What is Polar: Definition and 1000 Discussions

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  1. S

    Understanding Velocity in Polar Coordinates

    Homework Statement I don't understand why when we derive the velocity equation of motion in polar coordinates we start with position equal to R times R hat and not (theta times theta hat + R times R hat). Homework Equations none really.. The Attempt at a Solution Is there an assumption I'm...
  2. W

    Translations in polar coordinates

    Hi, I'd like to describe what I need to do visually: In other words, I just need to translate my semi-circle (which is actually just a large circle in limited viewspace) so that it moves beyond the origin. Right now I'm using the standard formula for a circle centered at a distance r from the...
  3. T

    Kinematics in Polar Coordinates

    Homework Statement A particle starts at (d, 0) in polar coordinates and has a velocity of \vec{v}=(u \sin{\theta} - v)\hat{r} + u \cos{\theta} \hat{\theta} where v > u Find the position vector of the particle as a function of time. Homework Equations \vec{v}=\frac{d\vec{r}}{dt}...
  4. Y

    Solve Cauchy-Riemann Equations with Polar Coordinates

    hey, I know this might be abit silly, but u know the cauchy-reimann formula for a complex function to be diffrentiatable? here is a link to what I am talking about: http://en.wikipedia.org/wiki/Cauchy-Riemann_equations my question is: how do I write it in polar coordinates?:redface:
  5. T

    Polar coordinates from Google Maps

    Hi. I have a pair of latitude and longitude (55.730397,12.358181) from Google Maps. I would like to convert it to POLAR COORDINATES in two-dimensional coordinate system. I am interested in the angle in the polar coordinates. I can't find any formula for this convertion? Thanks! /Taz
  6. M

    Arc Length Polar Coordinates

    Homework Statement r = e^θ find arc length from (1,0) to origin Homework Equations ∫ab sqrt (r^2 + (dr/dθ)^2) dθ The Attempt at a Solution ∫10 sqrt ((e^θ)^2 + (e^θ)^2) dθ ∫10 sqrt (2(e^θ)^2) dθ ∫10 sqrt (2) (e^θ) dθ sqrt (2) ∫10 (e^θ) dθ need help converting limits in...
  7. F

    Seperable solutions of Laplace equation in circular polar coords

    Homework Statement I'm considering Laplace's equation in 2D, written in circular polar coordinates (so that's u_rr + 1/r*u_r + (1/r^2)*u_theta,theta). I've worked out what all the seperable solutions are. My question is: is this set of seperable solutions complete. (That is, can all...
  8. M

    Divergence and curl of spherical polar coordinates

    Homework Statement Hi, i am trying to find the div and curl in spherical polar coordinates for the vector field, F I have attempted both and would really appreciate it if someone could tell me if the answers look ok as I am really not sure whether i have correctly followed the method...
  9. M

    Div, grad and curl in cylindrical polar coordinates

    Homework Statement Hi, i am trying to find the div, grad and curl in cylindrical polar coordinates for the scalar field \ phi = U(R+a^2/R)cos(theta) + k*theta for cylindrical polar coordinates (R,theta,z) I have attempted all three and would really appreciate it if someone could tell me...
  10. X

    Center of mass of a semi circle using polar coordinates

    Homework Statement Semi circle of Radius R given. Find center of mass using polar coordinates, not double integrals. Homework Equations .5 intergral(r^2dpheta) (1/M) integral y dm r=R The Attempt at a Solution .5(2/piR^2) integral(R^3sinpheta do pheta) from 0 to pi, when I evaluate it I...
  11. M

    Line Integral on R2 Curve in Polar Coordinates

    Homework Statement Consider a curve in R2 given in polar coordinates r=r(θ) for θ1<= θ <= θ2. Show that the line integral is equal to the integral from θ1 to θ2 of f(r*cosθ, r*sinθ) sqrt (r^2 + (dr/dθ)^2) dθ Homework Equations x= cos θ, y= sin θ The Attempt at a...
  12. Q

    Exploring Limits in Polar Coordinates

    Homework Statement find limit if exist, or not then why f(x,y) = xy / sqrt(x2+y2) as (x,y) --> (0,0) The Attempt at a Solution can i change to polar coordinates x=rcost y=rsint so f(r,t) = rcostsint so as x,y tends to 0, r t will tend to 0 too?but cos(t) at 0 gives me 1...
  13. S

