What is Polar: Definition and 1000 Discussions

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  1. N

    Two Particle Schrodinger Equation in Polar Coordinates

    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)...
  2. S

    Polar decompostion of Hermitian Matrix

    Homework Statement I need the steps to follow when finding the polar decomposition of a hermitian matrix If someone could direct me to a website that would help, or put up an example here please. thanks :) Homework Equations The Attempt at a Solution
  3. W

    If the polar ice caps were to melt .

    If the polar ice caps were to melt... wouldn't the sea levels decrease? Water ice is less dense than liquid water, so the volume (and displacement of liquid water) is greater when its frozen. But when you melt that, the volume decreases, and some of the water that was initially displaced by...
  4. Z

    Equation of a Tangent Line to a Polar Curve

    I need to find the equation of the tangent line to the curve x=t4+1, y=t3+t; t=-1 I have already found that the slope of the line is -1 by finding (dy/dt)/(dx/dt) I just need to figure out how to solve for y1 and x1 Thanks in advance
  5. D

    Laplace in Polar Coordinates: Solving the Polar Coordinate Equation

    Homework Statement solve the polar coord equation Homework Equations Urr+(1/r)Ur+(1/r2)U\vartheta\vartheta=0; 1\leqr\leq2, 0\leq\vartheta\leq\pi/4 U(1,\vartheta)=0 U(2,\vartheta)=\vartheta U\vartheta(r,0)=0 U(\vartheta,\pi/4)=0 and has the form...
  6. E

    Double Integral in Polar Coordinates

    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...
  7. G

    How to Label Axes on a Polar Plot?

    If you were add axis labels to a polar plot what would you use for labels in place for a y-axis label and a x-axis label?
  8. B

    Setting up double integral for polar coordinates and integrating

    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...
  9. S

    Rectangular to Polar Conversion

    Homework Statement I need to convert this to polar form; anyone have any ideas where to start? Homework EquationsThe Attempt at a SolutionI know this is incorrect but I am a bit overwelmed on this one. any help would be wonderful! thanks! Homework Statement Homework Equations The Attempt at...
  10. A

    Understanding the Reciprocal Form of Sin and Cos in Polar Coordinates

    Homework Statement Prove this equation Homework Equations The Attempt at a Solution I almost get the answer. But I don't know why all of the sin and cos are in reciprocal form.
  11. X

    Mechanics problems, about the use of polar coordinates

    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...
  12. joema

    Polar coordinates of complex impedance

    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...
  13. A

    How to draw a curve in polar coordinates?

    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?
  14. F

    Why is there this pattern in the polar curves cos[at] U sin[at]

    Homework Statement Polar plot the following sin[t] U cos[t] sin[2t] U cos[2t] sin[3t] U cos[3t] sin[4t] U cos[4t] sin[5t] U cos[5t] Notice that cos[t] and sin[t] are the same graph rotated 90 degrees only? Interesting! Just like the cartesian graph. Now here is something more...
  15. G

    Polar Coordinates, Six-Pointed Star, and a Hexagon

    Homework Statement Hey I have to create a six-pointed star and a hexagon with polar coordinates using MATLAB. I don't need help with using MATLAB, I just need help with the math. Note that I don't really need to know how the math sense this assignment is for a CSE course. I just don't...
  16. N

    Transform explicit function to polar form

    Hello, I'am new here and happy to find this great forum! Here's my first question: there's an explicit function as follows: y=2.sin(x)-1 The transformation to polar form (r=3cos(\theta)) - x=r.cos(\theta) - y=r.sin(\theta) So I get: r.sin(\theta)=2.sin(r.cos(\theta))-1 Now you see...
  17. X

    Polar to cartesian coordinates for stream function

    Homework Statement Consider a velocity field where the radial and tangenetial components of velocity are V_r=0 and V_theta=cr, respectively, where c is a constant. Obtain the equations of the streamlines. Homework Equations x=rcos(theta) y=rsin(theta) The Attempt at a Solution I...
  18. N

    Finding the Smallest n for Real z^n in Complex Numbers

    I have solved part a, I just have no idea how to go about doing part b. If anybody could point me in the right direction, that would be greatly appreciated! Homework Statement a. Express z = \frac{1 + \sqrt{3}i}{-2 -2i} in the form rcis\theta b. What is the smallest positive integer n...
  19. H

    Solve Polar Coordinates: (-2*sqrt3) – (2*i) = 4*e^(i*7*pi/6)

    Question: Given (-2*sqrt3) – ( 2*i) = 4*e^(i*7*pi/6) Perform the following: (a) Convention I: angle go from (0) to 2*pi. (b) Convention II: angle goes from (-)*pi to (+)*pi. = = = = = = = = = = = = = = = = = = = = = = = = = = = Part (a): Convention I: angle go from (0) to...
  20. M

    Polar Form Confusion: Understand Damped & Driven Wave Amplitude

    Hello All, I'm reviewing some notes for a course and am confused by one step that they do. They are deriving an equation for the ampiltude of a wave that is being damped and driven by a force. I understand it all except for one step in which they state that: (\omega_{o}^{2} - \omega^{2}) -...
  21. D

    Polar moment of inertia/polar radius of gyration via integration

    Homework Statement Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with respect to point P. http://imgur.com/8Kc1S Homework Equations Jp = Ix + Iy Ix = &int y^2dA Iy = &int X^2dA The Attempt at a Solution A = 2(a/2)(a) +...
  22. M

    How Do You Determine the Key Angles for a Three-Leaf Rose in Polar Coordinates?

