

In his pottery class, Roy noticed that when
cylindrical container with clay is rotated, the clay forms a parabolic
shape. After some experimenting, he notices that the surface of the clay
is a paraboloid of revolution generated
by rotating the parabola y = h + ω^{2} x^{2}/(2g)
about the yaxis, where ω is the angular velocity
and g is the gravitational acceleration. He now wonders how he can determine
the angular velocity so that the clay will conform to a given height and width.
He
would
like to use this for a mold.
What is known:
Mold size required is 30 cm high and 40 cm wide as shown
in the diagram at the left.
