Coriolis and Foucault Pendulum

[jose]

I guess this question is very easy, but after it occurred to me, it has been torturing me for quite a while.

I don't understand how the Coriolis effect and Foucault pendulum work. I thought everything inside the Earth was moving along with it (inertia).

If we are in a moving train, and throw a ball to the floor, the floor is moving along with the train. Why the same doesn't apply to the Foucault pendulum and to big masses of water?

Thanks,
Jose

 

[Shooting Star]

For the sake of simplicity, consider a Foucault pendulum fixed at one of the geographical poles of the earth. Neglect friction where the string is tied.

We can consider the pendulum to be swinging in a fixed plane with respect to any inertial frame of reference (the absolute space of a Newton) with respect to which the Earth rotates. There is no reason for the pendulum to do otherwise. From the earth, then, it will look like as if the plane of swing is rotating.

If you take a frame of reference fixed to the earth, then we have to consider non-inertial forces arising out of the rotation of the earth, one of which is the Coriolis force which acts on a body moving with respect to the earth, and it makes the pendulum move exactly so.

We observe balls moving in trains for short distances and times only, and so it seems to us that the ball is not being subject to these non-inertial forces. On a long run, the deviations will become more evident.

For big rivers, one side of the bank gets more eroded than the other because of the Coriolis force, since the water is a moving in a rotating frame of reference and tends to go sidewise. For big masses of water like the oceans, there are more forces to be taken into consideration than what has been briefly outlined above.

I hope this helps a bit.

 

[jose]

Thank you shooting star. I wasn't aware that there were non-inertial forces, and that idea troubles me a little bit.

Say I am in a train which travels really fast. If I attach a pendulum to the train (I don't start to swing it) ... I will expect the string to fall at 90degrees with regards to the roof (since it's not accelerating). Where are the non-inertial forces? I thought that the non-existence of non-inertial forces is what allows us to walk on an airplane, and on Earth, which is rotating ~1000mph.

If you have a pointer of literature for this, I would appreciate it.

 

[Shooting Star]

Non-inertial forces are present in any accelerating system of reference, the rotating frame being a subgroup. The effects are not due to the velocity but due to the vector acceleration. The train, if it is moving uniformly in a straight line, is almost equivalent to an initial frame of reference, and the deviations would be too slight to measure ordinarily. This is why you can walk around in the trains and the planes. If for example, you ride the train a full circle around the equator, you will certainly notice the cumulative effects of the deviations from the behavior in an initial frame of reference. When a plane or train banks, the centrifugal effects are immediately only too apparent. The non-inertial effects at the surface of the earth, in our daily lives, are overwhelmed by the far stronger effects due to gravity. A falling body is deflected sideways, which we do not generally notice over the distances we watch bodies fall.

However, on a large scale, wind and ocean currents, giving rise to the cyclonic storms as well as “the global conveyor” is directly related to the rotation of the earth. These are very noticeable things. The big cyclones spin in opposite directions in opposite hemispheres.

As a thought experiment, imagine yourself fixed to the frame of a disk rotating with respect to an IFR, and a particle is static somewhere in the plane. There is nothing to explain here. Now make your frame of reference the one which is rigidly attached to the disk. Now the particle is in a circular orbit about the centre of the disk. The combination of all the non-inertial forces is what is making the particle move about in a circular trajectory in the disk frame.

http://en.wikipedia.org/wiki/Fictitious_force
http://www.physics.orst.edu/~mcintyre/coriolis/
http://cseligman.com/text/physics/fictitious.htm

 

[tiny-tim]

Hi Jose!

If we are in a moving train, and throw a ball to the floor, the floor is moving along with the train.

… and so we are an inertial observer … the physics is the same, and the ball behaves exactly as if the train were stationary.
​

Yes … but it doesn't if the train is going in a circle, does it (there'll be a centrifugal force and a Coriolis force )?

And a train going along (or stationary on!) a straight track East-West is really going round in a very large circle of latitude!

 

[jose]

oh wow.. that's very interesting...

So I know airplanes coming from Asia to the US take longer than planes going from the US to Asia. Is this because winds, Coriolis, or both? :P

Thanks a lot guys.

 

[tiny-tim]

just wind …

oh wow.. that's very interesting...

So I know airplanes coming from Asia to the US take longer than planes going from the US to Asia. Is this because winds, Coriolis, or both? :P

Thanks a lot guys.

Hi jose!

It's just wind!

(and probably air traffic control as well! )