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Callisto
 4 years ago
How do the plane polar coordinates work?
Callisto
 4 years ago
How do the plane polar coordinates work?

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experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1you know polar coordinate system right!!dw:1349364467374:dw

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Yes.. a little... But NOT in vectors!!

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1no they are just same.dw:1349364550790:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1we know that we write (x, y) as our point. In polar coordinate we write (r, theta) < this means this is a vector space. you have been using it unknowingly.

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Since it's related to sine, and cosine, it's not linear translation, right?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349364748021:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1yep. now let's go back to unit vector for a while. in cartesian how do you represent a vector?

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0xi + yj? i and j are unit vectors

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1yes ... and in cartesian coordinate?

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Huh?! Are they different??

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1Woops sorry ... polar coordinate??

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Well... Isn't it what I got stuck?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1\[ r \hat r + \theta \hat \theta\]

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1now we need to find the relation between \( \hat r , \hat \theta \) and \( \hat i, \hat j \)

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349365095537:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349365280570:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349365350758:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1how do we define unit vectors?

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0vector/length of vector?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349365586284:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1can you write the relation between \( \hat r \) and i,j

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0unit vector of r = (xi + yj) / (x^2 + y^2) ? I know it's strange...

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349365738630:dw

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Oh, should I express it in terms of theta?

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0unit vector of r = (xi + yj) / (x^2 + y^2) \(= \frac{(rcos) \theta i +(rsin\theta)j}{r^2cos^2\theta+r^2 sin^2 \theta} \) \(= \frac{(rcos) \theta i +(rsin\theta)j}{r^2 } \) Hmm.. doesn't look good, sorry!!

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349366033743:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1can you check page no 14 again?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1you got your first relation right?

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Eh.... I was about to say no, but then, yes :

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1for second relation there are many tricks. this is my favourite. polar coordinate is orthogonal coordinate system. \[ \hat r \cdot \hat \theta = 0\] so change \( \theta = \theta + 90 \) you will get second relation.

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Hmm, sorry!! OS is not loading properly here... And... please give me sometime to work it out first.. :(

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1sure till then i'll work out on the original methoddw:1349366641329:dw

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Sorry... May I know what that e is?? I meant he wrote \(\hat e_\theta\) or \(\hat e_r\) there.

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349366770653:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349367409678:dw

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0So, they are the unit vectors?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349367720837:dw

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Right, your trick works :

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0PQ as a vector? or...?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349367904332:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1i hope you are understanding.

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0PQ (vector) =\(r (cos(\theta +d\theta) cos\theta )i + r (sin(\theta+d\theta) sin\theta)j\) Sumtoproduct formula?

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1yep .. .cos C  cos D .. and ...

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0\[PQ = r[cos(\theta+d\theta)cos\theta] i + r[sin(\theta+d\theta)sin\theta]j\] \[=2rsin(\theta+\frac{d\theta}{2})sin\frac{d\theta}{2}i +2rcos(\theta+\frac{d\theta}{2})sin\frac{d\theta}{2}j\]

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349368740990:dw

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Isn't that PQ something horrible??

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1lol ... no. Looks like i forgot cos C  cos D

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349369192240:dw

Callisto
 4 years ago
Best ResponseYou've already chosen the best response.0Enough hint already!! (shhh!!~)

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349369373117:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349369423357:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349369566965:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349369666573:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1**************************************************************************************************************************************************************

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349369888678:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1349369925726:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1similarly for theta dw:1349370057135:dw

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.1*************************************************************************************** A more general approach.