# What is Polar: Definition and 1000 Discussions

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1. ### Help please with De Moivre's Theorem (raising a complex number to a power)

Hi all any help on this would be great I cant seem to progress with the theorem, z= -2 + j > R sqrt (-2)'2 + (-1)'2 r = 2.24 0= Arctan(-1) = 26.57 Polar form = 2.24(cos(26.58)+jsin(26.58) -2 Demoivre - (cos0+jsin0)'n = cosn0 +jsinno Could some one...
2. ### Dipole in polar coordinates

I don't know how to get the result referring to the previous task. Is my decision correct?
3. ### A Converting this vector into polar form

In the following%3A%20https://pubs.rsc.org/en/content/articlehtml/2013/sm/c3sm00140g?casa_token=3O_jwMdswQQAAAAA%3AaSRtvg3XUHSnUwFKEDo01etmudxmMm8lcU4dIUSkJ52Hzitv2c_RSQJYsoHE1Bm2ubZ3sdt6mq5S-w'] paper, the surface velocity for a moving, spherical particle is given as (eq 1)...
4. ### Confused about polar integrals and setting up bounds

So I want to subtract the two surfaces, right? I really don't know where to start... I am guessing this would be some sort of triple integral, however I am very confused with the bounds. Any help would be greatly appreciated! Thanks!!
5. ### Non polar molecule with polar bonds?

Consider for example Carbon Dioxide. Oxygen is more electronegative than carbon so should obtain the "lion's share" of the paired electrons in the double bonds. But (as I see it anyway) the oxygen atoms on either side of the central carbon "assist" the carbon atom to maintain an even share of...
6. ### A Polar Fourier transform of derivatives

The 2D Fourier transform is given by: \hat{f}(k,l)=\int_{\mathbb{R}^{2}}f(x,y)e^{-ikx-ily}dxdy In terms of polar co-ordinates: \hat{f}(\rho,\phi)=\int_{0}^{\infty}\int_{-\pi}^{\pi}rf(r,\theta)e^{-ir\rho\cos(\theta-\phi)}drd\theta For Fourier transforms in cartesian co-ordinates, relating the...
7. ### Integration of acceleration in polar coordinates

I made this exercise up to acquire more skill with polar coordinates. The idea is you're given the acceleration vector and have to find the position vector corresponding to it, working in reverse of the image. My attempts are the following, I proceed using 3 "independent" methods just as you...
8. ### Polar and non-polar compounds and their solubility

Hi Please can anyone explain why Naphthalene is soluble in liquid Ammonia when Naphthalene is Non-polar and Ammonia is Polar?
9. ### Calculating the partial derivative in polar coordinates

Hello, I am trying to solve the following problem: If ##z=f(x,y)##, where ##x=rcos\theta## and ##y=rsin\theta##, find ##\frac {\partial z} {\partial r}## and ##\frac {\partial z} {\partial \theta}## and show that ##\left( \frac {\partial z} {\partial x}\right){^2}+\left( \frac {\partial z}...
10. ### I Wavefunction in polar coordinates and its bra ket notation

The wavefunction of ##|\psi\rangle## is given by the bra ket ##\psi (x,y,z)= \langle r| \psi\rangle## I can convert the wavefunction from Cartesian to polar and have the wavefunction as ## \psi (r,\theta,\phi)## What bra should act on the ket ##|\psi\rangle## to give me the wavefunction as ##...
11. ### Cartesian and polar coordinate in Simple pendulum, Euler-Lagrange

$$L = \frac {mv^2}{2} - mgy$$ It is clear that ##\dot{x}=\dot{\theta}L## and ##y=-Lcos \theta##. After substituting these two equations to Lagrange equation, we will get the answer by simply using this equation: $$\frac {d} {dt} \frac {∂L}{∂\dot{\theta}} - \frac {∂L}{∂\theta }= 0$$ But, What if...
12. ### Polar to rectangular form

I'm having trouble trying to calculate how the answer below was achieved from an example i have seen, see below: 208L0 - 2.5L90 x 27.42L36.9 which is then calculated to 255.12L-12.4. I have tried converting everything to rectangular form, subtract where required and the convert back to polar...
13. ### A Solving Laplace's equation in polar coordinates for specific boundary conditions

