I'm studying from the book "Classical Mechanics" by Goldstein and from a coursebook my Professor provided me.
In the coursebook, it says that "the Coriolis effect disappears at the equator (Where the rotation vector $\vec\omega$ of the Earth is horizontal)"
Now here's my reasoning: Take the Coriolis term:
Nearby the north pole, this would cause a force pointing towards the equator if you were moving from west to east. The closer you get to the equator, the more this force starts pointing "upwards" if you were to describe the vector from the surface of the Earth.
At the equator, this vector is perpendicular to the tangent of the equator and pointing outwards.
Intuitively, this would mean that if you move from west to east on the equator you would be accelerating away from Earth.
Now if my reasoning is correct, this doesn't mean the Coriolis effect disappears, only it turns into some sort of centrifugal force, but this seems weird because it's described by another term.
Where did I go wrong?