Polar coordinates Definition and 569 Threads

Homework Statement The lecture notes say that ∇ = urr + (1/r)ur + (1/r2)uθθ. I'm not sure how this comes about. The notes never explain it. Homework Equations (?) The Attempt at a Solution No attempts on the actual homework problem until this ∇ thing is cleared up.

Hi I'm working on area and volume integrals. I was wondering, when you convert to do the integral in polar, cylindrical or spherical co-ordinates, is there a standard set of limits for the theta variable in each case? for example from 0 -pi for polar, 0-2pi for cylindrical? If not how...

Homework Statement Find the area of the shaded region. r=sqrt(θ) Homework Equations A = integral from a to b 1/2r^2dθ The Attempt at a Solution I know how to solve the question, I just don't know what to use for a and b. I tried 0 and 2pi but I am getting the wrong answer...

Homework Statement Find the area enclosed by the inner loop of the curve r=1-3sinθ Homework Equations A=o.5\int r^2 dθ The Attempt at a Solution I found the integral but i don't know how to find the interval at which i will be integrating from. I tried finding when r=0 and it turns...

what is the best way to graph in polar coordinates say r = 3 - 5 \cos \theta is it to plot several points then make a curve between them or ?

Greetings everyone, I am having difficulties grasping the polar form of the ellipse equation, and there seems to be more than one way to express an ellipse in this form, if I am not mistaken. For example on the following webpage http://farside.ph.utexas.edu/teaching/301/lectures/node155.html...

Homework Statement 1. Use polar coordinates to find the volume of the given solid. 2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4. 2. The attempt at a solution My attempt as following: 2<=r<=4, and 0<=theta<=2pi So I do a double integral of...

Homework Statement Use Polar coordinates to evaluate were C denotes the unit circle about a fixed point Z0 in the complex plane The Attempt at a Solution I've only used polar integrals to convert an integral in sin and cos into one in therms of z, find the residues and then use the...

The cone centre is the z-axis and has base ρ=1 and height z=1, I'm looking at the lecture notes and it says the limit φ=0 to 2pi, z=0 to 1, ρ=0 to (1-z). Could someone tell me where the (1-z) comes from please? Why is it not 0 to 1?

Homework Statement The Cartesian coordinates of a point are given. (3,-5) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. Homework Equations r^2=x^2+y^2 tanθ=(y/x) →...

Homework Statement Im righting this down for my roommates since he's having tons of trouble trying to figure this out and I can't answer it. also sorry for having to hotlink it. http://i.imgur.com/afShz.jpg the equation is on the image since its very difficult to type it all out...

what is the area inside the graph of r=2sinθ and outside the graph of r=sinθ+cosθ? so i compute for the values of 'r',... but, i only got one intersection point which is (45°, 1.41). there must be two intersection points right? but I've only got one. what shall i do? i cannot compute for...

Staff was trying to understand a matter of calculation. I hope someone can explain me in detail how to solve this limit using polar coordinates: http://img36.imageshack.us/img36/2667/semttulokej.png

Homework Statement Let \hat r = <x_r , y_r> and \hat\theta = <x_\theta , y_\theta> Draw these vectors at points (x,y) = (1,0), (2,0), (3,0), (1,1), (0,1), (0,2). Here is the entire http://www.math.tamu.edu/~vargo/courses/251/HW5.pdf assignment so you can see what context it is in...

Homework Statement For a Foucalt Pendulum: Relative to horizontal Cartesian x and y axes fixed to the Earth (with x as East) the equations of motion for horizontal motion are: x′′ + ω02x -2ωy′ = 0 and y′′ + ω02y + 2ωx′ = 0 [where x′, x′′, y′, y′′ are first and second time...

Homework Statement Three charges are arranged as presented below. Q1= 5.00E-9C, Q2= 6.00E-9C and Q3= -7.00E-9C. http://img15.imageshack.us/img15/9250/physicskf.png D) Find the direction of the above electric field using the polar coordinate system 0°< θ <360° Homework Equations...

Homework Statement Using f(z) = f(re^iθ) = R(r,θ)e^iΩ(r,θ), show that the Cauchy-Riemann conditions in polar coordinates become ∂R/∂r = (R/r)∂Ω/∂θ Homework Equations Cauchy-Riemann in polar coordinates Hint: Set up the derivative first with dz radial and then with dz tangential...

Homework Statement Evaluate the double integral by converting to polar coordinates. ∫∫ arctan y/x dA; R is the sector in the first quadrant between the circles 1/4= x^2+y^2 and x^2+y^2=1 and the lines y=x/√3 and y=x. Homework Equations arctan y/x= θ The Attempt at a Solution...

