Let's say a ball moves in an azimuthal path around a rotating disk. The Coriolis force on the ball is given by $-2m \omega \times v$. My intuition tells me that there would be no Coriolis force because the velocity is in the counter clockwise direction as is the direction of rotation. However, when I look at the cross-product in the Coriolis Force, the angular velocity points up given by the right-hand rule and the velocity points in the theta hat direction which is in the $xy$ plane so the cross-product would not equal zero. The only way the cross product could equal zero is if the velocity is also pointed straight up but the velocity can never point up. Where is the flaw in my train of thought?
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$\begingroup$ So you have a rotating disk, and a ball also rotating but with a different angular velocity? $\endgroup$– PukCommented Apr 9, 2023 at 1:15
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$\begingroup$ Note that a pseudovector (or axial vector) as opposed to a standard vector, does not always point in what one would call an "intuitive direction". See this and this PSE post. $\endgroup$– joseph hCommented Apr 9, 2023 at 1:25
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Not exactly clear on your statement, but the velocity for the Coriolis force is the velocity with respect to the non-inertial reference frame.
answered Apr 9, 2023 at 2:15