Hello everybody, Currently I am doing my master's thesis and I've encountered a physics problem which is very difficult for me to solve. The problem I have is finding equations for the magnetic scalar potential inside and outside a ferromagnetic wire for specific boundary conditions...
14. ### Python Numerical integration over a disk with polar coordinates

In my job, I was given the task of calculating a force that operates an ultrasound transmitter on a receiver. The calculation is made by assuming that each point on the transmitter is a small transmitter and integration should be made on the surface of the transmitter. Since the transmitter is...
15. ### I Moving center of coordinates in the polar graph

I have a function in polar coordinates: t (rho, phi) = H^2 / (H^2 + rho^2) (1) I have moved the center to the right and want to get the new formulae. I use cartesian coordinates to simplify the transformation (L =...
16. ### A Analytical solution for an integral in polar coordinates?

Hi, I am trying to find open-form solutions to the integrals attached below. Lambda and Eta are positive, known constants, smaller than 10 (if it helps). I would appreciate any help! Thank you!
17. ### I Transform from polar to cartesian

Probability distribution - uniform on unit circle. In polar coordinates ##dg(r,a)=\frac{1}{2\pi}\delta(r-1)rdrda##. This transforms in ##df(x,y)=\frac{1}{2\pi}\delta(\sqrt{x^2+y^2}-1)dxdy##. The problem I ran into was the second integral was 1/2 instead of 1.
18. ### Double integral with polar coordinates

Greetings! I have the following integral and here is the solution of the book (which I understand perfectly) I have an altenative method I want to apply that does not seems to gives me the final resultMy method which doesn't give me the final results! where is my mistake? thank you!
19. ### LaTeX Plane polar noncoordinate basis (Latex fixed)

I am trying to do exercise 8.5 from Misner Thorne and Wheeler and am a bit stuck on part (d). There seem to be some typos and I would rewrite the first part of question (d) as follows Verify that the noncoordinate basis ##{e}_{\hat{r}}\equiv{e}_r=\frac{\partial\mathcal{P}}{\partial r},\...
20. ### Polar Covalent Bond in HCl question

If my understanding is correct, the polar covalent bond in HCl creates a polar molecule because the molecule is unsymmetrical. 1. Does this mean that the partially positive H of one HCl molecule will be attracted to the partially negative Cl of another HCl molecule and vice versa, to create a...
21. ### Electronics Will this electronic circuit work? (back-to-back polar capacitors)

All I need is for someone to look at my schematic and tell me if this circuit will work. Thanks.
22. ### Polar Ice Caps and the Earth's Speed of Rotation

Is it correct to say that the melting of the polar caps due to climate change may increase Earth's speed of rotation?
23. ### Acceleration in Polar Coords, Intuitive Definition video

Summary:: I wish this video (and YouTube in general) was around when I took intermediate level mechanics as an undergraduate physics student: I wish this video (and YouTube in general) was around when I took intermediate level mechanics as an undergraduate physics student:
24. ### I Vector squared in polar coordinates

Hi I was always under the impression that i could write a2 = a.a = a2 Equation 1 where a⋅ is a vector and a is its modulus but when it comes to the kinetic energy term for a particle in plane polar coordinates I'm confused ( i apologise here as i don't know how to write time derivative with...
25. ### Computing the polar moment of inertia (calculus)

Question: Diagram: So the common approach to this problem is using polar coordinates. The definition of infinitesimal rotational inertia at O is ##dI_O=r^2\sigma\, dA##. Therefore the r. inertia of the triangle is $$I_O=\int_{0}^{\pi/3}\int_{0}^{\sec\theta}r^2r\,drd\theta$$ whose value is...
26. ### Basic question pertaining to Polar Coordinates & how to employ them

I have a question that might be considered vague or even downright idiotic but just wanted to know that once we find out the velocity & acceleration of a body in angular motion in plane polar coordinates, and are asked to integrate the expressions in order to find position at some specified time...

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50. ### How to find the length of a vector expressed in polar coordinates?

The velocity of a particle below is expressed in polar coordinates, with bases e r and e theta. I know that the length of a vector expressed in i,j,k is the square of its components. But here er and e theta are not i,j,k. Plus they are changing as well. Can someone help convince me that the...