Foucault pendulum sharing the rotation of the earth about its own axis, the suspension point of the pendulum traces out a circular path during one sidereal day. At the latitude of Paris, 48 degrees 51 minutes north, a full precession cycle takes just under 32 hours, so after one sidereal day, when the Earth is back in the same orientation as one sidereal day before, the oscillation plane has turned by just over 270 degrees. If the plane of swing was north-south at the outset, it is east-west one sidereal day later. This also implies that there has been exchange of momentum;
Foucault pendulum to describe the rotation angle of the swing plane of Foucault's pendulum. From the perspective of an Earth-bound coordinate system with its "x"-axis pointing east and its "y"-axis pointing north, the precession of the pendulum is described by the Coriolis force. Consider a planar pendulum with natural frequency "ω" in the small angle approximation. There are two forces acting on the pendulum bob: the restoring force provided by gravity and the wire, and the Coriolis force. The Coriolis force at latitude "φ" is horizontal in the small angle approximation and is given by where Ω is the rotational frequency of