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hope you are well, So , in my physics class we use graphical method to determine the radius of curvature and as we know this method isn't very accurate, so when I watch a YouTube video I find this relation:

enter image description here

So is this relation always true? Because I was able to find it before watching the video, but with the condition of $ay=0$.

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  • $\begingroup$ Yes. You can derive it if you know the mathematics here. $\endgroup$
    – naturallyInconsistent
    Commented Apr 23, 2023 at 2:45
  • $\begingroup$ I would consider this to be the definition of the radius of curvature of a curve $\vec{r}(t)$. So it must always be true by definition. $\endgroup$
    – d_b
    Commented Apr 23, 2023 at 5:02

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