What is Polar: Definition and 1000 Discussions

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  1. I

    Expressing the limits of integration for radius in polar coordinates

    i'm trying to integrate some some function bounded by the x-y domain of x2+y2=6y which is a circle on the x-y plane shifted upward where the outer part of the circle is 6. i'm trying to integrate a double integral.. ∫∫f(x)rdrdθ i don't know how to express my limits of integration for r...
  2. T

    Double integral over a region needing polar coordinates.

    1. Evaluate the double integral ∫∫arctan(y/x) dA by converting to polar coordinates over the Region R= { (x,y) | 1≤x^2+y^2≤4 , 0≤y≤x } My attempt at solving Converting to polar using x=rcosθ and y=rsinθ I get ∫∫arctan(tan(θ))r drdθ I understand that I have to integrate first with respect...
  3. PsychonautQQ

    Optimizing Integration: Converting to Polar Coordinates

    Homework Statement Evaluate the integral by changing to polar coordinates. Double Integral: (x^2+y^2)dydx, where dy is bound between 0 and (4-x^2)^(1/2) and dx is between and -2 and 2 The Attempt at a Solution okay so I can turn this into Double Integral: (r^2)rdrdθ My question is...
  4. J

    Can elements replace Hydrogen in polar molecules & act similarly?

    Today in 9th grade ADV Biology, we learned about how the two Hydrogen atoms in a Water molecule are relatively positive compared to the Oxygen atom. This is because the Oxygen's pull on Hydrogen's electron is greater than the Hydrogen's, or that its Electronegativity is greater. This unequal...
  5. R

    Polar integration - Length and Area of curve

    The area of a polar curve is given by A=(1/2)∫ r2 d (theta). this can be interpreted as δA= ∏r2δ(theta)/2∏ (treating the area element as the area of a sector of a circle with angle δ(theta).) taking limit of δ(theta)→0, dA= ∏r2 d(theta)/2∏=1/2 (r2d(theta) ) there fore A=1/2∫r2 d(theta)...
  6. PsychonautQQ

    Finding volume in Polar Coordinates

    Homework Statement Find the volume of the wedge-shaped region contained in the cylinder x^2+y^2=9 bounded by the plane z=x and below by the xy planeHomework Equations The Attempt at a Solution So it seems a common theme for me I have a hard time finding the limits of integration for the dθ term...
  7. PsychonautQQ

    Evaluating an Integral in Polar Coordinates

    Homework Statement Evalutate the double integral sin(x^2+y^2)dA between the region 1≥x^2+y^2≥49 The Attempt at a Solution so r^2 = x^2 + y^2 dA = rdrdθ so I can turn this into double integral sin(r^2)rdrdθ where the inner integral integrated with respect to dr goes from 1 to 7...
  8. N

    MHB Converting from Cartesian to polar form

    another question: convert $|\frac{1-i}{3}|$ to polar form i am getting $\frac{\sqrt{2}}{3} e^{\frac{i\pi}{4}}$ but the solutions say: $e^{\frac{-i\pi}{4}}$ i did $ x = r\cos(\theta)$ and $y=r\sin(\theta)$ so $\frac{1}{3} = {\frac{\sqrt{2}}{3}}\cos(\theta)$ $\frac{1}{3} = \cos(\theta)$ And...
  9. 2

    Comp Sci [fortran90] cartesian to polar coordinate

    Write a short FORTRAN90 subroutine to convert Cartesian coordinates (x, y, z) to spherical polar coordinates (r, q, f) using • Write a FORTRAN90 program which uses this subroutine to convert the following (x, y, z) coordinates which are read from a text file and stored within a single vector...
  10. B

    MHB Solving a Polar System Integral - Can You Help?

    I have a task to solve it in polar system: x²=4y-y²; x²=8y-y²; y=x; x=0. So in polar: r=4sin phi; r=8sin phi; phi=pi/4; phi=pi/2. The integral - int(from pi/4 to pi/2) d phi int(from 4 sin phi to 8 sin phi) r dr. My answer is 3pi - 1/4 but seems like its not true. Somebody has another answer?
  11. J

    Lagrangian in cartesian and polar

    Homework Statement Consider the following Lagrangian in Cartesian coordinates: L(x, y, x', y') = 12 (x^ 2 + y^2) -sqrt(x^2 + y^2) (a) Write the Lagrange equations of motion, and show that x = cos(t); y =sin(t) is a solution. (b) Changing from Cartesian to polar coordinates, x = r...
  12. H

    Finding dS in Polar: dx, dy, and More

    Ok, so we know that x=rcos(\theta) So what is dx? *** Furthermore, can I get dS in polar by finding dx and dy in polar and then substituting them into dS for rectangular? Is there an easier way to solve for dS in polar?
  13. N

    MHB What is the correct way to convert to polar form?