    Graphing θ=π/4 in Polar Coordinates

    How will you graph θ=π/4? In polar coordinates you can graph an equation like, r=a(1-sinθ) which gives a cardioid graph. But when my teacher giving me a class of sketching in polar coordinates then he ask to sketch θ=π/4. But as we know that in polar coordinates (r,θ). so in θ=π/4, there is...
  14. D

    Circular Error Probability in polar error expression

    After doing various searching through the google, most of the circular error probability I found are expressed interm of \sigma_x and \sigma_y, which the CEP(circular error probability) usually looks like (assume normal distribution): P(r) = \int\int...
  15. N

    Using the div-flux theorem (Gauss) to derive divergence in polar coördinates?

    Apparently one can deduce the form of divergence in polar (and spherical) coördinates using the theorem of Gauss and Ostrogradsky, namely that the volume integral over the divergence is equal to the flux integral over the surface. I can't see a way to do that, do you?
  16. O

    Convering double intgral to polar coordinates

    Homework Statement Hey am studing for my up coming exam and i am having trouble with transforming double intrgral to polar coordinates i have no idea where to start or anything so can someone explain it to me Homework Equations this is example \oint^{\infty}_{0}\oint^{\infty}_{0}...
  17. X

    Problem with polar double integral

    Hello everybody, I am having trouble doing this polar double integral. The problem says.. Find the area of the region.. \frac{1}{2}y^2 \leq x \leq 2y 0 \leq y \leq 8 It is hard for me to come up with the limits of integration. Checking the answer would be easy because I can...
  18. N

    Solving I2 in Polar Form: Exploring Complex Numbers

    I got this equation 5<0° = -14.14<-45° + 2.24<116.6° I2 And i solved I2 this way I2 = -14.14<-45° / 2.24<116.6° I2 = 8<150.29° I want to know complex numbers is the same way as normal math or not thanks in advance
  19. A

    Understanding Special Relativity Through Polar Coordinates

    Hi guys! I was reviewing some basic stuff in Special Relativity, specifically the part where it can be proven that a straight line connecting two events is the path that maximizes the interval between these two events. The proof is easy using the metric with cartesian coordinates ds^2 =...
  20. S

    Polar Unit Vectors: Defining in Relation to Cartesian System?

    Can polar co-ordinate system only be defined in a "background" Cartesian co-ordinate system? What I'm confused about is this: the definition of the polar unit vectors or the polar basis is in terms of the parameter theta. Now, before we go about defining our basis we need to define this theta...
  21. L

    H20 Polar: Oxygen Electronegativity Causes Electron Disparity

    The electronegativity of Oxygen is higher than that of H, thus the electrons tend to stay a little more on the oxygens electron orbitals, right?
  22. D

    Exploring PDE Solutions in Polar Coordinates

    Solving a PDE with Polar coordinates yu_x-xu_y=0 x=r\cos{\theta} \ \mbox{and} \ y=r\sin{\theta} u(r,\theta) Does u_x\Rightarrow u_r \ \mbox{or} \ u_{\theta} \ \mbox{and why?} Thanks.
  23. P

    How to calculate volume of a rotated polar function

    Hello, I've just found a book which mentions the formula for calculating the volume of a rotated polar function: \int_{\theta_1}^{\theta_2} \frac{2}{3} \pi r^3 sin(\theta) d\theta How does one calculate this? In an https://www.physicsforums.com/showthread.php?t=457896", I calculated that the...
  24. P

    Volume created by the revolution of a polar function around the initial line

    Hello, I was wondering if anyone could help me with deriving the volume created by the rotation of a polar equation around the initial line. So, I thought about adding the surface area of cones (multiplied by d\theta) if each cone the triangle created with s-length of f(\theta) and r-length...
  25. P

    Polar Coordinate Symmetry with Double Angles

    Homework Statement Given the equation r²=25sin2Θ Asked to find symmetry with respect to line Θ = pi/2 Homework Equations w.r.t. Θ = pi/2: (r,Θ) - (r, pi-Θ) and (r, Θ) - (-r,-Θ) The Attempt at a Solution For the first case, I plugged in (pi-Θ) for Θ, but I'm confused about what to do...
  26. S

