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]

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

 

[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?