Will this rotate like a Foucult's pendulum ? Why not ?

[bksree]

Hi
A Foucault's pendulum consist's of a heavy weight at the end of a long string with the string so suspended that it allows movement in any plane (eg. a string supported from a bearing fixed to the ceiling). The plane of the pendulum then rotates opposite to that of the Earth thus at the rate Ω * cosθ where θ is the co-latitude of the place.

Suppose a vertical rod is supported on frictionless thrust and radial bearings and placed on the ground.
Will this rod rotate in a similar manner ? If not, Why ?

TIA

 

[mfb]

If I understand your setup correctly, it will just continue to rotate at any initial rotation you give to the object (including 0 as option).
This is like Foucault's pendulum if you let it rotate in a circle - there is no (reasonable*) way to see the effect of a rotation.

*the angular frequency should depend on the direction of rotation, but the difference between those values is very small. Certainly not as nice as the original experiment.

 

[bksree]

I didn't quite understand what you said. My question is : The plane of the Foucault's pendulum will make a circular rotation in 24 h if it is carefully released and allowed to move without any twist of the cable (if it is directly above the N pole).
In a similar way, will the vertical pole arrangement also rotate if it is released without any angular velocity ?

TIA

 

[mfb]

Does your rod move like a pendulum? In that case, I don't understand the part "and placed on the ground". Can you draw a sketch?

If the rod moves like a pendulum, and if it is free to rotate around its pivot, it will show the same rotation of its pendulum axis.

 

[bksree]

Thank you for the reply. Please see the sketch in the attached file for the arrangement of the vertical rod.

TIA

 

[256bits]

I think it is like mfb said in his first post.

The rod will rotate at the same rate that you originally gave it.
At a pole, if you give the rod no rotation wrt the earth, the rod still has the same angular velocity as the earth, so you notice nothing measurable.

At other latitudes you might be able to observe some attempt at precession since the axis of rotation is changing direction as the Earth rotates.

 

[mfb]

That is not what I expected, but the result is the same: The rod will just continue to rotate with its (arbitrary) initial angular velocity.

 

[bksree]

The rod has no initial velocity. My question is : Will it rotate opposite to the Earth (like the plane of Foucault's pendulum) because it is supported on frictionless surfaces (bearings) ?

TIA

 

[mfb]

The rod has no initial angular velocity relative to what?
To an observer, rotating together with earth? It will stay like that, and rotate together with Earth as seen from space.
To an observer in space? It will stay like that, and rotate once per day as seen from earth.

 

[bksree]

The rod has no initial angular velocity relative to what?
To an observer, rotating together with earth? It will stay like that, and rotate together with Earth as seen from space.
To an observer in space? It will stay like that, and rotate once per day as seen from earth.

Thanks for the reply.
The rod has no initial angular velocity w.r.t earth.
If the rod is located vertically in the N pole, why should not the rod rotate opposite to the Earth once per day as the Earth rotates underneath it ? The rod is supported on frictionless surface.

Isn't this arrangement similar to a Foucault's pendulum (upside down). The foucault's pendulum is hung from frictionless bearings allowing its plane to rotate, so shouldn't the same effect happen here also.

 

[mfb]

Angular momentum conservation. The rod will just keep its rotation.

Isn't this arrangement similar to a Foucault's pendulum (upside down).

It is not. You have no pendulum, and you do not look at the orientation of a pendulum axis (you cannot, as you do not have that).