    Double integral in polar coordinates problem

    Homework Statement \int_{y=-infinity}^{infinity} \int_{x=-infinity}^{infinity} (x^4+y^4)/(1+x^2+y^2)^4 dx dy Homework Equations i'm not sure what the new limits are after the transformation to polar coordinates and how to solve the integral. The Attempt at a Solution i have my...
  27. V

    Find the arc length of a polar function from 0 to 2pi

    Homework Statement This is another problem my teacher game me. Given the Polar function r=6*sin(t/2) where the variable t is the angle theta in radians, and that t is between 0 and 2*Pi inclusive. Find the distance around the perimeter of the graph. Hint: this is arc length , round to the...
  28. L

    Polar and cartesian coordinates

    Homework Statement Write the following polar equation in Cartesian coordinates: r= 2/(3cos(theta)-9sin(theta)) Homework Equations r = (x^2 + y^2) ^.5 x=rcos theta y=rsin theta sin^2(x)+cos^2(x) = 1 The Attempt at a Solution I'm stuck on how to do this. Any push in the right...
  29. M

    What is Area in Polar Coordinates?

    Homework Statement Find the area of the infinitismal region expressed in polar coordinates as lying between r and r+dr and between theta and theta+dtheta Homework Equations A= [integral] (1/2)r^2 d[theta] The Attempt at a Solution To be honest I solved many of this kind of...
  30. jegues

    Moment of Interita about x-axis in Polar Coordinates

    Homework Statement A plate with constant mass per unit area \rho is bounded by the curve (x^{2} +y^{2})^{2} = 9(x^{2} - y^{2}) . Find its moment of inertia about the x-axis. Homework Equations The Attempt at a Solution Okay well first I plugged in...
  31. F

    Domain's in polar co-ordinates.

    Alright, so I'm having a problem converting to polar co-ordinates Never been confused by polar before :(I'm trying to convert the domain of an integral to polar co-ordinates The domain would be something like D:{(x,y)| 1<x<2 , 0<y<(2x-x2) 1/2} First I recognize that y=(2x-x2) 1/2 is the...
  32. J

    Use polar coordinates to find the volume of the given solid.

    Homework Statement Bounded by the paraboloid z = 4 + 2x2 + 2y2 and the plane z = 10 in the first octant. Homework Equations The Attempt at a Solution Plugging in 10 for z I got 3=x2+y2. From this, I set 0\leqr\leq3\sqrt{}. I wasn't sure what to do with the first octant, but I...
  33. M

    Compute Integral Using Jacobian Det in Polar Coordinates

    Homework Statement Determine the Jacobian determinant for "polar" coordinates and use that to compute the intergral . . . Blah blah blah that's not the point. Homework Equations (x,y) maps by T to (r, theta) or (theta, r) detT = jacobian The Attempt at a Solution Anyways, first I...
  34. N

    Double integrals in polar coordinates

    I was overlooking a problem that my teacher solved and i can't understand a step see took i was wondering if someone you tell me how she got from this step Double integral rcos(o)(rsino)rto this Double integral (r/2)^3(2sinocoso)
  35. S

    Changing cartesian integrals to equivalent polar integrals.

    Homework Statement 6...y ∫...∫ x dx dy 0 ...0 The Attempt at a Solution for reference: π=pi 6...y ∫...∫ x dx dy 0 ...0 y=6=x=6. rcosΘ=6 r=6/cosΘ goes to π/2 6secΘ ∫ ...∫... r cosΘ r dr dΘ π/4...0 π/2.....r=6secΘ ∫ ... [((r^3)/3)cosΘ] dΘ π/4......r=0 π/2...
  36. M

    R = cos(theta) in polar coordinates?

    r = cos(theta) in polar coordinates?? Hullo everyone! Hows it going? I am confused with how to interpret the graph of r = cos(theta) in polar coordinates. I tried graphing it manually. and this is how I interpreted it: r(0) = cos(0) = 1 r(pi/2) = 0 r(-pi) = -1 r(3pi/2) = 0 r(2pi)...
  37. B

    Polar Coordinates: Arc length of two overlapping curves

    This question may be something of a dumb one. I feel I should know this, but well, I don't. I'm being asked to find the perimeter inside of the curve r=15sin(theta) and outside of r = 1 Setting up the equation I can do. If it were just an indefinite integral, this would be cake. My...
  38. S

    Calculating Polar Curve Length with Period of 3π: r = psin3(θ/3)

    Homework Statement Find the length of the polar curve r = psin3(\theta/3) Hint: The period of the curve is 3\piHomework Equations L = \intsqrt(f(\theta)2 + f'(\theta)2)d\thetaThe Attempt at a Solution I know from the hint that 0\leq\theta\geq3\pi The only problem I have is how do I start this...
  39. M

    Polar molecules like water Spin why?

