How does Foucault's pendulum work in a place other than the poles?

Question

I find it easy to understand how Foucault's pendulum works at the poles, the pendulum oscillates in a fixed plane and we, along with the earth, rotate around it. So it appears that the pendulum's plane of oscillation rotated.

But how does that work if you are not at the pole? Surely then, if the earth rotates, you and the pendulum travel along with it? What have I missed? Something just does not click. If I am in London watching a pendulum, and as the earth revolves the pendulum moves with me and the earth?

Answer 1

You are going in the right direction: Since on a different latitude the pendulum will be rotating with earth, it will change the rotation due to the coriolis force. As the pendulum being at a pole is an extreme case, so is the position at the equator: Here there's no reason for the rotation Foucault's pendulum is famous for.

An intuitive guess would therefore be to say $\omega = 2\pi \sin \theta$, $\theta$ being the latitude - and indeed, it is. A bit further down on the Wikipedia you will also find the derivation in detail.

On Wiki Commons you find some more pictures not included in the Wiki page, that also illustrate this, like this one - sadly, it's a bit small.

Answer 2

The rotation of the pendulum must be free from all Earth's rotational effect. Therefore, it's not the Coriolis effect that interfere's with the rotation, but rather that we rotate while the pendulum oscillates in place. It helps to imagine that in between the poles and equator, there's some function between 0 rotational per 24 hours and 1 rotation per 24 hours.