I was looking at the equation of a circle in polar coordinates on wikipedia, http://en.wikipedia.org/wiki/Polar_coordinate_system and I understand that a is the radius of the circle, and that (r0, phi) is the center of the circle. But I don't see what the r and theta refer to :(.

i just need to know something about the integral with polar coordinates , to know the interval of the teta angle of any domain the proffesor said that we put the pen on the x-axis and move it , i for one moment was not focusing and the doctor had to go to another class can anyone explain ? thank you

I'm studying for my final and tutors/my professor isn't available over the weekend. Could someone please spend a little time to help me? My problem is stated as: Let R be the right half of the circle x2+(y-1)2=1. Use a double integral polar coordinates to find the area of the region R. I...

Transformation from Cartesian to spherical polar coordinates In dimensions: x=r sinθ cos \varphi and y= r sin θ sin \varphi z=r cos θ Show one example of: ∂z\alpha/ ∂xμ . ∂xμ/ ∂z\alpha = δ\alpha\beta Now here is my answer: δyx=(∂y/∂r . ∂r/∂x) + (∂y/∂θ . ∂θ/∂x) + (∂y/∂\varphi...

Homework Statement Let F = <-y/(x2+y2, x/(x2+y2>. Recall that F was not conservative on R2 - (0,0). In this problem, we show that F is conservative on R2 minus the non-positive x-axis. Let D be all of R2 except points of the form (-x,0), where x≥0. a) If (x,y) is included on D, show that...

I'm having trouble figuring out how to find what "r" is. I know r is the radius, but how do I go about finding it? Like what do I look for in a particular problem?

Homework Statement "Consider the graph of r = e^{\theta} in polar coordinates. Then consider the graph of (\theta \cos{\theta}, \theta \sin{\theta}) where \theta \in \mathbb{R} on the Cartesian plane (x - y axis). How are the two graphs related? What relationship (if any) can we define between...

A bee goes from its hive in a spiral path given in plane polar coordinates by r = b*ekt , θ = ct, where b, k, c are positive constants. Show that the angle between the velocity vector and the acceleration vector remains constant as the bee moves outward. (Hint: Find v · a/va.) attempts...

The problem and my work is shown in the image below. However, I feel like I did something horrible wrong but I'm not sure where! I'm sorry if my handwriting is illegible. If you're having difficulties please leave a comment and I will not hesitate to type it out as a response. Any...

∫∫cos(x^2 + y^2)dA, where R is the region that lies above the x-axis within the circle x^2 + y^2 = 9. Answer: .5pi*sin(9) My Work: ∫(0 ->pi) ∫(0 -> 9) cos(r^2) rdrdθ u = r^2 du = 2rdr dr = du/2r .5∫(0 ->pi) ∫(0 -> 9) cos(u) dudθ .5∫(0 ->pi) sin(u)(0 -> 9) dθ .5∫(0 ->pi)...

Homework Statement (a) we define the improper integral (over the entire plane R2) I=\int\int_{R^2}e^{-(x^2+y^2)}dA=\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(x^2+y^2)}dy dx=\lim_{a\rightarrow\infty}\int\int_{D_{a}} e^{-(x^2+y^2)} dA where Da is the disk with radius a and center the...

I have a question regarding problem solving tips. When given an iterated integral and asked to convert it to polar coordinates, how do you select the bounds of theta - do you have to understand how the graph of r operates and therefore know where the theta bounds are based on the rectangular...

Equations given: r=A\theta \theta=\frac{1}{2}\alphat^{2} A=\frac{1}{\pi} meters per radian \alpha is a given constant Asks to show that radial acceleration is zero when \theta=\frac{1}{\sqrt{2}} radians. I have tried rearranging, plugging in, and deriving to try to solve this...

I have an ellipse. Quite simple, ecc=0.60. And I'm doodling with calculus I learned 40 years ago. I can find the tangent to the ellipse, that is, the slope of the tangent, using cartestian coordinates. At the point where the tangent skims the top of the minor axis (b) the slope is 0 and and...

Homework Statement Show that the parity operation (reflection through the origin) on a point (\rho, \varphi, z) relative to fixed (x, y, z) axes consists of the transformation: \rho \to \rho \varphi \to \varphi \pm \pi z \to -z Also, show that the unit vectors of the cylindrical polar...

Homework Statement Hi, I have the coordinates of an "expression" for a point in a cartesian coordinate system. I'm trying to write it in a polar coordiante system (in function of r and theta) but I don't know how to find the answer a = y-component of the point b = x-component of the point...