    I don't remember ANYTHING from this section when I took Trig but we're finding the area of curves in the polar coords. Looking at the book they give us this equation r=2cos3\theta I can see, and I know how to figure out its a 3 leaf "rose" symmetrical about the theta= zero axis, but I can't...
  23. M

    Find the Area in polar coordinates

    Homework Statement I am doing even problems in my book to study and i want to check this answer to see if it is right. q: Find the area enclosed by one leaf of the three-leaved rose r=sin3(theta) Homework Equations A= integral 1/2 r2 d(theta) The Attempt at a Solution i used the...
  24. O

    The work energy theorem in polar coordinates

    Homework Statement Mass m whirls on a frictionless table, held to circular motion by a string which passes through a hole in the table. The string is slowly pulled through the hole so that the radius of the circle changes from l1 to l2. Show that the work done in pulling the string equals...
  25. S

    Path Integral - Cartesian to Polar Coordinates

    Homework Statement Transform to polar coordinates and evaluate... \int^{a/\sqrt{2}}_{0} dx\int^{\sqrt{a^2-x^2}}_{x}\sqrt{x^2 + y^2}dy Homework Equations x^2 + y^2 = r^2 x = r cos \theta y = r sin \theta I've been struggling to make sense of this problem, it should be easy, I'm...
  26. H

    Converting Polar Triple Integral to Spherical One

    Homework Statement Evaluate the following triple integral by switching it to spherical coordinates? The integrand is r dzdrdθ The limits for the inner integral are 0 to r The limits for the middle integral are 0 to 3 The limits for the outer integral are 0 to 2π Homework Equations...
  27. R

    Solving Polar Equation r = θ + sin(2θ) for x = -2: Homework Problem

    Homework Statement Using this polar equation: r = \theta + sin(2\theta) Find the angle \theta that relates to the point on the curve when x = -2 I'm not sure where to start...but my guess is to convert the equation to another form...any help is appreciated.
  28. U

    Change to cartesian double integral to polar coordinates and evaluate

    Homework Statement integrate 1/((1+x^2+y^2)^2) dx dy Both x and y going from 0 to infinity Homework Equations x^2+y^2 =r The Attempt at a Solution After that I get 1/(1+r^2) ^2 Cannot visualize the function, do not know what the limits are. If I could have any help it...
  29. S

    Volume of Polar Solids with Cross Sections

    Homework Statement I'm trying to find the volume of a Polar shape with semi-circular cross sections. Since it is a polar graph, does that mean the cross sections are to be swept across the graph from 0 to 2π in triangular sections? I'm aiming to create one side of a three...
  30. R

    What is the approach for integrating 2θsin2θ in a polar equation problem?

    Homework Statement r = \theta + sin(2\theta) for 0 \le \theta \le \pi a. Find the area bounded by the curve and the x-axis b. Find the angle \theta that corresponds to the point on the curve with x-coordinate -2 c. For \frac{\pi}{3} < \theta <\frac{2\pi}{3} ...
  31. Z

    Evaluate the iterated integral by converting to polar coordinates

    Homework Statement Where the region is: D = {(x,y)| 0\leqx\leq2;0\leqy\leq\sqrt{}2x-x^2} Double integral over region D with f(x,y) = \sqrt{}x^2+y^2 and respect to dA Homework Equations Trig. Identities: x = rcos(theta) y = rsin(theta) x^2+y^2 = r^2The Attempt at a Solution First, I graphed...
  32. cryora

    Polar Coordinate Area between two curves

    Homework Statement Find the area enclosed by the curves: r=\sqrt(3)cos(\theta) and r=sin(\theta) Homework Equations The area between two polar curves is given by: A=(1/2)\int{R^2 - r^2dr} where R is the larger function and r is the smaller function over an interval. The Attempt at a...
  33. J

    Length of the day change if polar ice caps melt.

    Homework Statement Question requires assumption that the Earth is spherical, all the ice is located at the axis of rotation. Basically if all the ice was to melt uniformally over the surface of the earth, what would be the change in the length of the day? Mass of ice: m= 2.3*10^19 kg Mass of...
  34. F

    Is there actually such thing as center of mass in polar coordinates?

    Homework Statement Or any coordinates really. In the normal Cartesian plane, the center of mass is defined from the x, y , and z distance as follows \bar{x} = \frac{1}{Area(R)}\iint_R x dA \bar{y} = \frac{1}{Area(R)}\iint_R y dA \bar{z} = \frac{1}{Area(R)}\iint_R z dA Now is there one for...
  35. X

    Converting the Laplacian into polar coordinates

    I need to convert the Laplacian in two dimensions to polar coordinates. \nabla^2 u=\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2} I am having problems with computing the second derivatives using the chain rule. For example, the first derivative with respect to x...
  36. S

    Finding area between polar curves

    Homework Statement Find the area of the region inside the lemniscate r^2 = 2sin(2\theta) and outside the circle r = 1 It sucks because I wish I could post a graph, but the graph on my calculator looks like a circle around the origin with radius 1, with an infinity symbol going diagonally...
  37. T

    What is the graph of a polar curve with specific r and theta values?

