What is Polar: Definition and 1000 Discussions

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  1. N

    Points of intersection with polar equations

    Homework Statement I have to find all of the points of intersection of the curves... r2 = sin(2θ) r2 = cos(2θ) The Attempt at a Solution sin(2θ) = cos(2θ) 2sinθcosθ = cos2θ - sin2θ 2sinθcosθ - cos2θ = -sin2θ cosθ(2sinθ - cosθ) = -sin2θ This is where I'm having a problem, I'm...
  2. A

    Evaluate the double integral by converting to polar coordinates

    Homework Statement Convert to polar coordinates to evaluate \int^{2}_{0}\int^{\sqrt(2x-x^2)}_{0}{\sqrt(x^2+y^2)}dydxThe Attempt at a Solution Really I'm just not sure how to convert the limits of integration. I know \sqrt(2x-x^2) is a half-circle with radius 1, but I'm not really sure where...
  3. R

    Changing equilibrium equations from cartesian to polar

    Homework Statement Transform the equilibrium equations from cartesian to polar coordinates using x = rcos(theta) and y = rsin(theta): \frac{\partial\sigma_{xx}}{\partial{x}} + \frac{\partial\sigma_{xy}}{\partial{y}} = 0 \frac{\partial\sigma_{yx}}{\partial{x}} +...
  4. N

    Intersection pts of polar equations

    Homework Statement I have to find the area of the region that lies inside the curves: r = sin(θ) r = sin(2θ) The Attempt at a Solution I'm assuming the first step would be to find the points of intersection so I know WHERE to integrate from/to, so I set the equations equal to each...
  5. S

    Third derivative and polar coordinates

    I'm studying for a maths test. I know that the second derivative of the position R(t) of a particle moving in the plane, in polar coordinates, is (r''-r(\vartheta')2)er + (r\vartheta''+2r'\vartheta')eo. o = \vartheta How to differentiate this to find R'''(t), in polar coordinates and...
  6. D

    Equiangularity of a Polar Equation

    Homework Statement Show that the equation below connects the point (r_{0}, \theta_{0}) to the point (r_{1}, \theta_{1}), \theta_{0}\neq\theta_{1}, along a curve that everywhere forms the same angle with the rays \theta=constant. And here's the equation. I can't get the Latex to work... no...
  7. S

    Confused on double integral in polar cords

    Homework Statement Use polar coordinates to find the volume of the solid enclosed by the hyperboloid -x^2-y^2+z^2=1 and the plane z=2. The Attempt at a Solution Solving for z of the equation of the hyperboloid I find z = Sqrt(1 + x^2 + y^2). Letting z = 2 to determine the curve of...
  8. P

    Continuum Mechanics Homework - Vector Field in Polar Coordinates

    Hi, so I scanned an image of the problem statement and my attempt at the solution. I don't know if I am headed in the right direction and need some guidance. This is my first post ever and I hope I am doing this properly. Thank you for any help you guys can provide.
  9. T

    Forgetting my inverse tangent, polar form of compelx number ASTC

    Homework Statement Find the polar form of 2i − 1 Finding polar form is easy r(cosx + isinx) call the real part a and imaginary part b r = sqrt(a+b) theta = arctan (-2) = - 63.43 This is the wrong angle for theta as it's 116.57 (which is 180 - 64.43), and I guess this if...
  10. S

    Double integral, polar coordinates

    Homework Statement Evaluate \int\intT (x^2+y^2) dA, where T is the triangle with the vertices (0,0)(1,0)(1,1) Homework Equations The Attempt at a Solution \int d\theta \int r^3 dr Thats how far I got, not really sure about boundries on r. First integrals boundrie should be 0 to pi/4. Is...
  11. E

    How to solve the Laplace equation in a half disk with given boundary conditions?