Homework Statement Find the points at which the following polar curves have a horizontal and vertical tangent line. (a) r = 3 + 6 cos(theta) Homework Equations The Attempt at a Solution x = r cos(theta) = (3 + 6 cos(theta)))cos(theta) = 3cos(theta) + 6 cos(theta)^2 y =...

Hi! Is there somebody, who can help me with this exercise: "Use polar coordinates to find the limit. [If (r, θ ) are polar coordinates of the point (x,y) with r ≥ 0, note that r --> 0+ as (x,y) --> (0,0)]

Homework Statement "Find the area of the region that lies inside both curves (as an example), r=((sqrt(3)) cos(theta)) , r=sin(theta). This is Calculus 3. Areas and lengths in polar coordinates. Homework Equations Guys, I'm very confused because when the polar graphs are complicated we...

Hi, Say I have an acceleration vector in polar coordinates: a = -30e_r where the unit vector e_r points in the same direction as the Cartesian unit vector j. How can I integrate that vector so that I have the velocity vector in polar coordinates? I know that if I have an acceleration vector...

Homework Statement Find dy/dx Problem in picture below Homework Equations The Attempt at a Solution [PLAIN]http://img28.imageshack.us/img28/7162/76013837.png The answer for this is dy/dx = -cos\theta sin\theta + (1-sin\theta)cos\theta/-cos^2\theta - (1-sin/theta)sin\theta I cannot figure...

I took the divergence of the function 1/r2\widehat{r} in spherical coordinate system and immediately got the answer as zero, but when I do it in cartesian coordiantes I get the answer as 5/r3. for \widehat{r} I used (xi+yj+zk)/(x2+y2+z2)1/2 what am i missing?

Hey, I've been stuck on this question for quite a while now: Homework Statement 1a. Write down an expression for the position vector r in spherical polar coordinates. 1b. Show that for any function g(r) of r only, where r = |r|, the result \nabla x [g(r)r] = 0 is true. Why does this...

Homework Statement The diagram (omitted) shows the curve C with polar equation r=e^(\theta), where 0\le\theta\le(pi/2). Find the maximum distance of a point of C from the line \theta=(pi/2), giving the answer in exact form. The Attempt at a Solution I'm not really sure how to attack...

Homework Statement Evaluate by changining to polar coordinates : #19 in this picture http://i52.tinypic.com/2ngbt5z.jpg Homework Equations x = cos θ y = sin θ r^2 = x^2 + y^2 + z^2 ∫∫∫w f(x,y) dxdy = ∫from θ1 to θ2 ∫from r1 to r2 f(cosθ, sinθ) (r dr dθ)The Attempt at a Solution The first...

Homework Statement Evaluate by changining to polar coordinates : #19 in this picture http://i52.tinypic.com/2ngbt5z.jpg Homework Equations x = cos θ y = sin θ z = z r^2 = x^2 + y^2 + z^2 ∫∫∫w f(x,y) dxdy = ∫from θ1 to θ2 ∫from r1 to r2 f(cosθ, sinθ, z) (r* dr dθ)The Attempt at a Solution The...

Homework Statement Consider two non-identical, non-interacting particles of mass M that are constrained to move on a circle of radius R. Write down the Schrodinger equation for this problem and find the eigenfunctions and energy levels of this system. Homework Equations (see below)...

Homework Statement Evaluate \int\intD(x+2y)dA, where D is the region bounded by the parabolas y=2x2 and y=1+x2Homework Equations dA = r*drd\vartheta r2=x2+y2 The Attempt at a Solution Well, I know I need to put D into polar coordinates, but I'm lost on this...

Link: http://imageshack.us/photo/my-images/39/18463212.jpg/ This is a very long problem so I drew it to make things simpler. Part a) tells me to set up a double integral in polar coordinates giving the total population of the city. I have the following: 2π...4 ∫...∫ δ(r, θ) r dr...

Homework Statement The problem and answers are given in full through the following image: http://ekdhl.net/files/mechanics.JPGHomework Equations Equations 2/13 and 2/14 are these: \textbf{v} = r'e_{r} + r\theta 'e_{\theta} \textbf{a} = (r''-r\theta '^{2})e_{r} + (\theta ''r + 2r'\theta...

The question is: "In polar coordinates, what is the impedance of a circuit that has an admittance of 7.09 millisiemens at 45 degrees?" The official answer is: "141 ohms at an angle of -45 degrees". I don't understand this. 7.09 millisiemens is 141 ohms, and the positive phase angle...

Hi all I'm trying to find out how to draw a curve in polar coordinates. Can anyone help me with a book or something and help me find out how to draw curves in polar coordinates?