Unit vectors in cylindrical and spherical coordinates

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How do you find the unit vectors in cylindrical and spherical coordinates in terms of the cartesian unit vectors?

Lots of math.

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00:00 - Intro
01:07 - Position Vector
01:36 - Cylindrical coordinates
02:53 - Finding r-hat
04:25 - Finding theta-hat
06:46 - z-hat, PLEASE
07:46 - Spherical coordinates
11:47 - Finding r-hat
13:47 - Finding theta-hat
17:06 - Finding phi-hat
  1. Dot Physics
  2. physics
  3. physics explained
  4. cylindrical coordinates
  5. unit vectors
  6. spherical coordinates
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Комментарии
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thank you! our professors just dropped a conversion matrix without really delving into why it works

magicflour
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I’m leaving you a little heart too ❤️. Thanks. Very helpful

Titurel
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You literally did the work I could never get in this vid we always just drew graphs to get the equations without getting what does what but you saved a of effort by this video, your notations could use work and you did some tiny mistakes here and there BUT you have my total thanks ❤❤❤

Z-eng
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Wooow😍... The way you explained 👏👏👏
... And the honest mistakes in between 😂, but you were right. You did it right😇👍

I am subscribing to this dude😏... Now I will get things better.

boogychan
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Why is theta hat = dr/dtheta / mag (dr/dtheta) ?
Followed steps just couldn’t intuitively see why this starting point?

dalegriffiths
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why did we go assume that unit vector r cap is the differential of vector r with respect to r, and unit vector theta cap is the in the same way the differential of vector r with respect to theta.

bhupeshyadav
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Thanks so much, didn't understand shit from my professor on this

hzkzg
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Can someone please explain why taking the partial derivative divided by the magnitude give us the unit vector

AnisNen
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can you share the link where you did the derivative of unit vectors?

orpheuspericles
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The r-vector in the 2D plane doesn't have a z-component. If you mean another r-vector in the 3D space, at least a different notation can be used.

monisha
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Thanks too much...our professor is just..saying anything random nonsense.

civrajukumar