We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry’s phase or geometric phases.

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During a period of the pendulum, the angular momentum changes its magnitude continuously and flips to its opposite direction twice. The plane perpendicular to it is well defined, except at the singular times when the angular momentum is zero. In an experimental setting it is more natural to use the direction of the swing of the pendulum as the orientation rather than the perpendicular direction as we do. For the theoretical treatment in this article our choice is more convenient.

3.

If the pendulum has high energy and rotates around its suspension point without coming to a rest and turning around, we would have to take gyroscopic forces into consideration. In the case where the pendulum oscillates back and forth these forces average out.

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As Foucault noted (Ref. 1) a nonrotating frame comoving with the Earth is not an inertial frame either, because the Earth is rotating around the Sun, and the Sun is rotating around the center of the Milky Way. On the time scale of one day, we may neglect these effects and treat the motion of the center of the Earth as straight line motion.

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