Foucault Pendulum Precession

Worked Example

Consider a Foucault pendulum situated at a latitude of 45° North. The Earth rotates at an angular velocity of 360° per sidereal day (approximately 23 hours, 56 minutes, and 4 seconds). The rate of precession of the pendulum's plane of oscillation is given by:

ω_p = -360° × sin(45°)

Calculating this value, we find that the precession rate is approximately -254.56° per sidereal day. Therefore, after 0.25 sidereal days (about 6 hours), the pendulum's plane of oscillation will have rotated.

Latitude: 45°\n Elapsed sidereal days: 0.25\n Precession rate: -254.5584412271571° / day\n Plane angle: -254.5584412271571°/day × 0.25 days = -63.63961030678927°

This rotation is in the clockwise direction when viewed from above in the Northern Hemisphere.

Experiment

Use the interactive tool below to explore how the precession of the Foucault pendulum depends on the latitude. Change the latitude to observe the different precession rates in the Northern and Southern Hemispheres, and see what happens at the Equator and the poles.

1. Set the Latitude to 45 to see the pendulum precession in the Northern Hemisphere.
2. Set the Elapsed sidereal days to 0.25 and observe the unwrapped plane angle of approximately -63.64°.
3. Change the Latitude to -45 (Southern Hemisphere) and notice that the precession reverses direction to +63.64°.
4. Change the Latitude to 0 (Equator) and verify that the status becomes No precession.

Explore this interactive visualization fully at https://riano.app/module/foucault-pendulum-precession.

Limitations

This model provides a simplified, leading-order calculation of the precession of a Foucault pendulum. It uses the assumption of small-amplitude oscillations and a slow Earth rotation approximation. It does not solve the full latitude-dependent pendulum ordinary differential equations, nor does it account for damping forces such as air resistance or imperfections in the pendulum's pivot mechanism, which would cause the pendulum to eventually come to a stop in reality.

References

• The Foucault Pendulum (Richard Fitzpatrick, UT Austin)

The provided reference offers a detailed derivation and explanation of the forces acting on a Foucault pendulum, including the Coriolis force and how it leads to the precession of the plane of oscillation.