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Well, I know that the linear velocity is $V=ω*r$ where $ω$ is the linear velocity and $r$ is the radius. By the way the Guglielmini's experiment, my professor told me that when we stay on the tower the linear velocity is bigger because the distance from the centre of the Earth is bigger. But previously we said that $r$ is the radius, the distance from the centre of the parallel (which is a circle).

Consider these images:

enter image description here

enter image description here

Well, in the first our $r$ is the distance from the centre of the Earth, in the second is the distance from the centre of the parallel. I think that it's impossible that $r$ is the distance from the Earth, because near the Poles $r$ is similiar than on the equator. But I think that I think wrong, but I don't understand where is the error. Maybe it changes depending on the circumstances, sometimes we have to refer to the distance from the centre of the Earth, sometimes to the radius. But when and how?

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  • $\begingroup$ I don't really understand what your actual question is. Can you please make it clearer or bold the part where your question is? $\endgroup$
    – Sumant
    Apr 22, 2017 at 13:33
  • $\begingroup$ @Sumant Practically, why in the Guglielmini's experiment do we consider the distance from the centre of the Earth instead of the distance from the centre of the parallel? $\endgroup$
    – Curio
    Apr 22, 2017 at 13:35

1 Answer 1

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There are two ways of writing the relationship between the linear velocity $\vec v$ and the angular velocity $\vec \omega$.

enter image description here

One is a vector equation $\vec v = \vec \omega \times \vec r$ where is the radius vector from the centre of the Earth.

The other is a scalar equation $|\vec v| = |\vec \omega| \, |\vec r| \sin \theta$n or simply $v = \omega \,r\sin \theta$ where the angle $\theta $ is defined in the diagram.

The $r\sin \theta$ are the distances shown in your second diagram and are the projections on the radius vector onto the plane of the revolution.

So your professor is implying that if the magnitude of $\vec r$ gets bigger then the magnitude of $\vec v$ gets bigger because the projection of $\vec r$ onto the plane of revolution gets bigger.

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