the free surface of a rotating fluid is
Free surface If a liquid is contained in a cylindrical vessel and is rotating around a vertical axis coinciding with the axis of the cylinder, the free surface will assume a parabolic surface of revolution known as a paraboloid. The free surface at each point is at a right angle to the force acting at it, which is the resultant of the force of gravity and the centrifugal force from the motion of each point in a circle.[4] Since the main mirror in a telescope must be parabolic, this principle is used to create liquid mirror telescopes.