Figure: The Foucault pendulum and the rotating frame of the Earth explicated

Image 1 Caption: A Foucault pendulum at Monash University in Australia. You see a the pendulum bob and its arm, a compass plate (i.e., a compass without a needle) across which the penulum bob oscillates, and a background image of the Earth centered on Australia.

But if the Foucault pendulum had been at the North Pole and you looked down on the pendulum and Earth from north celestial pole (NCP), the pendulum would oscillate in a fixed plane relative to the observable universe and the Earth would rotate counterclockwise relative to the observable universe. In an absolute physical sense the Earth is rotating.

However, if you are taking the Earth as a rest frame, the plane of pendulum oscillation rotates clockwise or, in other words, pendulum is in precession). The precession period at the North Pole is a sidereal day = 86164.0905 s = 1 day - 4 m + 4.0905s (on average).

Further explication:

1. Inertial frames are NOT in rotation relative to the observable universe---except for rotating frames converted to inertial frames to rotating frame using inertial forces (see Mechanics file: frame_rotating.html).

   But note that very strong gravitational fields (like those very near black holes) may cause inertial frames to be intrinsically in rotation relative to the observable universe, but this is a tricky point for which yours truly CANNOT find a clear explication. The best so far (and it does NOT say much) is Wikipedia: Inertial frame of reference: General relativity.

2. A Foucault pendulum illustrates the effect of the rotating frame inertial force the Coriolis force when viewed from the rotating frame of the Earth

   The effect is the precession of the plane of the Foucault pendulum's oscillation relative to the the frame of the Earth.

   The precession is caused by the torque of the Coriolis force.

   Torque is the twisting manifestation of a force.

3. Now why does the Coriolis force have this effect for the Foucault pendulum when we do NOT usually see this effect for most pendulums?

   The pivot the Foucault pendulum is frictionless, and so the pivot CANNOT exert any torque on the Foucault pendulum. Even a relatively small torque by friction would overcome that of the Coriolis force which is rather weak in this case. Of course, any rigid-direction pivot would completely stop the precession.

   Another reason for NOT seeing precession is that even for a Foucault pendulum, the precession period is rather long. The formula for precession period is

     P = ( 1 sidereal day )/sin(L) where L is latitude.
   
       = 1 sidereal day at L = 90°  .
   
       = [sqrt(3)/2] sdays = (0.8660 ...)  sidereal days at L = 60°  .
   
       = sqrt(2) sdays = (1.4142 ...) sidereal days at L = 45°  .
   
       = 2 sidereal days at L = 30°  .
   
       = ∞ sidereal days at L = 0°  .  

   (Wikipedia: Foucault pendulum: Examples of precession periods). Note, a Foucault pendulum needs some kind of driver to keep it oscillating, but a driver that exerts NO torque.

   In the Northern Hemisphere (Southern Hemisphere), the precession is clockwise (counterclockwise) relative to the rotating frame of the Earth when looking down on the Earth from north celestial pole (NCP) (south celestial pole (SCP)) (Wikipedia: Foucault pendulum: Mechanism).

   The simplest locations for a Foucault pendulum are at the poles. There a Foucault pendulum oscillates in a plane fixed relative to the observable universe.

   The second simplest location is the equator where the plane of oscillation does NOT precess at all relative to the Earth. The above period formula shows why this is so mathematically: when L = 0, sin(L) = 0, and the period goes to infinity.

4. The Foucault pendulum is, in fact, a way to demonstrate that Earth surface locations are NOT exactly inertial frames on the small size scale.

   Large size scale non-inertial frame effects are evidenced by weather (particularly anticyclones and cyclones: see Mechanics file: coriolis_force.html) and long-range artillery ballistics.

   

5. Image 2 Caption: The image shows a Foucault pendulum located in the dome of the Pantheon in Paris.

6. Leon Foucault (1819--1868) used a Foucault pendulum (which he did invent) to demonstrate the Earth's rotation relative to the fixed stars (or as we would say now the observable universe) in 1851 (see Wikipedia: Leon Foucault (1819--1868); Wikipedia: Foucault pendulum: History; Wikipedia: Pantheon: Under Louis Philippe I, the Second Republic and Napoleon III (1830-1871)). The original Foucault pendulum was a huge one located in the Pantheon.

   It had length 67 meters and was released at a distance of 50.25 meters (3/4 times its length).

Images:

1. Credit/Permission: © User:Decogenasim, 2014 / CC BY-SA 4.0.
   Image link: Wikimedia Commons: File:Foucault Pendulum in Monash University.jpg.
   
2. Credit/Permission: User:R%C3%A9mih, 2011 / CC BY-SA 3.0.
   Image link: Wikimedia Commons: File:Foucault-rotz.gif.