Proving Earth is rotating by a water bucket at North Pole If we put a bucket of water on the North Pole and if the water goes to the sides won't that prove that the earth is rotating?
 A: The angular velocity due to the earth's axial rotation at the surface of the earth, is very very small. It is about 15 degrees per hour/0.004 degrees per second, or roughly $0.0000729 \ rad \ s^{-1}$. Such a rotational speed is so small that there probably would be no measurable motion (due to centrifugal forces) of the water to the inner side of the bucket - unless you have a huge bucket able to carry a huge volume of water.
But something analogous to your thought experiment, that can be detected, which does demonstrate the earth's rotation is the fact that at the equator, there is a bulge.
Equatorial bulge as taken from this Wikipedia article:
The Earth has a rather slight equatorial bulge: it is about 43 km (27 mi) wider at the equator than pole-to-pole, a difference which is close to 1/300 of the diameter. If the Earth were scaled down to a globe with diameter of 1 meter at the equator, that difference would be only 3 millimeters. While too small to notice visually, that difference is still more than twice the largest deviations of the actual surface from the ellipsoid, including the tallest mountains and deepest oceanic trenches.
The rotation of the earth also affects the sea level, the imaginary surface that is used to measure altitudes from. This surface coincides with the mean water surface level in oceans, and is extrapolated over land by taking into account the local gravitational potential and the centrifugal force.
The difference of the radii is thus about 21 km. An observer standing at sea level on either pole, therefore, is 21 km closer to Earth's center than if standing at sea level on the Equator. As a result, the highest point on Earth, measured from the center and outwards, is the peak of Mount Chimborazo in Ecuador rather than Mount Everest. But since the ocean also bulges, like Earth and its atmosphere, Chimborazo is not as high above sea level as Everest is.
