Why Newton's bucket cannot account for Earth's rotation

This note illustrates, at an undergraduate level, how an a priori legitimate assumption of uniform gravity can lead to intuitively satisfying but false results. Considering the simple situation of a liquid contained in a bowl at rest with respect to the ground at the North Pole, we look for the shape of its surface, taking Earth's rotation into account. The classical problem of a rotating fluid is converted to that of the determination of Earth's shape. (paper)