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A particle is sliding in a cone maintaining contact with it all the time. Analyzing the situation in spherical coordinates I was able to find that in the total acceleration of the particle there will be a component along $\hat{\theta}$ ,where $\theta$ is the polar angle(here $\theta=\alpha$ ),the equation is

$\ddot{r}=\left(\ddot{r}-r \sin \theta\dot{\phi}^{2}\right) \hat{r}$+$(2 \dot{r} \dot{\phi} \sin \theta+r \ddot{\phi}) \hat{\phi}-r \dot{\phi}^{2} \cos \theta \hat{\theta}$

But looking it intuitively I feel that there should be no component along $\hat{\theta}$, because any component along $\hat{\theta}$ would pull the particle away from the contact with the cone.

Why is my intuition wrong?

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  • $\begingroup$ This is just the centripetal acceleration keeping the particle traveling in a circle. $\endgroup$ – Triatticus Mar 28 at 20:23

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