Re: Entropy - Actually a question about working in Polar Coordinates

[iScience]

show that $\frac{d\hat{r}}{dt}$=$\hat{θ}$$\dot{θ}$

also, $\frac{d\hat{θ}}{dt}$=-$\dot{θ}$r


i've tried finding the relationship between r and theta via turning it into Cartesian coord.s, and I've tried the S=theta r but still no luck.

S=theta r

dS/dt=d(theta)/dt r which is similar to the RHS of the second equation I'm supposed to show. but i don't know how to turn dS/dt into dtheta hat /dt

 

[D H]

What are the cartesian coordinates of those polar coordinate unit vectors? What happens when you differentiate with respect to time?

 

[iScience]

my appologies about the title


$\hat{r}$=$\hat{x}$+$\hat{y}$

d$\hat{r}$/dt = d($\hat{x}$+$\hat{y}$)/dt=d$\hat{x}$/dt+d$\hat{y}$/dt

$\hat{θ}$=?

 

[D H]

Is $\hat x + \hat y$ a unit vector? (No.)

And that is not $\hat r$.

 

[Chestermiller]

As DH is requesting, do you know how to express $\hat{r}$ and $\hat{\theta}$ in terms of $\hat{x}$, $\hat{y}$, sinθ, and cosθ?

 

[iScience]

oops, sorry i misread aGAiN.. i have that habbit.

please clearify this for me

$\hat{x}$= the x component of $\hat{r}$? if it is, i can find x.. if it's not. then i am even more lost than i thought i was.

 

[D H]

You've been given a very good hint. Look in your textbook and your class notes. This homework question was not asked out of thin air. If this is a homework problem from your textbook, that information is right there in your book. It's in the same chapter as the question is in.