okay, I've come up with an idea. If I bought this thing and marked the base and globe with arrows and let it sit on my desk, shouldn't this be as good as a swinging weight? The globe is free from friction as you can get, I believe and not connected to the base in any way, shouldn't the base rotate with the rotating earth and the globe will NOT rotate with it? Let me know what you think and I will buy it if you all agree.
If you do get one of these, the first test would be to try is to give the suspended globe a spin. How long does it continue to spin? Does spinning it the opposite direction make a significant difference? If it eventually stops (it will), why does that happen? If it takes a long time to stop (a good fraction of a day or longer), then, when you conduct your experiment, how do you know it was truly "stopped" when you started, and you aren't just seeing the result of some residual spin imparted when you released the globe?
Instead of using a suspended mass, if you use a pendulum, some of these problems are addressed. The biggest one is that if a pendulum is swinging in a plane, that plane is fixed with respect to (wrt) inertial space, so you have a fixed reference independent of the presumed-spinning earth. On the other hand, the mass in your apparatus probably
is rotating wrt inertial space, but you have no way of knowing how much it's spinning except wrt the Earth itself, so you have no reference to measure the presumed slow rotation of the earth you're testing for against. The plane of a swinging pendulum is constrained to be parallel to the vertical, but if it's allowed freedom to rotate about the vertical, it will remain as close to the original orientation as it can.
That's why there are Foucault pendulum experiments and not "Foucault suspended mass" experiments. The pendulum can provide an inertial frame of reference.