Coriolis force does not contribute to the energy equation
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Quantifying the Coriolis Force

From a rotating reference frame, any object in motion will be influenced by the Coriolis force. Its strength depends on only a few variables, and the relative direction of their vectors. First of all, the object’s linear (tangential) velocity must be considered. Only the component of velocity that is perpendicular to the rotating frame’s axis of rotation contributes to the Coriolis force. Angular velocity, then, is also a factor in the equation for the Coriolis force. In particular, one must determine the cross product of linear velocity and angular velocity. The final factor in the Coriolis force is the mass of the object.
Image: Persson. (1998). Bulletin of the American Meteorological Society, 79(7). 1373-1385.
Gaspard Gustave Coriolis (1792-1843) was a French mathematician. He generalized the concepts of work and energy to rotating systems.
Image: http://venus.wisc.edu/vortex_model.html

The vector equation for the Coriolis force is shown above. The underlined and bolded characters are vectors whose magnitudes and directions must be considered. As mentioned, the cross product between rotational velocity (omega) and linear velocity (v) multiplies only the vector components that are orthogonal. The result of the cross product is orthogonal to both v and Ω. Its direction can be determined by the right hand rule. Take your right hand and orient your index finger, middle finger and thumb as shown below.


From a rotating reference frame, any object in motion will be influenced by the Coriolis force. Its strength depends on only a few variables, and the relative direction of their vectors. First of all, the object’s linear (tangential) velocity must be considered. Only the component of velocity that is perpendicular to the rotating frame’s axis of rotation contributes to the Coriolis force. Angular velocity, then, is also a factor in the equation for the Coriolis force. In particular, one must determine the cross product of linear velocity and angular velocity. The final factor in the Coriolis force is the mass of the object.
Image: Persson. (1998). Bulletin of the American Meteorological Society, 79(7). 1373-1385.
Gaspard Gustave Coriolis (1792-1843) was a French mathematician. He generalized the concepts of work and energy to rotating systems.
Image: http://venus.wisc.edu/vortex_model.html

The vector equation for the Coriolis force is shown above. The underlined and bolded characters are vectors whose magnitudes and directions must be considered. As mentioned, the cross product between rotational velocity (omega) and linear velocity (v) multiplies only the vector components that are orthogonal. The result of the cross product is orthogonal to both v and Ω. Its direction can be determined by the right hand rule. Take your right hand and orient your index finger, middle finger and thumb as shown below.

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