Feasibility of Space Elevator?

[SomethingClever]

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Correct me if I'm wrong, rocket scientist, but wouldn't it go flying off into space if the connection is severed?

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Not that I'm said rocket scientist, but he means the part that's tethered to the ground.

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Well, I guess it depends where the connection is severed. But the most likely place for it to be severed would be closer to earth than to the top part, for obvious reasons.

Wouldn't the majority fly off into space, leaving just the small part below the sever to fall to earth?