What is Polar: Definition and 1000 Discussions

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  1. S

    Expressing Impedance in Polar and Complex Number form HELP

    Expressing Impedance in Polar and Complex Number form HELP! Homework Statement A Single Pahse, 50Hz, A.C. Generator is to be used to supply two single phase A.C. induction motors in parallel. The no-load terminal voltage of the generator is 400V. And it has an output resistance of 0.2ohms...
  2. S

    Work from the bottom of Unit circle to its top in Polar Coordinates

    Homework Statement Calculate the work W_{A B} done by the force F using Newton's laws (F=ma, etc), when a particle moves from the point A to the point B along the unit circle. The angle is \theta. No friction. How do you define kinetic energy in polar coordinates?Homework Equations...
  3. D

    Calculating impedance in complex number and polar form

    Homework Statement I have a motor with a full load output rating of 2.8 kW with an effciency off 70% and at 80% of full load runs with a Power Factor of 0.8 lagging. A second motor has afull load output of 4.2kW with an effciency of 85% and at 80% of full load runs with a PF of 0.75...
  4. D

    Expressing motor loads in polar form

    Homework Statement I am having difficulty with a question on my Electrical course and the expressing a motor load voltage and current in polar form. The motor is single phase 2.8 KW efficiency 70% and 80% of full load runs with a power factor of 0.8 lagging. Voltage 400v. Express the motor...
  5. P

    Change of limits when integrating with polar coordinates

    Homework Statement ∫ e^(\pix^2) dx, with limits -∞ to ∞ Homework Equations ∫∫ dxdy = ∫∫ rdrdθ The Attempt at a Solution Hi, here's what I've done so far: Introduce a dummy variable y to get ∫∫ e^\pi(x^2 + y^2) dxdy, with limits -∞ to ∞ for both dx and dy...
  6. M

    Multi-variable integration with polar coordination

    Homework Statement \int\int of R ( sin( x^2 + y^2) ) dA where the region 4\leq x^2+y^2 \leq 49 Homework Equations not too sure but i know that dy dx = r d(r) d(theta) The Attempt at a Solution i don't understand how to change into polar coordinates in order to integrate. I'm...
  7. A

    How to Write Down w* in Polar Form for a Given Complex Number?

    Homework Statement Hi guys I have been given a question, write down w* in polar form where w=2< -(pi/3). I can work out the question when it is in cartesian form just not this way, any help woud be great. Homework Equations The Attempt at a Solution
  8. F

    What is the area enclosed by the curve r=(1+Cos\theta),0\leq \theta \leq 2\pi?

    Find the area enclosed by the curve r=(1+Cos\theta),0\leq \theta \leq 2\pi |cos \theta|\leq1 Maximum r =2(1+1)=4 When r=0, 2+2Cos\theta=0 Cos\theta=-1 Key angle=0 \theta=\pi,3/2\pi Area of curve =1/2\intr^2 dtheta
  9. C

    Integration in Polar Coordinates (double integrals)

    Homework Statement We define the improper integral (over the entire plane R^2) I as a double integral [-inf,inf]x[-inf,inf] of e^-(x^2+y^2)dA as equal to the lim as a-> inf of the double integral under Da of e^-(x^2+y^2)dA where Da is the disk with the radius a and center at the origin...
  10. M

    Confusion regarding to polar form representation of AC quantity

    I'm sure my question is very simple to most of u guys. But I have the following confusion. Let's say we have an AC voltage source in a circuit. In rectangular form it's phasor form is v= -4 - 16 j . I want to write this phasor in polar form. Well, The phasor is in 3rd quadrant of complex...
  11. O

    Polar Orbit Change and Line of Sight Time

    Homework Statement A satellite is in a circular polar orbit 240 km altitude. When the satellite is over the South Pole the engine is fired to achieve a polar orbit that has apogee directly over the North Pole. After the impulsive burn an observer on the North Pole observes the satellite has...
  12. A

    Deriving the divergence in polar coordinates

    Homework Statement I want to find the divergence operator in polar coordinates (theta and r). I know how to write this operator in cartesian coordinates. The Attempt at a Solution I let F(F1,F2) be a vector field. I calculated the partial derivatives of F1 and F2 with respect to x...
  13. R

    Use polar coordinates to evaluate.

