Paraboloid

paraboloid

(Or equilibrium paraboloid.) The geometrical figure obtained by rotating a parabola about its axis.

In experimental meteorology and oceanography such a figure is sometimes used as the lower boundary of a model atmosphere or ocean, and is especially important because, at a proper rotation rate, it is an equipotential surface for apparent gravity in the model. If ω is the rotation rate of the apparatus, g the acceleration of local earth's gravity, z the coordinate parallel to the vertical rotation axis, and r the radial coordinate, an equilibrium paraboloid is given by

This surface is the laboratory equivalent of the spheroidal equipotential surfaces of the earth's apparent gravity field.

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(Also called effective gravity, virtual gravity.) For a rotating planet such as Earth the resultant of the force (per unit mass) due to gravity and the centrifugal force.