    Water molecules are polarized, so why don't the molecules in a glass of water simply line up with opposite + and - ends and come to a halt?
  40. M

    Curvature in polar coordinates

    hi i need a affirm of curvature in polar coordinates. i need now please
  41. F

    Help Polar, Horizontal Tangents.

    Homework Statement For the three leaf rose: r = sin(3\theta), find the co-ordinates of the five points where the tangent lines are horizontal. Interpret the significance of the five points. Homework Equations \frac{dy}{dx} = \frac{r'sin(\theta)+ rcos(\theta)}{r'cos(\theta) - rsin(\theta)}...
  42. C

    4d Cartesian to Polar Transform

    Howdy everyone, I'm on a quest for something that is proving a bit elusive at the moment: a Cartesian to polar transform (along with its inverse) for \mathbb{R}^4. I'm well aware of how to derive the transform for both \mathbb{R}^2 and \mathbb{R}^3, as it is just a matter of looking at the...
  43. B

    Double integral help please? polar and cartesian

    Homework Statement Okay here's the problem: Consider the region R interior to a circle(of r =2) and exterior to a circle(r=1). 1.Using cartesian coords and double integral, calc the area of annulus. 2. repeat calculation above but using double integral with polar coords The...
  44. L

    Need help with Gradient in Polar Coordinates

    Homework Statement Well the problem is a electromagnetism problem: I need to find the charge density. Given E= kr^3 r^ Homework Equations formula is gradient E=p/e0 The Attempt at a Solution They got the gradient of E to be 1/r^2 (d/dr) (r^2 Er) i have no idea how they did...
  45. R

    The area shared by two polar curves

    Homework Statement Find the area of the lemniscate r2=6cos(2w) located to the right of the line r=3/2sec(w). Homework Equations Area of a polar region is the integral from a to b (in this case a and b are where the curve intersects the line, I believe) of 1/2*r2d(w). The Attempt at...
  46. R

    Converting a Cartesian equation to polar form

    Homework Statement Convert the following Cartesian equation to polar form. x^2/9 + y^2/4 = 1 Homework Equations r*cos(t)=x r*sin(t)=y r=Sqrt(x^2 + y^2) y/x = Arctan(t) The Attempt at a Solution I get ugly looking things like r^2(cos^2(t)/9 + sin^2(t)/4) = 1 but being a simple ellipse (edit...
  47. K

    What is the polar form of -2^i?

    Homework Statement Convert -2^i to polar and rectangular form Homework Equations mag(a+ib)=sqrt(a^2+b^2) exp(i*angle)=cos(angle)+i*sin(angle) The Attempt at a Solution im not sure how to get the polar (or rectangular form) of -2^i. i know the answer is exp(-2.448rad)... i just don't know the...
  48. W

    Transforming Complex Solutions into Polar Form

    Homework Statement Show that the solution x(t) = Ge^(iwt), where G is in general complex, can be written in the form x(t) = Dcos(wt - \delta). D(w) and \delta(w) are real functions of w. Homework Equations z = Ae^(i\phi) The Attempt at a Solution So I know I should start by...
  49. R

    Polar Coordinates: Apollo 13 Reentry: Calculating Theta

    in this situation where apollo 13 is reentering the atmosphere, how would you determine what theta is in the polar coordinate system for velocity? [PLAIN]http://img37.imageshack.us/img37/7366/shuttlek.jpg Wouldn't the angle gamma be equal to theta since gamma is equal to the angle of the...
  50. Z

    How te expand [tex] \nabla f \cdot (p-p_0) [/tex]in spherical polar coordinates

    how to expand grad f * (p-p_0) in spherical polar coordinates in spherical polar coordinates: \nabla f = \frac{\partial f}{\partial r} e_r+ \frac{1}{r sin\theta}\frac{\partial f}{\partial \phi} e_{\phi}+ \frac{1}{r}\frac{\partial f}{\partial \theta} e_{\theta} p=(r,\phi,\theta) and...
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