    Homework Statement http://img162.imageshack.us/img162/9831/97118623.jpg Homework Equations The Attempt at a Solution I first drew R, and from the circle equation, I know the radius of the circle is 12.5. Since the region is in the first quadrant, that'll mean that my limits of...
  14. R

    Changing a double integral to polar coordinates

    Homework Statement Rewrite by converting to polar coordinates, carefully drawing R. \int^{2}_{0}\int^{\sqrt{2x-x^2}}_{0}\sqrt{x^2+y^2}dydxHomework Equations The Attempt at a Solution I believe I have the inside part of it right. What I did was replace the x^2 and y^2 in \sqrt{x^2+y^2} with...
  15. J

    Evaluating Polar Int., Find Error: \frac{\pi}{8}-0.25ln(2)

    Evaluate the integral by changing to polar coordinates \int\int arctan(y/x) Given that 0 \leq x \leq 1 and 0 \leq y \leq x Now I've changed the integral to \int\int \theta r dr d\theta Such that 0 \leq \theta \leq \frac{\pi}{2} and 0 \leq r \leq \sqrt{2} And evaluating this...
  16. C

    Green's theorem applied to polar graph

    Homework Statement Use Green's theorem to compute the area of one petal of the 28-leafed rose defined by r = 5sin(14 \theta) Homework Equations A = \frac{1}{2} \int_c{x dy - y dx} \int \int_c{M_x + N_y}dx dy The Attempt at a Solution I'm really more confused about just what to do...
  17. M

    Pendulum in polar coordinate system problem

    Homework Statement A pendulum consists of a particle of the mass m and a thread of the length l (we don't consider the threads mass). The acceleration caused by gravity is g. Solve the particles displacement and the force caused by the tension in the thread T in a polar coordinate system. The...
  18. 1

    Help with integrating polar coordinate equations

    Homework Statement I need to integrate the equation shown below in the picture. It is a polar coordinate function with r(double dot) being the acceleration radial and theta(double dot) being angular acceleration. I need to integrate with respect to time, to get equations for r(dot) and r...
  19. M

    Cartesian , Polar and Exponential FormHelp needed thanks .

    Homework Statement how can i convert this : - 2 (cos pai / 4 + i sin pai / 4 ) to Cartesian , Polar and Exponential form ? Homework Equations z = ( a + i b) The Attempt at a Solution r= -2 tan inverse = pai/4 / pai/4 ?? Thank you very much for helping me out
  20. M

    Cartesian , Polar and Exponential FormHelp needed thanks .

    Express -2(cos pai/4+i sin pai/4 ) in Cartesian , Polar and Exponential form ? how can i convert this : - 2 (cos pai / 4 + i sin pai / 4 ) to Cartesian , Polar and Exponential form ? Thank you very much
  21. M

    How Do Trigonometric Identities Derive the Area Element in Polar Coordinates?

    Homework Statement using only trigonometric identities, derive the differential area element in polar coordinates? any help with this problem or at least a start? Homework Equations i found this so far dA=(dr)(rd θ) The Attempt at a Solution i have tried to figure this one out...
  22. L

    Another Polar Coordinates + Integration Question

    I came across this example on the net : We are integrating over the region that is the area inside of r = 3 + 2 sin θ and outside of r = 2, working in polar coordinates (r,θ). What is the limits of integration for θ? # I already know the answer. But I have no idea how to arrive at the...
  23. B

    Cartesian to spherical polar coordinates

    Hi there, I am getting confused about how to work this out. I know that to convert cartesian coordinates to spherical coordinates you can use: theta=arccos(z) phi=arcsin(y/sin(theta)) my problem is that I have a list of coordinates, let's call them THETA and PHI. I change them into X,Y,Z...
  24. L

    Need help with Polar Coordinates, esp. for integration

    Any web resources regarding changing the variable of integration from cartesian to polar coordinates that goes beyond the basic : x = r cos theta y = r sin theta r = sq rt (x^2 + y^2)I totally don't get how to find the limits of integration using polar coordinates and my undergrad textbooks...
  25. M