    Homework Statement Solve the Laplace equation: delta u = d2u/dx2+d2u/dy2 inside the half disk 0<r<R, 0<phi<pi Temperature on the bottom side of the disk is zero, u(x,y=0)=0. Temperature on the upper side of the disk is u(r=R, theta) = u0(phi), 0<phi<pi Homework Equations I'm...
  12. W

    Solving for the Fourth Root of i in Polar Form

    Homework Statement evaluate i^1/4 Homework Equations - The Attempt at a Solution don't know how to find the angle on argd
  13. A

    Laplace solution in polar coordinates

    Hello, its been a pleasure finding you:smile: I have an asignment due to the end of this week and due to some problems, i hadn't found time to get to it so far. I have to calculate the exact solution of the Laplace equation in polar coordinates, in a hollow disk in the domain Ω where...
  14. Loren Booda

    Polar Populations: Similarities and Differences in Arctic Cultures

    How are the Arctic natives of America similar to those of Eurasia?
  15. I

    Question about converting x = pi/6 to polar form

    Homework Statement Convert t = pi/6 into polar form. Homework Equations x = r*cos(t) y = r*sin(t) The Attempt at a Solution t = pi/6 cos(t) = cos(pi/6) cos(t) = sqrt(3)/2 x/r = sqrt(3)/2 sqrt(3)r = 2x sqrt(3)sqrt(x^2 + y^2) = 2x sqrt(3x^2 + 3y^2) = 2x 3x^2 + 3y^2 = 4x^2...
  16. mnb96

    Polar coordinates: derivation from rotation group

    Hello, I posted a similar question long time ago, but after working on it I am still unable to arrive at a solution. Let's have a group of linear transformations (rotations in the xy-plane): R_\theta=\{ (\begin{array}{ccc} cos\theta & -sin\theta \\ sin\theta & cos\theta \end{array}) \\ ...
  17. K

    Circular Motion using polar coordinates - Mechanics

    Homework Statement A particle of mass m is constrained to slide on the inside of a vertical smooth semi- circular ring of radius r. The position of the particle is described by a polar coordinate system whose origin is at the centre of the circle with axes along the orthogonal unit vectors...
  18. P

    Polar to Cartesian conversion - how related?

    Homework Statement Find the cartesian equation for the curve r=csctheta The Attempt at a Solution I understand how to get the answer, by changing it to r=1/sin, and then rsin=1, and then since y=rsin, then y=1. What I'm not understanding is the relationship between y=1 an r=csc. I...
  19. L

    Dynamics with Polar coordinates

    Hey guys, I have attached the question with the diagram. So far i have found my magnitude of velocity = 90mm/s. im just really stuck now, i can't find my angle to find my components Vr and V(theta) I also know that you can solve this problem by finding a relationship between theta and "r"...
  20. W

    What is the polar form of the complex number 3-4i

    Homework Statement What is the polar form of the complex number 3-4i? Homework Equations z=r*cos(theta)+i*r*sin(theta) The Attempt at a Solution 5(cos(arctan(-4/3))-i*sin(arctan(-4/3))) This is what I thought the correct answer would be, but it was a multiple choice quiz and...
  21. M

    Calculus Problems, triple integral and polar coordinates stuff

    Hi I have a homework set due this week, 14 problems, I have done 11 of them, but these 3 are giving me trouble, help would be great :) Homework Statement 1.A cylindrical drill with radius 4 is used to bore a hole through the center of a sphere of radius 8. Find the volume of the ring shaped...
  22. V

    Factoring and Plotting a Polar Equation

    Homework Statement The question is: Factor and Plot the polar equation r^2-r+(1/4)sin^2 4 theta Homework Equations N/A The Attempt at a Solution I have no idea how to do this.
  23. P

    Straight Line from polar co-ordinates

    Hi All, This is my first post. I am an Electronics Engineer and came by this great forum while searching something for my presently running project. Could anyone please help me with the following: I have two points A(magnitude1,phase1[deg]) and B(magnitude2,phase2[deg]) on the input side...
  24. C

    Finding the area enclosed by curves in polar form

    Homework Statement a) r=a(2+ cos(\theta)) Find the area of the region enclosed by the curve giving answers in terms of \pi and a b) Show that the area enclosed by the loop r=2(1-sin(\theta))\sqrt{cos(\theta)} is \frac{16}{3} and show that the initial line divides the area...
  25. D

    Globular clusters cylindrical polar coordinates

    Homework Statement Two globular clusters A and B have cylindrical polar coordinates relative to the centre of the galaxy (r, z, Ø) given by A = (5,2,15°) and B= (4.6,65°), where the r and z coordinates are in kiloparsecs. Homework Equations Find a and b the position vectors of each...
  26. C

    What is the Area Between Two Polar Curves?

