From the Earth's rotation. Use of a space elevator will slow the Earth's rotation. Nothing new here; every prograde space launch slows the Earth's rotation a tiny bit.where is it getting all the tangential energy needed to achieve an orbital velocity?
No. It draws the energy needed to reach orbital velocity by slowing the Earth's rotation rate.climbing is vertical--it will have to draw the energy needed to reach the orbital velocity by pulling the 'weighted end' of the 'elevator' to a lower orbit.