relativistic energy/momentum equation seems to have a problem: E^2 = (mc^2)^2 + (pc)^2 There is only one variable, p. Unless we want to entertain the idea that m can change. What gives?