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Illustration Coriolis force, velocity and angular velocity - Vectors

Coriolis force
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A body (e.g. an airplane) with the mass \( m \) moves above the earth with the velocity \( \boldsymbol{v} \). The earth rotates with angular velocity \( \boldsymbol{\omega} \) pointing along the earth axis. Since the body is in a rotating system, it experiences a Coriolis force \( \boldsymbol{F}_{\text c} \), which is orthogonal to \( \boldsymbol{v} \) and \( \boldsymbol{\omega} \).

The velocity vector \(\boldsymbol{v}\) and the angular velocity vector \(\boldsymbol{\omega}\) include the angle \(\varphi\) which determines the magnitude of the Coriolis force. At the equator the angle is small, so the Coriolis force is also small.