    Homework Statement Find the area between the two curves: r=2sin(\theta), r=2(1-sin(\theta)) Homework Equations A=\frac{1}{2} \int_{\beta}^{\alpha} r^2 d\theta The Attempt at a Solution I've got the points of intersection at (1,\frac{1}{6}\pi) and...
  27. 8

    Double integral transforming into polar coordinates

    Homework Statement By transforming to polar coordinates, evaluate the following: \int^{a}_{-a}\int^{\sqrt{}{{a^2}-{x^2}}}_{-\sqrt{{a^2}-{x^2}}}dydx Homework Equations The Attempt at a Solution I can get the right answer to this but only after guessing that the inner limits...
  28. T

    Imaginary Numbers to Polar form

    Homework Statement (1+i)i = reiθ Find the real values of r and θ. The Attempt at a Solution Well, after doing a similar(ish) question I decided taking logs would be a good start: i loge(1+i) = loger + iθ From here, I have no idea where to go. Using a power of i is killing me...
  29. C

    Finding the area enclosed by curves in polar form

    Homework Statement a) Find the area enclosed by the curve r=2+3cos(\theta). b) Find the area enclosed by the curve (x^2+y^2)^3=y^4 (after converting to polar form) Homework Equations The general equation for the area of a sector of curve: A=\frac{1}{2} \int_{\beta}^{\alpha} r^2...
  30. L

    Which would be the stronger nucleophile in a polar aprotic solvent?

    Homework Statement Which would be the stronger nucleophile in a polar aprotic solvent? a) H2O or H2S b) (CH3)3P or (CH3)3NHomework Equations The Attempt at a Solution I'm really confused because in my book, it says that in protic solvents, the larger atoms (I-) are stronger nucleophiles than...
  31. J

    Angle of intersection: polar versus cartesian

    Is it correct that the angle of intersection of two curves is the same in x,y coordinates as in r,theta coordinates? If so, why is this?
  32. S

    Green's Theorem and polar coordinates

    Homework Statement Using Green's Theorem, (Integral over C) -y^2 dx + x^2 dy=____________ with C: x=cos t y=sin t (t from 0-->2pi) Homework Equations (Integral over C) Pdx + Qdy=(Double integral over D) ((partial of Q w.r.t. x)-(partial of P w.r.t. y))dxdyThe Attempt at a Solution I'm...
  33. C

    Convert x^2+y^2=4y-2x to Polar Equation

    Homework Statement Establish an equation in polar coordinates for the curve x^2+y^2=4y-2x Homework Equations n/a The Attempt at a Solution I know that x^2+y^2=r^2 so I used substitution, and now have r^2=4y-2x. Now this next part, I'm really not sure if I'm allowed to do this... i...
  34. W

    What makes a Molecule Polar? Dipole?

    Hi, 1st year chem guy here...I'm missing this idea. Is it all based upon Electronegativity? I can see why HBr or HCl and other 2 atom compounds would be polar. 2 atoms with different charges or even sizes creating an un-even pull. I'm guessing H2O is polar as the 4 remaining electrons on...
  35. G

    Evaluate double integral by changing to polar coordinates

    what'd I do wrong? I was told I didn't include the bound y<=x but that still hasn't helped me figure out where I miss stepped thanks -Ben
  36. G

    Double Integrals: cartesian -> polar and solve

    Double Integrals: cartesian --> polar and solve here is everything: #19: I am stuck...This is to be solved using cylindrical polar coordinates and a double integral. I understand simpler ones such as find the volume of the solid under the cone z= sqrt(x^2 + Y^2) and above the disk (x^2 + y^2...
  37. H

    Converting between cartesian and polar coordinates

    Homework Statement Particle is moving with velocity v= ui along the line y=2. What is its v in polar coordinates Homework Equations The Attempt at a Solution I think I'm being really stupid here but not entirely sure where to start. If you integrate to find position you have it as...
  38. D

