Polar Definition and 1000 Threads

The 2D Laplacian in polar coordinates has the form of $$ \frac{1}{r}(ru_r)_r +\frac{1}{r^2}u_{\theta \theta} =0 $$ By separation of variables, we can write the ## \theta## part as $$ \Theta'' (\theta) = \lambda \Theta (\theta)$$ Now, the book said because we need to satisfy the condition ##...

Hello all! I'm just wanting a quick clarification on how finding the area under a polar graph works. Say we have the polar graph of ##r\left(\theta \right)=\frac{\arctan \left(2\theta \right)}{\theta }## as shown below: I know that the area under the graph between ##0## and ##\frac{\pi...

Evaluate the double integral by converting to polar coordinates. Let S S be the double integral symbol S S xy dydx Inner limits: 0 to sqrt{2x - x^2} Outer limits: 0 to 2 The answer is 2/3. I know that x = rcosϴ and y = rsinϴ. S S rcosϴ*rsinϴ r drdϴ. S S (r^3)cosϴ*sinϴ drdϴ. I am stuck...

Evaluate the iterated integral by converting to polar coordinates. Let S S = double integral symbol S S y dx dy The outer integral is from 0 to a. The inner integral is from 0 to sqrt{a^2 - y^2}. I started by letting y = r sin ϴ S S r sinϴ dxdy. I then let dxdy = r dr d ϴ S S r sin ϴ rdr...

I have made graph of event horizon of Kerr black hole by giving simple command of polar plot. The problem is that the point where the event horizon and static limit meets should be along y-axis but instead its on x-axis. I have tried everything but not getting it right. What mistake I am...

Homework Statement If (r, θ) are the polar coordinates of a point then describe the region defined by the restrictions -1 < r < 0, π/2 < θ < 3π/2 Homework Equations No clue The Attempt at a Solution I tried drawing the curve in a polar grid by starting at π/2 and finishing at 3π/2. I was...

Homework Statement The curve ##C## has polar equation ## r\theta =1 ## for ## 0<\theta<2\pi## Use the fact that ## \lim_{\theta \rightarrow 0}\frac{sin \theta }{\theta }=1## to show the line ## y=1## is an asymptote to ## C##.The Attempt at a Solution **Attempt** $$\ r\theta =1$$ $$\...

Homework Statement you are given the standard form z = 3 - 3i Homework EquationsThe Attempt at a Solution so to convert this to polar form, i know that ##r = 3√2## but how do i find theta here? There are so many mixed answers it seems online that I can't tell... i know that ##(3,-3)## is in...

Homework Statement well this is not exactly a homework, i had an argument whith my teacher about my grade in a test, because i put a complex number in the form of R,theta and she claims that the form was costheta+isentheta, and i know that but i need to prove in a book that...

Hi all, I was doing some math and I stumbled upon a very interesting thing. When I do ln(-1), I get πi, and when I turn that into polar coordinates on the calculator, it gives me πeiπ/2 . Why is that? I'm very curious to know, because they are so intertwined! Thank you

How do i get an idea, or a 'feel' of the components of the acceleration in polar coordinates which constitute the component in the eθ direction? from what i know, a= (r¨−rθ˙^2) er + (rθ¨+ 2r˙θ˙) eθ ; (where er and eθ are unit vectors in the radial direction and the direction of increase of the...

Homework Statement http://i.imgur.com/4FPnTNS.jpg Homework Equations (Written in above photo) The Attempt at a Solution (Written in above photo) I have tried hard in figuring out what's wong I have done done, but what I finally got is still option d instead of the model answer e. Are there...

Homework Statement I plotted the drag polar graph (Drag coefficient vs. lift coefficient) for an aircraft and are required to find the equation of the drag polar to determine values for [C][/D0] and k, using the graph or any other method. I've plotted the graph which I've included. Homework...

General question, how do you determine the limits of integration of a polar curve? Always found this somewhat confusing and can't seem to find a decent explanation on the internet.

Homework Statement Homework Equations r=sqrt(a^2+b^2) θ=arg(z) tan(θ)=b/a The Attempt at a Solution for a)[/B] finding the polar form: r=sqrt(-3^2+(-4)^2)=sqrt(7) θ=arg(z) tan(θ)=-4/-3 = 53.13 ° 300-53.13=306.87° -3-j4=sqrt(7)*(cos(306.87+j306.87) I don't know if my answer is correct...

