Hi, if the velocity of a partical is u = (u,v,w) in cartesian coordinates (,x,y), and (ur, uθ, uz) in cylindrical polar (z,r,θ), could someone please explain why:z

dv/dx - du/dy = (1/r) d/dr(r uθ) ?

I tried using the chain rule to get:

dv/dx - du/dy = (cosθ)dv/dr - (sinθ)du/dr ...........(1)

Then use

= cosθr+ sinθxy

= -sinθθ+ cosθxy

To write= uru+ uθrin terms ofθandx,y

then equate components with=uu+ vxto get:y

u = urcosθ - uθsinθ

v = ursinθ + uθcosθ

Then subbing those values into (1) and simplifying, I end up with it equal to

d/dr(uθ)

I don't know where the extra r terms come from (or if they just cancel out somehow??) Could someone please point out if I'm doing something wrong?

Thanks,

~Squiggles