What is the significance of \hat{\theta} in polar vector coordinates?

[ice109]

i don't understand the point of \hat{\theta} if a vector is completely described by \textbf{r}=r \hat{\textbf{r}}

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

 

[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 \textbf{r}=r \hat{\textbf{r}}". 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 \textbf{r}=r \hat{\textbf{r}} then you don't need \theta'.

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

 

[learningphysics]

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

 

[ice109]

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 \textbf{r}=r \hat{\textbf{r}}". 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 \textbf{r}=r \hat{\textbf{r}} then you don't need \theta'.

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

does \textbf{r} 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 \hat{\textbf{r}} and \hat{\theta}. 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 \hat{\theta}}

the picture represents my understanding of the the polar coordinates in terms of the cartesian coordinates where \textbf{A} 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 \textbf{A} by just scaling the \hat{\textbf{r}} a little and making its \theta argument little bigger?