NOTES
So where does the angular momentum go? The angular momentum lost to the Earth as the rock moves outward and when the rock is released remains with the rock and is returned to the Earth after an orbit or two - but the angular momentum that is transferred from the Earth's rotation to the Earth's orbit by tidal forces on the Earth-elevator-rock system doesn't go with the rock, and so isn't returned when the rock impacts again. This transfer of angular momentum is associated with the energy generated during the rock's motion up the elevator, and you can't get the momentum back from orbital motion to rotational motion without adding that energy back.