[robertpaulsen]

"The speed increases linearly with the radius distance from the point of rotation."

I agree. Obviously, it must.

My question is, what causes the speed to increase? Yes, as the elevator rises, angular speed increases, but the elevator is "rubbing" against one side of the cable on the way up.

Let me put it this way. Think of a space launch. We don't fire the rockets straight up. They'd just fall right back down.

At a certain altitude, the rocket pitches to pick up that angular speed.

[-YYZ-]

As I understand it, things climbing the elevator would basically be borrowing momentum from the earth's angular momentum, provided through the tension in the "cable". The physics of this idea are well understood, it just the implementation details that are a bit fuzzy yet.