    Homework Statement Sketch a graph of the polar curve whose points satisfy the following: As theta increases from 0 to pi/2, r decreases from 4 to 2. As theta increases from pi/2 to pi, r decreases from 2 to 0. As theta increases from pi to 3pi/2, r decreases from 0 to -1. As theta increases...
  38. Q

    Integration changing to polar coordinates

    Homework Statement http://i1115.photobucket.com/albums/k554/shirozack/polarchange.jpg The Attempt at a Solution why is the limits for the polar angle pi/3 to pi/2? shouldn't it be pi/2 to pi/3? because x goes from 0 to 1/2, since x =rcos(T) 0 = cos(T) , T = pi/2 1/2 =...
  39. P

    Double integral conversion to polar coordinates

    i have no idea how to use the functions on here to ill try my best. \int(upper bound a lower bound 0)\int(upper bound 0 lower bound -sqrt(a2-y2) of the function x2y.dxdy firstly trying to map it out... i think its the quarter circle in the top left quadrant with boundaries 0 to a along...
  40. Z

    Parametric to Polar Conversion

    Homework Statement Convert the two equations x=x(t) and y=y(t) to a polar equation of the form r=r(\theta) Homework Equations x=r*cos(\theta) y=r*sin(\theta) r^{2}=x^{2}+y^2 The Attempt at a Solution Perhaps I'm over-thinking this, but in order to eliminate the parameter t, I...
  41. J

    Solving Dynamical Systems with Polar Coordinates

    I've been solving some dynamical systems and have had to convert some of the ode's to polar co-ordinates, I've been using the formula r\dot{r} =x\dot{x} y\dot{y} to easily solve for \dot{r} I'm just wondering if there's an easy to use formula to find \dot{\theta} I've been trying...
  42. R

    Cauchy-riemann using polar co-ordinates

    I've been given a function U(x,y) where f(z) = U(x,y) + iV(x,y) and asked to check if it is harmonic and then work out what V(x,y) is U(x,y) = \frac{y}{(1 - x)^{2} + y^{2}} To check if it is harmonic I can see if d2U/dx2 + d2U/dy2 = 0 I've tried differentiating and it's fairly arduous, so...
  43. T

    Find Area with Polar Coordinates: Help for Exams

    Hello, I actually have an exam coming on series, sequences, polar coordinates and parametric equations. The only major thing I'm having problems with is finding area with polar coordinates. Especially when it comes to finding the "area under both curves" for example:"Find the area under both...
  44. L

    Parametric Paraboloid In Polar Coordinates

    I just want to see if my logic is sound here. If we have the paraboloid z=x2+y2 from z=0 to z=1, and I wanted a parametric form of that I think this should work for polar coordinates: \vec{r}(u,v)=(vcosu,vsinu,v^{2}) u:[0..2\pi],v:[0..1] Does this make sense?
  45. T

    Calculus Help - Polar Coordinated

    Homework Statement 1. Consider the graph of a function defined parametrically by x = g(t) and y = h(t). The slope of the curve at point (g(t), h(t)) is given by h′(t) g′(t) . Use this result and the standard parametrization of a polar curve r = f(delta) given above to show that the slope...
  46. S

    Double Integral in Polar Coordinates

    Homework Statement Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x2 + y2 = 256 and x2 - 16x + y2 = 0. Homework Equations The Attempt at a Solution Finding the intervals of integration for the polar coordinates. From the...
  47. C

    Rewrite polar equation as Cartesian (trig identities)

    Homework Statement x=2acos(theta- pi/3)cos(theta) y=2acos(theta- pi/3)sin(theta) Write everything in terms of x and y Homework Equations cos(a-b)=cos(a)cos(b)+sin(a)sin(b) sina/cosa=tana etc... The Attempt at a Solution I've tried a lot of rearranging, can't figure it out.
  48. Evo

    Remembering Knut: The Life and Legacy of a Beloved Polar Bear

    RIP Knut. :cry: continued... http://news.yahoo.com/s/yblog_thelookout/20110321/us_yblog_thelookout/world-mourns-loveable-polar-bear-knut
  49. D

    Graphing Polar Curves: Inner Loop with a Twist | Homework Help

    Homework Statement Hi, my teacher gave me this homework assignment and I'm having trouble graphing this one graph. I don't understand her notes that well and am having trouble getting the equation for this graph. See attached for the graph. The graph is a inner loop that is turned...
  50. B

    Find area between 2 polar curves

    Homework Statement Fine the area of the region inside the polar curve r=4sin(theta) and outside the polar curve r=2. Homework Equations area under polar curve = 1/2 integral (a,b) r^2 d\Theta The Attempt at a Solution I set up the integral like follows: integral (0,pi/2)...
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