    I started of with attempting to convert the numerator first $ | 1 + i | = \sqrt{1^2+i^2}$ $= \sqrt{1-1} = 0$ ? this is wrong obviously, i don't see why its $\sqrt{2}$ for the second part $ |\sqrt{3} - i|= \sqrt{3+1} = 2$ $ x = r \cos\theta$ $ y = r\sin\theta$ $x = 2\cos\theta$ $...
  14. M

    Graphing with polar coordinates Problem

    Homework Statement Draw the graph of r = 1/2 + cos(theta) Homework Equations The equation is itself given in the question. It is a Limacon. The Attempt at a Solution Step-1 ---> Max. value of r is 1/2 + 1 = 3/2 [ at cos (0) ] Min. value of r is 1/2 - 1...
  15. M

    What is the Polar Moment of Inertia and How is it Calculated?

    I know some of you may have given up on me understanding moment of inertia/second moment of area, but here is another problem. I am using the this table to get the equations for the polar moment of area of a hemicircle around the x-axis, then I am applying the parallel axis theorem to find the...
  16. P

    Understanding Polar Coordinate Unit Vectors

    Homework Statement The Attempt at a Solution I already know how to do a), but what I am wondering is what the question means by expressing position in the terms of those unit vectors.
  17. E

    Angular Momentum In Polar Coordinates

    Homework Statement Consider a planet orbiting the fixed sun. Take the plane of the planet's orbit to be the xy-plane, with the sun at the origin, and label the planet's position by polar coordinates (r, \theta). (a) Show that the planet's angular momentum has magnitude L = mr^2 \omega, where...
  18. I

    Re: Entropy - Actually a question about working in Polar Coordinates

    show that \frac{d\hat{r}}{dt}=\hat{θ}\dot{θ} also, \frac{d\hat{θ}}{dt}=-\dot{θ}r i've tried finding the relationship between r and theta via turning it into Cartesian coord.s, and I've tried the S=theta r but still no luck. S=theta r dS/dt=d(theta)/dt r which is similar to the RHS...
  19. Y

    Laplace equation in polar coordinates.

    \nabla^2 u=\frac {\partial ^2 u}{\partial x^2}+\frac {\partial ^2 u}{\partial y^2}=\frac {\partial ^2 u}{\partial r^2}+\frac{1}{r}\frac {\partial u}{\partial r}+\frac{1}{r^2}\frac {\partial ^2 u}{\partial \theta^2} I want to verify ##u=u(r,\theta)##, not ##u(x,y)## Because for ##u(x,y)##, it...
  20. P

    Sharp values of wavefunction in polar coordinates

    Homework Statement Consider the function in polar coordinates ψ(r,θ,\phi) = R(r)sinθe^{i\phi} Show by direct calculation that ψ returns sharp values of the magnitude and z-component of the orbital angular momentum for any radial function R(r). What are these sharp values? The Attempt at a...
  21. E

    Solving a Polar Plot with r^2 Area Problem: r^2=8cos(2θ)

    Area problem regarding r^2=8cos(2θ) and some other curve. I don't understand how to plot this. I started off with a table of values. I get confused when θ = π/2. I thought it would give r^2 = -8. But looking at mathematica it gives a leminiscate that crosses the origin. How come? Is it...
  22. A

    How Do You Graph Polar Coordinates in Gnuplot?

    I am brand new to Gnuplot and am having a problem trying to figure out how to graph in Polar Coordinates for a school assignment. What bothers me is we didn't go over other coordinate systems like Polar or Parametric at all for Gnuplot, and the internet tutorials I find seem to assume some basic...
  23. M

    What Is the Path Traced by a Point on a Rolling Bicycle Wheel?

    Hum I don't know if it is the right section, I mean I am taking cal 3 but this doesn't really uses calculus... anyway I'll post it here due to the nature of my class. Homework Statement A bicycle wheel has radius R. Let P be a point on the spoke of a wheel at a distance d from the center...
  24. PsychonautQQ

    What is the Area Between Two Polar Curves?

