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 vector diagrams deduce that the time to observe a full rotation of the Earth increased by the inverse of the sine of the latitude. formula_7 = formula_8 = formula_9 The Pendulum Sine Law also defines that the ratio of the observed Earth's rotation time at two separate latitudes in relation to a pendulum swing is equal to the inverse ratio of the sine of the two latitudes. formula_10 = formula_11 = formula_12 The sine of the latitude also indicates the degree of alignment of the pendulum central axis to the Earth's axis of rotation. At the poles the pendulum axis is parallel