Function of a Foucault pendulum

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To understand how the pendulum works the simplest way is to see an animation. First, suppose that the pendulum is suspended direct over the North Pole. Look at the animation to the left below, showing this case.

     

The pendulum here is supposed to hang direct over the North Pole. It swings all the time in the same direction relative to distant masses of the universe. Of course, an observer standing on Earth quite close to the pendulum follows Earth in its rotation. But  he apprehends that the plane of oscillation of the pendulum alters direction all the time counter clockwise. But it is not the direction of the plane of the oscillation that alters - instead it is Earth rotating underneath the bob. Relative to Earth the plane of oscillation of the pendulum at the North Pole undergoes a full clockwise rotation during a day.

 

Here the animation instead shows a pendulum suspended just over the equator. The whole pendulum with its suspension follows Earth in its rotation. Therefore there is no rotation underneath the pendulum, just a translation. An observer standing on Earth of course sees that the pendulum swings all the time in the same direction relative to Earth.

 

The animation is made by John Willsund

 

The animation is made by John Willsund

     

At the North and South Poles the plane of oscillation of the pendulum alters (seemingly) 360º in 24 hours, at the equator the plane of oscillation of the pendulum is not altering at all relative to Earth. In Motala, on a latitude 58º 33´ North between these to extremes, the time for a complete rotation 360º is about 28  hours.

So, the plane of oscillation of the pendulum rotates 307º in 24 hours in Motala (at an angular velocity 12,8º per hour). The velocity of the rotation is given by 15ºsin λ, where λ is the latitude.

 

The period of a complete rotation 360º for some places:

Place

Appr. latitude (λ)

Period t = 24/sin λ

  Clockwise rotation

Period (Roughly)

North Pole

90° N

24 (23h 56 min) hours

Stockholm, Sweden

59° N

28 hours

Motala, Sweden

59° N

28 hours

Berlin, Germany

52° N

30 hours

London, Great Britain

51° N

31 hours

Manila, the Phillipines

14° N

99 hours

Jakarta, Indonesia

6° N

230 hours

  Counter clockwise rotation  

Rio de Janeiro

23° S

61 hours

Cape Town

34° S

43 hours

South Pole

90° S

24 (23h 56 min) hours

 

For the eager to learn - how the bob keeps swinging, without stopping

The pendulum must all the time get some energy in order not to stop its motion due to air resistance, friction, etc

Therefore, in the middle of the wooden disc under the bob, there is a coil with a soft iron core. When the bob has passed a change in turning and is swinging back against the centre a pulse of current is sent to the coil that will be magnetized for a short moment. The bob then is attracted to the coil for a moment. In this way the swinging gets a little kick every time the bob passes after a turning-point.

Accordingly, there is a need for adding some energy to compensate for energy losses to keep the pendulum swinging. How much? Without adding energy the amplitude of the swing is declining with 5,5 cm pro 200 swings for our pendulum. This means a difference in level about 3,3 cm and that an  energy contribution  ΔEp=mgΔh ≈ 0,4 J, that is about 2 mJ/swing is needed to keep the motion going on with unchanged amplitude.