Would the Foucault pendulum experiment work on a rotating flat Earth? If the Earth were to be flat, but still rotating with a constant angular frequency, would the Foucault pendulum still show it's precessing motion?
The angular velocity of the precession can be derived to be:
$$
\omega = -(\Omega \cos\beta)\mathbf{k}
$$
where $\Omega$ is the angular frequency of the earth, $\mathbf{k}$ is the apparent vertical and $\beta$ is the angle between the apparent vertical and the rotation axis.
On a rotating disk, with the same rotational frequency as the Earth, one would expect that the formula for $\omega$ would still be valid, albeit with a different apparent vertical $\mathbf{k}$.
EDIT: Gravity on the disk is assumed to be uniformly perpendicular to the disk, such as most flat-Earth theories suggest.
N.B. I do not believe the Earth to be flat, this question is purely out of interest.
 A: Yes, it would work, but $\omega$ would be the same at all points on the disc, and equal to the rate of rotation of the disc itself.  So although the pendulum would precess, you could very easily know if you were on a flat disc by moving it around and comparing precession rates,
A: A rotating flat Earth can't actually exist. The bigger a planet is, the smaller the gravitational constant would have to be for it to have Earth's gravitational field strength and the slower it would have to be rotating for its centrifugal force to be balanced by gravity and be rotating barely slowly enough to form into a stable oblate shape. A flat Earth would be infinitely big and so would necessarily have a zero rotation rate.
Let's suppose it has a nonzero rotation rate and there's also some magic force it exactly balances the centrifugal force in its frame of reference so that the only fictitious force in its frame of reference that's not balanced by and equal and opposite force is the Coriolis force. According to this answer, precession can be caused by something other than the Coriolis force. Under certain conditions, if the Earth were rotating slowly enough, we still wouldn't be able to tell from watching the pendulum that Earth is rotating.
