# Paraboloid

From AMS Glossary

(Redirected from Equilibrium 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, This surface is the laboratory equivalent of the spheroidal equipotential surfaces of the earth's apparent gravity field.

*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