Earlier quoted context omitted.
The issue of the line falling back to earth is solved by putting the base of the elevator on water. If the top part of the elevator was cut of you could even detonate charges along the line to make sure all pieces fall into water.
Are we to assume they would be falling straight down? Because I'm pretty sure that's wrong. I'm not a physicist, though, and am happy to be corrected because every time the Space Elevator comes up, I want to know what happens when catastrophic failure occurs and how we'd mitigate that.
> Above GEO, the centrifugal force is stronger than gravity, causing objects attached to the cable there to pull upward on it. [...] On the cable below geostationary orbit, downward gravity would be greater than the upward centrifugal force, so the apparent gravity would pull objects attached to the cable downward.
So, without defensive countermeasures, the Space Elevator would indeed whip around the Earth.
But honestly, if I were designing such a thing, it would have break points, and maybe even a whinch at the base, to pull the line in. I'd also build it over water, and not over a population centre.
But I'm only a software engineer– it's likely a lot more challenging than this.