Hi there, I've been trying to solve the following problem, which I found looks pretty basic, but actually got me really confused about the definition of angular momentum. Problem The trajectory of a point mass m is described by the following equations, in spherical coordinates: r(t) = r_0 +...

Homework Statement I am trying to calculate the laplacian in polar coordinates but I failed.Please see the attached Homework Equations The Attempt at a Solution My solution to this was uploaded in the attached.I was wondering what's wrong with the purple brackets since they shouldn't exist(...

Homework Statement \frac{z-1}{z+1}=i I found the cartesian form, z = i, but how do I turn it into polar form?The Attempt at a Solution |z|=\sqrt{0^2+1^2}=1 \theta=arctan\frac{b}{a}=arctan\frac{1}{0} Is the solution then that is not possible to convert it to polar form?

I am learning about the polar coordinate system, and I have a few conceptual questions. I understand that in Cartesian coordinates there is exactly one set of coordinates for any given point. However, in polar coordinates there is an infinite number of coordinates for a given point. I see how...

Homework Statement Homework Equations NONE The Attempt at a Solution I'm trying to understand why the unit vector in the y direction is that formula. I get that e(theta) and e(r) are unit vectors used with polar coordinates that define direction and are perpendicular to each other always...

Hello everyone, 1. Homework Statement Question : Find the volume of the region which remains inside the cyclinder x 2 + y 2 = 2y, and is bounded from above by the paraboloid surface x 2 + y 2 + z = 1 and from below by the plane z = 0 Homework Equations The Attempt at a Solution This looks...

Homework Statement Integrate by changing to polar coordinates: ## \int_{0}^6 \int_{0}^\sqrt{36-x^2} tan^{-1} \left( \frac y x \right) \, dy \, dx ## Homework Equations ## x = r \cos \left( \theta \right) ## ## y = r \sin \left( \theta \right) ## The Attempt at a Solution So this is a...

Hello everybody. I am currently doing some research about the evolution of ozone holes over antartica. I am interested in 2002's season, since strong winds from the stratosphere managed to alter the wind's clockwise circulation about the continent making it one of the weirdest recorded. So...

Homework Statement On the surface of a river at ##t=0## there is a boat 1 (point ##F_0##) at a distance ##r_0## from the point ##O## (the coordinate beginning) which is on the right side of the coast (picture uploaded below). A line ##OF_0## makes an angle ##θ_0=10°## with the ##x-axis## whose...

Homework Statement Transform given integral in Cartesian coordinates to one in polar coordinates and evaluate polar integral. ##\int_{0}^3 \int_{0}^x \frac {dydx}{\sqrt(x^2+y^2)}## Homework EquationsThe Attempt at a Solution I drew out the region in the ##xy## plane and I know that ##0 \leq...

Homework Statement $$ U_{tt}=\alpha^2\bigtriangledown^2U$$ in polar coordinates if solution depends only on R, t. Homework EquationsThe Attempt at a Solution So, the books solution is $$U_{tt}=\alpha^2[U_{rr}+\frac{1}{r}U_r]$$. I am getting stuck along the way can't figure out this last step I...

Hello, I have a question about polar coordinates. It is \vec r = \begin{pmatrix}r cos\phi \\ rsin\phi \\ z\end{pmatrix}=r\cdot \vec e_r + z\cdot \vec e_z and than is \ddot{\vec r} = (\ddot{r}-r\dot{\phi}^2)\vec e_r + (r\ddot{\phi} +2\dot{r}\dot{\phi})\vec e_{\phi} + \ddot{z}\vec e_z The...

Homework Statement In this video , why for the xy plane projection , it's a circle with center = y = 1 , i can understand the r = 2sin theta ? why we can't ∬ r dr dtheta where , r = 1 , and with theta = 0 to 2 pi ? They are the same , right ? since volume = integration of area with z a-xis...

Can y=x^2-1 or y=1-x^2 be converted to polar functions? I was attempting it and kept running into problems. If it's not possible, why not?

Homework Statement Consider the 'ice cream cone' bounded by z = 14 − x2 − y2 and z = x2 + y2 .(a) Find the equation of the intersection of the two surfaces in terms of x and y. (b) Set up the integral in polar coordinates. Homework EquationsThe Attempt at a Solution I got part a without...

Water can dissolve O2 and CO2, both of which are non-polar...According to my understanding, water can only dissolve molecules which have polarity in their structure( like salt or sugar)...Oxygen gas is non-polar due to same atoms...I am not sure about CO2 but I think it is non-polar due to equal...

