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Question 1: Why in rotating frames, is it necessary that an object's acceleration is always directed radially outwards in the $\hat{r}$ direction and why is there no component in the tangential direction?

Question 2: In the equation

$$ m \frac{d^2 \vec{r}}{d t^2} = \vec{F}_{\text{real}} - \vec{F}_{\text{Coriolis}} - \vec{F}_{\text{centrifugal}} -\vec{F}_{\text{Euler}},$$

suppose there is no real force to balance Coriolis force (which is, say, tangential)… but the LHS of the equation has a term only in the r^ direction. How did I generate a contradiction or is there any flaw?

Please help, I am not able to understand rotating frames.

Qmechanic
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Kampann
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1 Answers1

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The straightforward answer is that there is no reason, in general, for $\ddot{\mathbf{r}}$ to only be in the radial direction. Derivatives of $\mathbf{r}$ can have both radial and tangential components. So your "contradiction" starts from a false premise.

Furthermore, none of the above has anything to do with whether there are real forces balancing the Coriolis force.

Vincent Thacker
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