WOLFRAM|DEMONSTRATIONS PROJECT

Liquid in a Rotating Cylinder

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angular velocity
radius of the cylinder
show invariant level curve
The surface of a liquid in a rotating cylinder of radius
R
with its axis in the direction of gravity takes the form of a paraboloid of revolution. One of the contour levels of this surface stays at the same height for all angular velocities. This contour level is a circle of radius
R
2
.