    Homework Statement Find the area inside r = 9sinθ but outside r = 2 Homework Equations Area = 1/2(Integral of (f(θ)^2 - g(θ)^2)dθ The Attempt at a Solution f(θ)^2 = 81sin^2θ = 81((1-cos(2θ))/2) g(θ)^2 = 4 f(θ)^2 - g(θ)^2 = 36.5 - cos(2θ)/2 integral of (36.5 -...
  25. PsychonautQQ

    Finding arc length of polar Curve

    Homework Statement Find the arc length of polar curve 9+9cosθ Homework Equations L = integral of sqrt(r^2 + (dr/dθ)^2 dθ dr/dθ = -9sinθ r = 9+9cosθ )The Attempt at a Solution 1. Simplifying the integral r^2 = (9+9cosθ^2) = 81 +162cosθ + 81cos^2(θ) (dr/dθ)^2 = 81sin^2(θ)...
  26. PsychonautQQ

    Finding area between two curves Polar Coordinates

    Homework Statement Find the area inside the circle r = 3sinθ and outside the carotid r = 1 + sinθ The Attempt at a Solution Alright so I graphed it and found that they intersect at ∏/6 and 5∏/6. I can't think of a good way to approach the problem. The carotid has some of it's area...
  27. PsychonautQQ

    Finding center of circle with Polar Coordinates

    Homework Statement r=7sin(∅) find the center of the circle in Cartesian coordinates and the radius of the circle The Attempt at a Solution My math teacher is impossible to understand >.< and then the stupid homework is online and crap blah this class but I REALLY want to understand the material...
  28. PsychonautQQ

    Polar Coordinates inverse Radius

    Homework Statement I have to turn this homework in online... I just want someone to check my work Convert from Cartesian coordinates to Polar coordinates (-1,-sqrt(3)) if r > 0 and if r < 0. Homework Equations The Attempt at a Solution if r > 0 then I believe the answer is...
  29. PsychonautQQ

    Polar Coordinates Tangent line

    Homework Statement I don't know how to make theta so ∅ = theta. find the slope of the tangent line at r = sin(6∅) when ∅ = pi/12 Homework Equations y=rsin(6∅) x=rcos(6∅) r=sin(6∅) tangent line equation y-y' = m(x-x') m = dy/dx The Attempt at a Solution when ∅ = pi/12 then...
  30. N

    Changing order of integration (double) in polar coord

    Homework Statement Change the order of the limits of integration of the following double integral and evaluate. Homework Equations \int_{0}^\frac{\pi}{2} \int_{0}^{cos(\theta)} cos(\theta)\,dr\,d\theta The Attempt at a Solution Evaluating as it is, I arrive an answer of...
  31. M

    Volume integration where the radius limit depends on the polar angle

    Hi, I want to calculate a volume integral of a function f(r,theta). The limits for azimuthal and polar angle is of course 0-2*pi and 0-pi, respectively. But the limits for the radius is 0 to an expression depending on the polar angle. Can I simply first integrate the r-part, say from r^4 to...
  32. A

    I'm pretty sure these molecules are polar

    Are there not dipole-dipole interactions between CHBr3, CH3Br, CH3Cl, and CHCl3? Assume they are all separate pure substances. My professor today said that the only intermolecular forces present were dispersion forces. Are the dipole attractions negligible due to fact they are too weak?
  33. M

    Unit vectors in polar co ordinates

    I have two questions 1) How the radial and traversal unit vectors are vector funcitons of scalar variable θ (angle between the position vector and polar axis. 2) To find velocity and accleration in polar co ordinates why it is need to write the traversal and radial unit vectors by...
  34. M

    Dipole of Magnetic field in polar coordinates

    Homework Statement Hi everybody... i have a bad problem with my brain: starting from the Vectorial form of the magnetic dipole: \vec{B}(\vec{r}) =\frac{\mu_0}{4 \pi} \frac{3 \vec{r} ( \vec{r} \cdot \vec{m}) - r^2 \vec{m}}{r^5} Homework Equations i want to derive the spherical...
  35. M

    Find the shortest path between two points in polar coordinates

    Homework Statement Find the shortest distance between two points using polar coordinates, ie, using them as a line element: ds^2 = dr^2 + r^2 dθ^2Homework Equations For an integral I = ∫f Euler-Lagrange Eq must hold df/dθ - d/dr(df/dθ') = 0 The Attempt at a Solution f = ds = √(1 + (r *...
  36. V

    Polar unit vectors form a basis?

