# Formula Coriolis force (+ direction) Angular velocity Velocity Mass

## Coriolis force

`$$ \class{green}{\boldsymbol{F}_{\text c}} $$`

Coriolis force is a

*fictitious force*acting on a moving body only in rotating reference systems (such as on the Earth). Coriolis force is always*orthogonal*to the angular velocity \( \boldsymbol{\omega} \) of the Earth and the velocity \( \boldsymbol{v} \) of the body under consideration, for example an airplane flying north. You can use the Coriolis force formula to understand, for example, why clouds in the northern hemisphere move in a spiral.If the cross product '\(\times\)' is written out, then the three components of the Coriolis force are:`\[ \boldsymbol{F}_{\text c} ~=~ 2m \, \begin{bmatrix} v_y \, \omega_z ~-~ v_z \, \omega_y \\ v_z \, \omega_x ~-~ v_x \, \omega_z \\ v_x \, \omega_y ~-~ v_y \, \omega_x \end{bmatrix} \]`

## Angular velocity

`$$ \class{brown}{\boldsymbol{\omega}} $$`

Angular velocity indicates the number of rotations per second. For example, the angular velocity of the Earth in units of \( 2 \pi \):

`\[ \omega ~=~ \frac{2\pi}{24 \, \text{h}} ~=~ 7.27 \cdot 10^{-5} \, \frac{1}{\text s} \]`Angular velocity is a vector with three components:`\[ \boldsymbol{\omega} ~=~ \begin{bmatrix} \omega_x \\ \omega_y \\ \omega_z \end{bmatrix} \]`

## Velocity

`$$ \class{red}{\boldsymbol{v}} $$`

Velocity of a body, relative to the rotating reference frame. Velocity is a vector with three components:

`\[ \boldsymbol{v} ~=~ \begin{bmatrix} v_x \\ v_y \\ v_z \end{bmatrix} \]`## Mass

`$$ m $$`

Mass of the moving body moving with velocity \( \boldsymbol{v} \) in the rotating reference frame.