A fluid in a rotating bucket will take on a parabolic shape (for example of some simple derivations of this result see http://en.wikipedia.org/wiki/Bucket_argument). The assumptions that play into the derivations that I've seen do not take into consideration a Coriolis effect. Suppose one did not know that the earth was spinning. Is it possible to measure the angular frequency of the earth using a bucket of fluid by considering how the Coriolis effect modified the curvature of the paraboloid in question?
Perhaps it's possible to optically measure the curvature of the paraboloid setup by the spinning process and from that determine the angular frequency of the planets rotation. I am concerned though that the effect of the rotation of the earth is so minuscule on the parabolic shape that it would be impossible to physically measure it.