    I keep reading about polar unit vectors, and I am a bit confused by what they mean. In the way I like to think about it, the n-tuple representation of a vector space is just a "list" of elements from the field that I have to combine (a.k.a. perform multiplication) with the n vectors in some...
  37. D

    Kernal density estimate in polar coordinates.

    Hi, I have a data set containing values for power and direction. I would like to produce a probability density estimate. The data can have multiple sources so I want to use a nonparametric method. I work in python which has a method for kernal density estimation (KDE), which I think should be...
  38. S

    Fortran [Fortran90] fdtd in polar coordinates, got infinity output

    hi all, attached here is my code for 2d fdtd in polar coordinates, from 'numerical electromagnetic: the fdtd method (umran s inan, pg 94-96) written in fortran90. I have try a few approach I could think about to troubleshoot this code but the output is still infinity. Anybody here can give me...
  39. R

    How to find the limit if integration of polar curves?

    Homework Statement r=3+2cosθ Homework Equations The Attempt at a Solution The text shows that it's from 0 to 2pi. How did it come to those limits without graphing? I set r=o. What do I do from there?
  40. A

    How does non polar molecules dissolve?

    how does non polar solute dissolve in non polar solvent?
  41. MarkFL

    MHB Find Tangent Lines to Polar Graph: r=2-3sin(θ)

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  42. P

    Optics Question: How do I clean polar sheets?

    So right now I am working on an amature astronomy project to develop a simple lab about the sun's declination. I am borrowing the cheapets linear polarized sheets that I could find ... Because they are least 10 - 15 years old, I would really like to clean them, but I don't know what to use...
  43. I

    Double Integrals with Polar Coordinates

    Homework Statement Use polar coordinates to find the volume of the solid bounded by the paraboloid z = 47 - 5x2 - 5y2 and the plane z = 2. Homework Equations x2 + y2 = r2 x = rcosθ y = rsinθ The Attempt at a Solution I substituted the z = 2 into the equation given, 2 = 47 -...
  44. P

    Polar graphs really important and tangents

    Hi, I really need help with this as exam is tomorrow The question is to find the points on the cardioid r=a(1+costheta) where the tangents are perpendicular to the initial line here is the answer http://gyazo.com/e8b4cbd36f0ef71d0cdf13be256d8618 Why is pi not included in the...
  45. Fernando Revilla

    MHB Integration in polar coordinates

    I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.
  46. Saitama

    How Do You Convert Polar Coordinate Equations to Cartesian Form?

    Homework Statement For a curve in Cartesian form, show that \tan \phi = \frac{xy'-y}{x+yy'} Homework Equations The Attempt at a Solution According to the book notation, ##\phi## is the angle between the radius vector and tangent at any point of the curve. I know that ##\tan...
  47. C

    Line element under coordinate transformation to get polar form

    Homework Statement Hello Guys, I am reading Hobson's General Relativity and I have come across an exercise problem, part of which frustrates me: 3.20 (P. 91) In the 2-space with line element ds^2=\frac{dr^{2}+r^{2}d\theta^{2}}{r^{2}-a^{2}}-\frac{r^{2}dr^{2}}{{(r^{2}-a^{2})}^{2}} and...
  48. V

    Velocity Vector in Polar Coordinates (Kleppner p.30)

    In polar coordinates we have \vec{r} = r \hat{r} \Rightarrow \vec{v} = \frac{d}{dt}({r \hat{r}}) = \dot{r}\hat{r} + r \frac{d \hat{r}}{dt} . In the book Introduction to Mechanics, K & K says the right term is the component of velocity directed radially outward. (Surely a typo, as the left...
  49. S

    How to translate from polar to cartesian coordinates:

    How to translate r = 2 /(2 - cos(theta)) to cartesian coordinates: so far: r = 2 /(2 - cos(theta)) r = 2 /(2 - cos(theta)) |* (2 - cos(theta)) both sides r (2 - cos(theta))= 2 2*r - rcos(theta) = 2 | know x = rcos(theta) 2*r - x...
  50. J

    Line integral around a circle in polar coordinates

    I know that \oint_{C}\mathrm{d}\vec{l} = 0, for any closed curve C. But when i try to calculate the integral around the unit circle in polar coordinates, I get a result different from zero. Here is my approach : \oint_{C}\mathrm{d}\vec{l} = \int_{0}^{2\pi}\hat{\phi}\mathrm{d}\phi =...
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