Question: A cylindrical centrifuge of radius 1 m and height 2 m is filled with water to a depth of 1 meter (see Figure 8.117(I)). As the centrifuge accelerates, the water level rises along the wall and drops in the center; the cross-section will be a parabola. (See Figure 8.117(II).)
(a) Find the equation of the parabola in Figure 8.117(II) in terms of h, the depth of the water at its lowest point.
(b) As the centrifuge rotates faster and faster, either water will be spilled out the top, as in Figure 8.117(III), or the bottom of the centrifuge will be exposed, as in Figure 8.117(IV). Which happens first?