    Line integral in polar coordinates

    Homework Statement calculate: \oint \frac{2-y}{x^2+(y-2)^2} dx + \frac{x}{x^2+(y-2)^2} dy where y = \sin{t} + 2, x = \cos{t}, 0 \leq t \leq \pi Homework Equations Green's Theorem. The Attempt at a Solution In what order should I do everything? I need to find the derivaties...
  26. G

    Secrets of the Microwave Oven: Grid Dimensions & Polar Molecules

    Homework Statement Microwave oven I. The glass window isn't important to the microwave oven's operation, but the metal grid associated with that window certainly is. The grid forms the sixth side of the metal box that traps the microwaves so they cook food effectively. What is the approximate...
  27. J

    Norming e^(-r/a) in Spherical Polar Coordinates - Integral Bounds

    What is e^(-r/a) in spherical polar coordinates, and what are the bounds for the integrals? (I need to know to norm a wave fxn given as e^(-r/a) in 3 dimensions.)
  28. M

    Cartesian to Polar in Double Integral

    Homework Statement Solve: \iint_{\frac{x^2}{a^2}+\frac{y^2}{b^2} \leq 1} \sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}} dx dy Homework Equations Cartesian to Polar The Attempt at a Solution Well - this Integral should be solved as a polar function (the radical should be...
  29. L

    Quick Qns : Convergence in Polar Coordinates

    Suppose we investigating the limit of a function on R^2 as (x,y) tend to (0,0). We convert the function into polar coordinates. Then "(x,y) tend to (0,0)" is equivalent to "r tend to 0"? Theta (the angle) does not matter?
  30. K

    Argument value in complex numbers in polar form.

    -1-(under root)3 i here we find that r=2(hypotenuse) a=-1(base) b=-(under root)3 when i take sin theat= p/h=-(under root)3 / 2 theat from sin is -60 when i take cos theta = b/h =-1 / 2 which gives 120 now one is -60 and other is 120, which is the angel , i have to follow and what...
  31. C

    Area under Polar Curves: Where did I go wrong?

    1.Where did I go wrong in finding the area enclosed inside r = 3 cos θ? Homework Equations I used the formula 1/2 ∫ ((f(θ)) squared dθ from alpha to beta The Attempt at a Solution I looked for the area of the semicircle from 0 to pi and then multiplied the whole thing by 2, since the...
  32. B

    Help evaluating a surface integral in polar coordinates

    Homework Statement I have to evaluate the surface integral of the following function over the top hemisphere of a sphere.Homework Equations \sigma (x,y,z) = \frac{\sigma_0 (x^2+y^2)}{r^2} z = \sqrt{r^2-x^2-y^2} \iint G[x,y, f(x,y)] \sqrt{1+ \frac{\partial f}{\partial x}+ \frac{\partial...
  33. M

    As if grizzlies and polar bears weren't enough

    Canada obviously feeling inferior to Australia in the dangerous creature stakes have decided to go one better: "Canadian scientist aims to turn chickens into dinosaurs" http://www.physorg.com/news170426405.html
  34. M

    Cartesian -> Spherical polar

    I have an integral \int \int_S x^2 + yz \ dS and wish to transform to spherical polar coordinates. How does dS become dS = r^2 \sin \theta d\theta d\phi ?? Where surface S is x^2 + y^2 + z^2 = 1
  35. P

    Basic Calculus Questions - polar integration and roots

    It's been a while since I studied calculus and basically I have a review sheet for a course I'm taking, but not a graded assignment. So, I was hoping if anyone knew a resource to point me in the right direction with a couple of problems: \int_0^\theta x^a dx Where a is not an element...
  36. E

    Polar Decompositions: Purpose of sqrt(T*T)

    About the equation T=Ssqrt(T*T), what purpose does the sqrt(T*T) serve?
  37. S

    Finding the 4th Roots of -16: Cartesian vs. Polar Form

    Homework Statement Compute the 4th roots of -16 in both Cartesian and polar form and plot their positions in the complex plane. Homework Equations z^1/n=(r^1/n)(e^i(theta)/n), (r^1/n)(e^i(theta)/n)(e^i2(pi)/n... The Attempt at a Solution How do I find the value of r, and theta??
  38. S

    Exploring Complex Numbers in Polar Form: Calculating Squares and Products

    Homework Statement Evaluate the square 0f 5e^(3(pi)i)/4 without using Cartesian form, and also the three different products. Homework Equations e^i(theta) = cos(theta) + isin(theta)? The Attempt at a Solution I have absolutely no idea here, nothing in my notes even begins to...
  39. K

    How Do You Convert a Polar Conic Equation to Cartesian Coordinates?

