During Lunar Eclipses, the Earth shows a shadow across the moon. The shadow shows a curvature. Also, the only shape that consistently has a circular shadow, regardless of its orientation, is a sphere. 

If the earth were flat and round, similar to a disk, it could cast a circular shadow, but only for lunar eclipses that occur at midnight. For a lunar eclipse at sunrise or sunset, the earth’s shadow would be an ellipse, a line, or a rectangle, depending upon how thick the disk was compared to its diameter.

The Foucault pendulum is a valid experiment showing Earth's rotation.