Unit Vectors for Polar Coordinates || 2D Coordinate Systems 

Do you know The Office's "Explain to me like I was five" joke? Dude, you just saved my night, for I couldn't sleep thinking about the r-hat components. For real, I appreciate your effort, no other professor did this amount of detail. Thank you so much 💙

There cannot be a better explanation than this. Thankyou sir, keep up the work

i created a RU-vid account just to freaking thank you man phenomenal explanation!! i hope i see more of you and keep it up mate!

This is what I justtttttttttt need! Crystal Clear and understanble. Keep up the good work, Handsome! 👏

Wow! That was an mind-blowing explanation. Crystal clear. Thanks!

One of the underrated RU-vid channels out there😢

Been looking for this explanation forever! Thanks a lot

Thanks bud , It clears my conceptual problem.

Thnx! Just what i needed!

Thank you so much for this

Best explanation on r hat. Tq

Very good explanation😊

Thanks a lot it was very useful and you made it look easy. Love from India

Thank you very much ❤

At the timeline 13:00, isn't 2nd quadrant of cos be negative? and sin be positive still?

Please/ I need formula of unit vactors in spheric coordinates. r^/theta ^ and fay^

Too good Refreshed my memories

could you please upload example question video how to solve cylinder coordinate system question? and please give me some idea to solve quickly.

If we use a polar coordinate system whose origin is either 1) moving with uniform velocity or 2) accelerating or 3) itself moving around another fixed point, can we use Newton's second law in the r hat and theta hat directions. I suspect we can still do so in case 1) but not if it's accelerating in 2) and 3). If not, how would we deal with such a system with an accelerating origin: I'm thinking something like a spinning ride which is itself on a spinning carousel. Hopefully you can comment on this. Thanks.

Thank you sir

Fantastic

Hi, can you explain why the position vector can never be described as a linear combination of r hat and theta hat whereas the velocity and acceleration vectors derived from the position vector are described in terms of a linear combination of r hat and theta hat. Indeed it seems velocity and acceleration vectors at each position are uniquely suited to this coordinate system since they are true vectors unlike the position vector (which starts at the origin and therefore only has an r hat component). This difference (between position vectors and their velocity/acceleration counterparts) seems to extend to the ability to take dot products in this coordinate system as well: dot products don't work for position vectors. Can you shed light on what all this means. Is there a deeper physical significance associated with this difference in the treatment of vectors which doesn't happen for the Cartesian coordinate system. I heard reference to velocity and acceleration being true vectors in the tangent spaces of each point etc and this fits well with a changing basis at each point (as with this coordinate system). I hope you can shed light on this.

How can we convert from polar to cartesian unit vectors?

😀😀😀 EXCELLENT But I really don´t get why we put these unit vectors on the point we are locating, and is strage because we localizate points with basis vectores in rectangular cordinates, but her we fist locate the point and before we put on it the basis, no sense for me. THANKS FOR YOU ANSWER. GREATTINGS FROM ECUADROR :)

GREaT