Weighing In On The Controversy
The material needed to do this is a piece of string and a little rock. Voilà! We've got ourselves a very precise instrument that can measure something pretty important: gravity. Now, the gravitational pull from a sphere is pretty easy to work out with our instrument. The rock always points directly down.
If we were on a flat Earth, the little rock would be pointing at the center of our disk-shaped planet, and the further we moved away from it (located at the North Pole) the wider the angle between the vertical and the string will be. The latest approach flat Earthers have used to disprove this method is claiming that there is no such thing as gravity. Because they really, really don't know how to deal with facts.
In Full Swing
If you make your little gravity detector a smidgen more sophisticated you can create a pendulum. And by using such an instrument you can demonstrate that the Earth is not only a sphere, but it's rotating too. This method was first performed by French physicists Léon Foucault in 1851. As a pendulum swings, the plane of its oscillations rotate and the time it takes to do a full circle depends on its latitude. This is aptly called Foucault’s pendulum. How could this happen if we were on a static disk? Well, it wouldn't.
The Insane Clown Posse Method
The Detroit musicians became meme-worthy in 2010 for asking “F#cking magnets, how do they work?” and magnets, or the magnetic field of the Earth, is by far my number one way to deal with flat-Earthers.
So our planet has a magnetic field generated by the motion of liquid iron alloy at the center of our planet. We can observe the field generated as it surrounds us and extends all the way into space, and you can follow the field lines (like you might have seen in school experiments with magnets) using a compass. Now the compass gives you a very specific direction, North-South, ending in two distinct points, which we call the magnetic poles. There is no way to create such a magnetic field on a flat disk.
They might claim that Earth is a ring magnet but that doesn't work. A ring magnet has a very specific magnetic field, where the direction of the magnetic field flips when you're inside the ring compared to when you are on the disk. Have you ever seen your compass suddenly point south while working north? And how would the magnetic field of such a ring be produced?
So, there you are. Feel free to use any or all of these if you want to challenge flat Earthers but definitely keep the last one in mind if you want to see them doing some mental acrobatics worthy of the Cirque du Soleil.