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Confusion with unit vectos

  1. Feb 27, 2014 #1
    Follow the 1st ideia: [tex]\\ d\vec{r} = dr \hat{r} + r d\theta \hat{\theta} \\ \\ \frac{d\vec{r}}{dr} = \frac{dr}{dr} \hat{r} + r \frac{d\theta}{dr}\hat{\theta} \\ \\ \frac{d\vec{r}}{dr} = \hat{r}[/tex] and now: [tex]\\ \frac{d\vec{r}}{dr} = \frac{d\vec{r}}{dt} \frac{dt}{dr} = \frac{d\vec{r}}{dt} \frac{1}{\frac{dr}{dt}} = \frac{\vec{v}}{v} = \hat{v}[/tex] However, is obvious that the unit vectos v and r are different. So, where I'm wrong?
  2. jcsd
  3. Feb 27, 2014 #2

    D H

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    Staff Emeritus
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    You've made this same mistake before, Jhenrique. Just because ##\frac{\partial \theta}{\partial r} \equiv 0## does not mean that ##\frac{d \theta}{d r} = 0##.
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