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Introductory Physics Homework Help
Simple question on proving polar coordinates
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[QUOTE="A2Airwaves, post: 4939313, member: 254480"] [h2]Homework Statement [/h2] Prove: $$\frac{d\hat{r}}{dt} = \dot{\phi} \hat{\phi }$$ and $$\frac{d\hat{\phi}}{dt} = -\dot{\phi} \hat{r }$$[h2]Homework Equations[/h2][h2]The Attempt at a Solution[/h2] 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? [/QUOTE]
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Simple question on proving polar coordinates
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