    Surface Integrals in Polar Coordinates

    Homework Statement Find the area cut from the surface z = 2xy by the cylinder x^2 + y^2 = 6. [Hint: Set up the integral using rectangular coodinates, then switch to polar coordinates.] Homework Equations A = \iint \sqrt{{z_x}^2+{z_y}^2+1}dxdy = \iint...
  39. R

    Understanding the Physical Significance of Polar Moment of Inertia

    Hi guys Can anyone explain what is physical significance polar moment of inertia. Well i know it's formula e.g in case of shafts but not it's physical meaning.
  40. B

    Chemistry Questions on polar and nonpolar molecules

    Some chem students need help with homework problems similar to these later this week. and I want to make sure I've got the concepts down before I try to explain anything. This is for introductory chemistry. 1. Can a molecule have only nonpolar bonds and have a dipole? My first thought was...
  41. D

    Exploring Polar Coordinates: Showing F(r) and Integral Equations

    Homework Statement Let the curve C be paramatized into polar coordinates given by: \[r\left( t \right)=\left( r\left( t \right)\cos \theta \left( t \right),\,\,\,\,\,r\left( t \right)\sin \theta \left( t \right) \right),\,\,\,\,\,a\le t\le b\] where r and theta is continuous derivatives...
  42. R

    Double Integrals in polar coordinates setup

    Use polar coordinates to find the volume of the given solid inside the sphere x^2 +y^2 + z^2 = 16 and outside the cylinder x^2 +y^2 = 4 I know how to set up the the integral to find the volume inside the sphere but I am not quite sure how to also find the outside of the cylinder. Can someone...
  43. C

    Cartesian to Polar Integral: Evaluate

    Homework Statement Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. int(-1to1)int((sqrt(1-y^2))to(sqrt(1-y))[x^2+y^2]dxdy Homework Equations x=rcostheta y=rsintheta The Attempt at a Solution...
  44. P

    Buncha polar graph/integral stuff

    Homework Statement 1. put in polar form x2+y2-3x+4y=0 my work: x2+y2=3x-4y r2=3rcos\theta-4rsin\theta r=3cos\theta-4sin\theta 2. put in cartesian form r2=tan\theta r2=y/x r=sqrt(y/x) 3. find slope at \theta=\pi/2 then find points where tangent line is horizontal...
  45. P

    Double integrals using polar coordinates

    Homework Statement Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x^2 + y^2 = 4 and x^2 - 2x + y^2 = 0 Homework Equations The Attempt at a Solution for my integral i got 0<= theta <=pi/2 for the theta...
  46. P

    Find the area of the region inside both polar graphs

    Homework Statement r1= 1+sin(theta) r2= 5sin(theta) Homework Equations see above? The Attempt at a Solution totally stumped. usually i would set the two curves equal to each other, but i have no idea how to do that. using my ti-89's solve function just gives me a weird answer...
  47. T

    Double Polar Integral Conversion and Integration on a Disk with Radius 3

    Homework Statement Convert to polar integral and integrate. \int_{D}\int xy dA where D is the disk with the center origin and radius 3. I am not sure about the limits. I know that x = rcos(\theta), y = rsin(\theta), dA = rdr*d\theta
  48. J

    Exploring Polar Rose: Where Did I Go Wrong?

    I'm trying to express the polar rose as an implicit function: r(t)=sin t x = sin t * cos t y = sin^2 t Since sin t * cos t = (1/2) * sin 2t and sin^2 t = (1/2) * (1-cos 2t) (2x)^2 + (1-2y)^2 = 1 4x^2 -4y + 4y^2 = 0 When I plot this, Maple plots a circle, where have I gone wrong?
  49. V

    Polar Coordinates Homework: Find Equations & Solutions

    Homework Statement Give the equations for the plane polar unit vectors ^ ^ r and (theta) - - in terms of the Cartesian unit vectors ^ and ^ and hence show that i j - - ^...
  50. S

    Important points in polar coordinates?

    I am going to have a test on polar coordinates next week. What are the most important things to remember?
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