Hi everybody, I have a code for Polar function in Bilayer graphene. I compile and run it. Everything is ok but at x=2, the value of Polar function is so large. I don't know why this happens ? Please help me //====================LIBRARY=================================================== #include...

If a general conic is ax^2+2hxy+by^2+2gx+2fy+c=0 I am told that, if P(p, q) is a point on this conic, then the polar of P(p, q) to this conic is apx+h(py+qx)+bgy+g(p+x)+f(q+y)+c=0 How is this derived?

Here is the problem I am dealing with... And this is how I approached it. Can anyone confirm that I did it correctly and got the right answer? Thank you.

Hi, I have a little doubt. I have, referred to the Sun, the cartesian positions and velocities of an asteroid (in x, y and z coordinates - 6 values). I can easely calculate the polar coordinates (longitude and latitude - along with distance). My doubt is: how do I calculate the longitude and...

Here is the given problem... And I first approached it by drawing the xy footprint to get my theta and radius limits to convert to polar. Then I overlooked the original xy function and pretty much took the area of that footprint (highlighted in green.) That gave me a very nice number...

Homework Statement Let ##x##, ##y##, and ##z## be the usual cartesian coordinates in ##\mathbb{R}^{3}## and let ##u^{1} = r##, ##u^{2} = \theta## (colatitude), and ##u^{3} = \phi## be spherical coordinates. Compute the metric tensor components for the spherical coordinates...

I need a planet to be orbiting it's sun in a polar orbit. Is this a stable configuration?

Homework Statement Homework Equations Average (area) = 1/Area * integrate of polar The Attempt at a Solution y= r* sin theta x= r* cos theta r^2 = x^2+y^2

Homework Statement Homework Equations s=r* theta The Attempt at a Solution

Note: All bold and underlined variables in this post are base vectors I was reading the book 'Introduction To Mechanics' by Kleppner and Kolenkow and came across an example I don't quite understand. The example is this: a bead is moving along the spoke of a wheel at constant speed u m/s. The...

Homework Statement What is the magnitude of the velocity vector if ##\vec{v} = 4 \hat{r} + 6 \hat{\theta}## Homework EquationsThe Attempt at a Solution I know how do do this in Cartesian coordinates (use the Pythagorean theorem), but not so sure how to do it in polar coordinates.

I have read that in polar coordinates, we can form the position vector, velocity, and acceleration, just as with Cartesian coordinates. The position vector in Cartesian coordinates is ##\vec{r} = r_x \hat{i} + r_y \hat{j}##. And any choice of ##r_x## and ##r_y## maps the vector to a position in...

Homework Statement This isn't exactly a "problem" per se , but I need to understand it for a course I'm taking. I'm trying to understand the significance and when to use the vector conversion matrices, or just the identities. I'll use an example that I made up, using rectangular to polar...

I am trying to find the slope of the tangent line of this polar equation: r = 4 + sin theta, (4,0) I put the equation into wolfram alpha and it gives me a 3D plot. If someone could help me find the slope of the tangent line, I would really appreciate it. Thank you.

I am trying to convert this polar equation to Cartesian coordinates. r = 8 cos theta I type the equation into wolfram alpha and it gives me a graph, but no Cartesian points. If somebody could help me find the cartesian points, I would appreciate it. Thank you.

1. The question The position of a particle is given by r(t) = acos(wt) i + bsin(wt) j. Assume a and b are both positive and a > b. The plane polar coordinates of a particle at a time t equal to 1/8 of the time period T will be given by _ Homework Equations r(t) = acos(wt) i + bsin(wt) j. The...

I am trying to find and solve the geodesics equation for polar coordinates. If I start by the definition of Christoffel symbols with the following expressions : $$de_{i}=w_{i}^{j}\,de_{j}=\Gamma_{ik}^{j}du^{k}\,de_{j}$$ with $$u^{k}$$ is the k-th component of polar coordinates ($$1$$ is for...

In my introduction to manifolds the following is stated: Polar coordinates (r, phi) cover the coordinate neighborhood (r > 0, 0 < phi < 2pi); one needs at least two such coordinate neighborhoods to cover R2. I do not understand why two are needed. Any point in R2 can be described by polar...

Homework Statement why x is p(cosθ)(sinφ) ? and y=p(sinθ)(cosφ)? z=p(cosφ) As we can see, φ is not the angle between p and z ... Homework EquationsThe Attempt at a Solution