r(t)=(2t, wt, 4t) in cylindric coordinates. How do I find v(t)?

Question

turingtest · Answer

w is omega?

anonymous · Answer

Yes

turingtest · Answer

I can't see how it is anything other than just differentiating wrt t

anonymous · Answer

I think the problem is that the unit vectors in cylindric coordinates also vary with time so it is not just v(t)=(2,w,4)

turingtest · Answer

so the directions here are$$\hat r,\hat\theta,\hat z$$I suppose, eh?

anonymous · Answer

right

turingtest · Answer

do you know the answer?

anonymous · Answer

No, however I just computed v(t)=(2, 2t*w, 4) but I don´t know if is correct or not.

anonymous · Answer

I also have no clue how I could ask wolfram alpha to check that.

anonymous · Answer

I used this formula but I am not entirely sure if this formula fits that problem.

turingtest · Answer

I have never seen that formula, so I can't verify it...

anonymous · Answer

I thought this is a "simple" problem.^^

turingtest · Answer

http://www.maths.ox.ac.uk/system/files/coursematerial/2012/1115/77/CylCoords.pdf that formula you have seems to be right, though I can't seem to see where they get the extra rho from

anonymous · Answer

The extra rho comes from the derevative of the unit vector e in the direction of phi.

turingtest · Answer

ahh, okay, I had to read that sheet a but closer to get it
thanks!

anonymous · Answer

No problem, you´re welcome.