- #1

- 9

- 0

## Homework Statement

Prove: $$\frac{d\hat{r}}{dt} = \dot{\phi} \hat{\phi }$$ and $$\frac{d\hat{\phi}}{dt} = -\dot{\phi} \hat{r }$$

## Homework Equations

## The Attempt at a Solution

I solved this for an Analytical Mechanics assignment a month ago, and completely forgot how it goes..

$$\hat{r} ⊥ \hat{\phi}$$

An change from r1 to r2 will create a ##Δ\phi## that is in the ##\hat{\phi}## direction...

and because ##\hat{r} ⊥ \hat{\phi}##, we can say the same happens for a change from ##\phi1## to ##\phi2## except in the ##-\hat{r}## direction. Assuming the change is infinitesimal, we can write ##Δr## or ##Δ\phi## as d/dt.

But then I'm confused because, why are we assuming a change from r1 to r2 is a rotation by ##Δ\phi,## and not a change of the length r..? Am I getting something completely wrong here?