May the Forces Be With You

Gravity and the Centrifugal Force

Notes

Now consider a wire in the shape of a parabola - now it's possible to find a spin rate that exactly balances the centrifugal force along the wire - wherever the bead is placed, it will tend to remain. The so the parabolic wire becomes an equipotential line - a line along which every point is at the same potential.

Note, however, that although there's no force along the wire, the force perpendicular to the wire is non-zero, and non-constant. A spring attached perpendicularly to the bead would stretch due to this variable force, depending on the bead's position.

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