There is no contradiction. The Focault pendulum, and other similar experiments, do indeed measure the rotation of the Earth regardless of any other motions. In other words, the results are linked to the length of the
sidereal day.
Here's a passage from the
previous link (emphasis mine)
Quote:
So it was possible, way back in 1850, to set up an experiment inside a room which had no view of the outside world, and prove that the Earth rotated! (6)
The next year, Foucault repeated his Pendulum experiment with a massive, spinning weight. He showed that this weight, just like his Pendulum, ignored local effects and lined itself up with the distant stars. He had invented the gyroscope!
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Navigators, Newton's work on the EoT and so forth on the other hand use the sun for reference, so the observations are linked to the length of the
solar day.
This rotation period is influenced by the combined effects of rotation and orbital motions around the sun, and is indeed is 24 hours; the Earth moves a bit in its orbit while rotating a full 360 degrees, so the sun hasn't quite come back to the original position in that time; the Earth has to rotate about 1 degree more, so it takes approximately 4 minutes longer than the sidereal day. (For a quick estimate, divide 24 hours by 365.25).
While your articles state 24 hours for Focault's pendulum, they're being a tad sloppy. Further, the experiment is better as a demonstration than a measurement; you're lucky if you can end up within 15% of the actual value.