    Homework Statement The equation of a conic in polar coordinates is: r = \frac{r_o}{1-\epsilon cos(\theta)}. \epsilon is the eccentricity, 0 for a circle, (0,1) for an ellipse, 1 for a parabola, and >1 for a hyperbola. What is this equation expressed in Cartesian coordinates...
  40. A

    Covariant derivative in polar coordinates

    I calculated the christoffel symbols and know that I have them right. I want to take the covariant derivative of the basis vector field e_{r} on the curve s(t) = (a, t/a). I differentiate it and get s' = (0, 1/a) and according to the metric, this is a unit vector because a will always be equal...
  41. G

    Converting double integral to polar coordinates

    Homework Statement \int\int(rsin2\vartheta)drd\vartheta sorry i don't see how to put the bounds in but they are 0<\vartheta<\pi/2 and 0<r<2acos\vartheta Homework Equations I know that r=sin\varthetaThe Attempt at a Solution Im really not sure where to start my text is terrible. I really...
  42. putongren

    How can both equations for polar coordinates be derived?

    Dear All, How do you derive both equations below. Let r be the position vector (rcos(θ), rsin(θ)), with r and θ depending on time t. These equations can be found in wiki under polar coordinates.
  43. L

    Length of curve in Polar coordinate system

    I want to caculate length of curve in Polar coordinate system like this: if r=r(a) then length of the curve is ∫r(a)da Is this right? if not ,why ? What's the right one ? I konw the way in rectangular coordinate system,I just want to do it in Polar coordinate system .
  44. C

    Conversion of cartesian coordinates to polar coordinates

    [b]1. Was wondering if anyone could help me confirm the polar limits of integration for the below double integral problem. The question itself is straight forward in cartesian coordinates, but in polar form, I'm a bit suspect of my theta limits after having sketched the it out. any help much...
  45. W

    Help w/ solving nonzero B.C PDE heat eq in polar coord.

    it is the typical pde heat equation in polar coord: \partialu/\partialt = \partial^2u/\partialr^{2} + (1/r) \partialu/\partialr + (1/r^{2}) \partial^2u/\partial\Theta^2 where: - 0 < r < 1 - 0 < \Theta< 2 \Pi - U(1, \Theta, t ) = sin3\Theta - U(r, \Theta, 0 ) = 0 I don't know how...
  46. R

    Finding Directrix and Sketching Hyperbola in Polar Coordinates

    Homework Statement Hyperbola formula 9x^2 - 4y^2 + 36x + 24y - 36 = 0. Convert to rectangular form, find coordinates of the vertices, find coordinates of the foci, find eccentricity, what is the equation of the conic section in polar coordinates if the pole is taken to be the leftmost focus...
  47. A

    Reduce a polar quantity by a percentage

    Homework Statement reduce a current in its polar form 95 -46.37° by 20% Homework Equations The Attempt at a Solution When dividing a polar number by a scalar one you just divide the magnitude by the scalar, the phase will remain unchanged, so to reduce the polar value by 20%...
  48. C

    Double integrals in polar coordinates

    Homework Statement Find \int{\int_{D}x dA} where D is the region in Q1 between the circles x2+y2=4 and x2+y2=2x using only polar coordinates. The Attempt at a Solution Well, the two circles give me r=2 and r=2 cos \theta, and the integrand is going to be r2cos \theta, but I have no...
  49. G

    Is There a Complex Gradient Formula for Polar Coordinates?

    Does there exist anything like a polar complex differentiation? So there exists a gradient equation in polar coordinates something like \nabla{f} = \frac{\partial f}{\partial r} e_r + \frac{1}{r}\;\frac{\partial f}{\partial \theta} e_{\theta} But this is not for a complex number f(z) where...
  50. C

    Gradient vector for polar coordinates

    Homework Statement Find the gradient vector of: g(r, \theta) = e^{-r} sin \theta Homework Equations The Attempt at a Solution I know how to get gradients for Cartesian - partially derive the equation of the surface wrt each variable. But I have no idea how to do it for...
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