Mold Shape


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. 