Formula Coriolis force - magnitude (velocity and angular velocity orthogonal) Winkelgeschwindigkeit Velocity Mass

$$\class{green}{F_{\text c}} ~=~ 2m \, \class{red}{v} \, \class{brown}{\omega}$$ $$\class{green}{F_{\text c}} ~=~ 2m \, \class{red}{v} \, \class{brown}{\omega}$$ $$\class{brown}{\omega} ~=~ \frac{1}{2} \, \frac{ \class{green}{F_{\text c}} }{ m \, \class{red}{v} } $$ $$\class{red}{v} ~=~ \frac{1}{2} \, \frac{ \class{green}{F_{\text c}} }{ m \, \class{brown}{\omega} } $$ $$m ~=~ \frac{1}{2} \, \frac{ \class{green}{F_{\text c}} }{ \class{red}{v} \, \class{brown}{\omega} } $$

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Coriolis force

$ \class{green}{F_{\text c}} $ Unit $ \text{N} $

Coriolis force is a fictitious force acting on a moving body only in rotating reference systems (like e.g. on the earth). Coriolis force always acts orthogonal to the angular velocity $ \omega $ (e.g. angular velocity of the earth) and the linear velocity $ v $ of the body under consideration (e.g. a ball on the rotation disc).

Note that for this formula the direction of the angular velocity must be exactly orthogonal (i.e. at a 90 degree angle) to the velocity.

Winkelgeschwindigkeit

$ \class{brown}{\omega} $ Unit $ \frac{1}{\text s} $

Angular velocity indicates the number of rotations per second. For example, the angular velocity of the Earth in units of $ 2 \pi $:\[ \omega ~=~ \frac{2\pi}{24 \, \text{h}} ~=~ 7.27 \cdot 10^{-5} \, \frac{1}{\text s} \]

Velocity

$ \class{red}{v} $ Unit $ \frac{\text{m}}{\text{s}} $

Velocity of a body of mass $m$ moving with velocity $v$ perpendicular to angular velocity $\omega$. For example, a ball pushed from the edge of the circling disc to the center of the disc.

Mass

$ m $ Unit $ \text{kg} $

Mass of a body moving with velocity $v$. For example, a ball on a rotating disk.