polar vector coordinates

ice109

i dont understand the point of [itex]\hat{\theta}[/itex] if a vector is completely described by [itex] \textbf{r}=r \hat{\textbf{r}}[/itex]

btw tex is doing something weird, apparently i can't make greek letters bold
[tex]\textbf{\delta}[/tex]

ice109

no one of you math geniuses can answer this for me?

HallsofIvy

I don't pretend to be a math genius but perhaps none of them understands your question. What do you mean by "a vector is completely described by [itex] \textbf{r}=r \hat{\textbf{r}}[/itex]". Are you talking about a specific vector? Because that certainly does not "completely describe" a general vector. If you have a vector "completely described" by [itex] \textbf{r}=r \hat{\textbf{r}}[/itex] then you don't need [itex]\theta'[/itex].

If you have formulas for both r' and [itex]\theta'[/itex], what makes you think that the vector is "completely described" by [itex] \textbf{r}=r \hat{\textbf{r}}[/itex]
? Perhaps it would help if you stated the precise problem.

learningphysics

[tex]\hat{\textbf{r}}[/itex] depends on [tex]\theta[/tex]... It changes according to the angle. Unless you know what [tex]\theta[/tex] is you can't draw [tex]\hat{\textbf{r}}[/itex]

ice109

does [itex]\textbf{r}[/itex] describe a general vector in cartesian coordinates? if it does then i don't see any difference between the position vector in cartesian coordinates and in polar coordinates.

in fact i don't even understand the physical meaning of a linear combination of [itex]\hat{\textbf{r}}[/itex] and [itex]\hat{\theta}[/itex]. actually that is erroneous , i have no problem visualizing the resultant of these two vectors, i would just need to connect them head to tail. what i don't understand is what i said before, what is the point of the [itex]\hat{\theta}}[/itex]

the picture represents my understanding of the the polar coordinates in terms of the cartesian coordinates where [itex]\textbf{A}[/itex] is the vector i'm trying to describe in terms of the the polar unit vectors. is it correct? and if it is correct why can't describe [itex]\textbf{A}[/itex] by just scaling the [itex]\hat{\textbf{r}}[/itex] a little and making its [itex]\theta[/itex] argument little bigger?

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