Force acting on bob of Foucault's pendulum

[bksree]

Hi
Assume that the Foucault's pendulum is located in N pole and is oscillating from W to E (x direction). The Z axis is vertically up. The force acting on the bob as it moves from equilibrium position towards E is in the -y direction causing the plane of the pendulum to rotate in CW direction (as viewed from above). When the bob retraces its movement (from E to equilibrium position) the force is in the + y direction, i.e. opposite to the previous case.
Then how does the plane of the pendulum rotate in a consistent manner (i.e. clockwise)

TIA

 

[dreamLord]

The plane of the pendulum rotates in a consistent manner because the Earth rotates in a consistent manner. Relative to an imaginary line on the ground marking the initial shadow of the pendulum bob,the new shadow of the bob(or in other words, the plane of the pendulum) will turn clockwise with time.

 

[bksree]

The plane of the pendulum rotates in a consistent manner because the Earth rotates in a consistent manner. Relative to an imaginary line on the ground marking the initial shadow of the pendulum bob,the new shadow of the bob(or in other words, the plane of the pendulum) will turn clockwise with time.

I agree that this is what is observed. The question is why ? if the coriolis force, which causes the plane to rotate, changes direction as mentioned above.

 

[Bobbywhy]

Just a comment about your choice of using directions E(ast) and W(est) to set up your experiment: If you stand at the North pole, can you point towards any direction other than South?

Wikipedia is usually a good place to begin when looking to answer the type of question you're asking. Best not to put 100% confidence in Wiki pages, but usually there is enough correct information to get a searcher started. For the Foucault pendulum there is a very good explanation of the mechanics, including pendulum behaviors at the poles, plus some good animations. Additionally there are further references if the researcher is not satisfied.

http://en.wikipedia.org/wiki/Foucault_pendulum

 

[sophiecentaur]

I agree that this is what is observed. The question is why ? if the coriolis force, which causes the plane to rotate, changes direction as mentioned above.

My view is as follows: The coriolis force is not a real force and it depends on the frame of reference. It will just cause the path of the bob over the ground not to be a straight line. Because this is an 'ideal situation' (with uniform gravitational field over the site of the pendulum) there will be no interaction with the ground so the bob will not experience any sideways acceleration - being just attracted to the centre of the Earth at all times. What the Earth is doing , beneath the pendulum is not relevant - except that someone on the (rotating) Earth will, of course, see the bob moving in an unexpected way.

 

[A.T.]

I agree that this is what is observed. The question is why ? if the coriolis force, which causes the plane to rotate, changes direction as mentioned above.

Check out this video at 1:30:

https://www.youtube.com/watch?v=49JwbrXcPjc

For a real world Foucault's pendulum those loops you see at the end are even thinner, so it looks like a oscillation plane. But in fact there is no oscillation plane in the rotating reference frame of the Earth. The pendulum makes thin, long loops and returns to the lowest point from a slightly different direction than it left towards.

The force acting on the bob as it moves from equilibrium position towards E is in the -y direction causing the plane of the pendulum to rotate in CW direction (as viewed from above). When the bob retraces its movement (from E to equilibrium position) the force is in the + y direction, i.e. opposite to the previous case. Then how does the plane of the pendulum rotate in a consistent manner (i.e. clockwise)

Applying a force, and then the opposite force for the same duration doesn’t cancel the displacement, just the change in velocity. The "plane" is advancing at a constant rate, because the accelerations cancel. If they didn't cancel, it would advance faster and faster.