What is a simple, vivid and compact way to demonstrate the rotation of the Earth? Something you could keep on your desk and that a middle-schooler or flat-earther could understand?
I considered aviation gyroscopes, but they have pendulous veins which continuously recalibrate them based on the direction of gravity and require noisy vacuum pumps.
I also considered a Foucult pendulum, but they either need to be very large or have motors to keep them going.
Something you could keep on your desk?
Two things comes to mind:
"A fibre-optic gyroscope(FOG) senses changes in orientation using the Sagnac effect, thus performing the function of a mechanical gyroscope. However its principle of operation is instead based on the interference of light which has passed through a coil of optical fibre, which can be as long as 5 kilometres (3 mi)."
These devices show that the Earth does indeed rotate on its axis. But you may need to explain things like interference and what's happeing inside the gyroscope to kids and middle-schoolers (unfortunately, you might not get anywhere with "flat earthers" since they do not appear to want to learn). Though they are fairly expensive costing anywhere from ten to twenty thousand dollars.
The Earth is very large and rotates very slowly (once per day). This requires extremely sensitive equipment like the gyroscopes mentioned, or measurements that cover a wide area (the coriolis effect on hurricanes or artillery), or drops of very long distances to observe sideways deflections (dropping weights down mine shafts). Nothing that fits in a desk will be simple. Anything simple that fits on a desk won't be effective.
It's like trying to show the Earth is round. Because the Earth is large, you need something to travel hundreds of miles to make the observation:
The simplest way to demonstrate the Earth's rotation would involve the movement of shadows in sunlight. For example, a sundial. A longer distance from the object casting the shadow to your desk will make it easier to see the shadow moving.
Of course, a flat-Earther would probably say that the moving shadow is a result of the movement of the Sun.
Watching the stars over several hours (either by making a note by eye from time to time, or using time-lapse photograph) gives convincing evidence of relative motion between stars and Earth. The fact that the stars return in their same pattern each night convinces us that the relative motion is a rotation.
To resolve the question: which is rotating, the Earth or the set of stars? general relativity offers us two interesting things to say. First, there is no need to insist on an answer which says that one perspective is 'wrong' and the other 'right'. Rather, one can set up physics either way. One can adopt a frame (A) where Earth does not rotate relative to the frame, or a frame (B) one where the stars do not move relative to the frame. Calculations of the type employed in general relativity work either way and agree with observations. However there is a difference: frame (B) can be an inertial frame, but frame (A) is not.
Let's now take the standard perspective for this kind of question, where we want to use an inertial frame. The question asks for evidence to show that Earth is rotating relative to any such local inertial frame. I have always found the Foucault pendulum to be particularly impressive here, but of course the question is right to say this cannot be accommodated on a desktop. The trouble is that anything that could sit on a desktop (e.g. a laser gyro) would have to have some quite sophisticated internal structure so someone looking at it would have to take it on trust that it is functioning how its manufacturer says, or else they would have to learn a lot of physics to understand it for themselves, or they would have to decide which group of people to trust concerning the evidence of the gyro. So with this in mind it is hard to offer really convincing evidence confined to any small device. The only way to become convinced is to widen ones perspective, so that it includes trips to the nearest science museum housing a Foucault pendulum for example.
Watch the Sun set. While this can not distinguish whether it's the Earth rotating or the Sun moving, it is a very profound experience that every child should have witnessed. And it is actually pretty astounding how fast the Sun sets behind whatever mountain or treeline you have in your location.
