Timeline for Representation Of Linear Velocity as Cross Product
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 9, 2023 at 0:09 | comment | added | Amit | I find the differential approach unnecessary here -- unless I'm missing something, here is the derivation I prefer: the radius of the rotation circle $R$ is clearly given by: $R=|\vec{r}|\sin{\theta}$. Where $\theta$ is the angle $\vec{r}$ makes with the $z$ axis. Now, writing the velocity's magnitude as $|\vec{v}| = wR = w|\vec{r}|\sin{\theta}$, we observe that if we define $\vec{w} = (0,0,w)$ this is the unique vector such that $|\vec{w} \times \vec{r}| = wR = |\vec{v}|$. Finally, we also observe that as a vector $\vec{v}$ is perpendicular to both $\vec{w}$ and $\vec{r}$ and we're done. | |
| Mar 29, 2022 at 10:48 | comment | added | VIVID | @Rahul If you treat that as a normal triangle (i.e. nothing about infinitesimal rotation) $dr = r\sin\phi$. But $\sin\phi \approx \phi$ for sufficiently small angles | |
| Mar 29, 2022 at 9:47 | comment | added | RAHUL | @VIVID, Sir, would you please elaborate why $dr=d\phi × r$ | |
| S Nov 21, 2020 at 23:42 | history | suggested | VIVID | CC BY-SA 4.0 |
improved formatting
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| Nov 21, 2020 at 19:53 | review | Suggested edits | |||
| S Nov 21, 2020 at 23:42 | |||||
| Apr 8, 2015 at 18:30 | vote | accept | CommunityBot | ||
| Mar 19, 2015 at 10:27 | comment | added | danimal | The right hand screw rule is just convention; we could define the cross product the opposite direction and it would be fine as long as the same new version was applied universally | |
| Mar 19, 2015 at 7:56 | comment | added | user74370 | Ok then basically i've been questioning the right hand screw rule itself..and do you know a proof for the right hand screw rule? Btw this is a good approach :-) | |
| Mar 19, 2015 at 7:46 | comment | added | sugatasen | And just so u know, if u tried v = rXω, that would be fundamentally wrong, bcuz of how the direction of ω us assumed by the right hand rule convention!, then of course you would obtain an illogical result, anyway , that's if u go by convention!! | |
| Mar 19, 2015 at 7:42 | history | answered | sugatasen | CC BY-SA 3.0 |