Does the Coriolis force act on all objects?

Question

Would, for example, a train traveling from south to north experience this force? If so, why? I would think it does not, since it is in contact with the Earth, so it does not experience the difference in speed when going from one point to the other.

Answer 1

It does. The fact that it is in contact with the earth (or rather, the rails), just means that it cannot move sideways under the force, because the rail restrict its movement. In the same way, if a train travels down a rail and has wind blowing from one side, there is still a force pushing it, but the rails will exert an opposite force so it can't be moved sideways by that force. Some sources [1–3] even claim the effect of the coriolis force can actually be observed in north-south travelling rails, where one side of the tracks wears off faster than the other.

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1. Kravets, V.V., Kravets, T.V. Evaluation of the centrifugal, coriolis, and gyroscopic forces on a railroad vehicle moving at high speed. Int Appl Mech 44, 101–109 (2008), p. 103.
2. The centrifugal myth, New Scientist 1435, Dec. 1984, p. 14
3. TU Delft, Global winds

Answer 2

If you recall the Coriolis force given by $$\mathbf{F}=-2m\mathbf{\Omega} \times \mathbf{v}$$ If for a minute, We don't get into the detail of the analysis but just see the magnitude of this. $$|\mathbf{F}|=2m|\mathbf{\Omega}_\text{earth}||\mathbf{v}_\text{train}|$$ Let's take the speed of the train to be $100 $ Km/Hour which is about $30$ m/sec and mass to be $1000$ Kg. Then $$|\mathbf{F}|\approx0.3 \ N$$ That doesn't go to do anything to your train. Though the effect can be made observable under high speed.

Answer 3

The fact that there is a force counteracting the Coriolis force just means that the Coriolis force isn't allowed to cause acceleration. It's like sitting on a chair; the chair counteracts gravity, but that doesn't mean that gravity doesn't act on you, it just means that you don't fall down. Just as gravity presses you to the chair, the Coriolis force presses the train to the side of the rail.

One way of thinking about the Coriolis force is that as an object moves towards the axis of rotation, the moment of inertia of the entire system decreases. To preserve angular momentum, the angular velocity must increase.

In the Northern hemisphere, a train traveling North actually causes the moment of inertia of the Earth to decrease slightly, which causes the angular velocity to increase (this, among other factors, means that the length of a day is not constant; it decreases ever so slightly whenever something moves towards the poles). Where does the increase in the angular velocity come from? It comes from the train. The train has to exert a force on the track in an Eastern direction to increase the angular velocity of the Earth. And since forces come in pairs, the Earth must exert a force on the train in a Western direction.

This is somewhat backwards, however, as the wording of the preceding implies that the conservation of angular momentum causes the Coriolis force, which in fact it is the Coriolis force that causes the conservation of angular momentum. It is because an object traveling towards the center of rotation exerts a force on the rest of the body in the direction of rotation that the angular velocity increases to keep the angular momentum constant despite the moment of inertia decreasing.

Answer 4

Yes, this force acts on all objects in motion on a revolving body. You can see this in action even on a merry-go-round. Please note that the force acts tangentially to the pivot/axis of rotation.