Polar coordinates Definition and 569 Threads

I thought I grasped coordinate changes well, but now I've run into some problems. Usually I would have some function f(x,y) and transformation equations like s = a*x+b*y . I would apply chain rule and stayed left with new equations in new variables. (old ones get away through...

This is an example problem that I can't understand how the answer came out to be this way: Q: Sketch the polar curve \Theta = 1. A: A picture of a line that goes diagonal with points that go (1, 1) (2, 1) (3, 1) etc. I do understand that if the angle is 1, then the line is such that it's 1...

Homework Statement I'm trying to solve a double integral of a function which is bounded by the ellipse: \frac{(x-2)^2}{16}} + \frac{(y-4)^2}{36}} = 1 And I can't figure out how to write this in polar coordinate form, and also what my bounds for theta and radius would be. Homework Equations I...

I'm trying to plot the graph r = sin 3t and find its area. This is how far I've gotten: The graph looks like a plane propellor with one propellor pointing downward, and two pointing up-left / up-right, with the length of each equal to 1. Now to get the area... I have to figure out where...

Could someone please convert this double integral to polar coordinates? 0<x<1, x*2<y<1 Int.Int f(x,y)dxdy

Homework Statement Find the surface area of the cone z=3x^2+y^2and above a region in the xy-plane with area 4. Homework Equations double integral sqrt( (dz/dx)^2 + (dz/dy)^2 +1) The Attempt at a Solution I was able to simplify the equation, I just don't know what to do...

Hi, I've just gone through a derivation and would like some confirmation that my reasoning is correct: Say the position of a particle is expressed in polar coordinates as (\phi,r) If we want to describe it's velocity v we need to differentiate both components(angular and radial) with...

Ok, got a few small problems. Just gaps in my knowledge I suppose, wonder if anyone can help. A bit stuck on how to work out the limits for theta. Everything else is fine, it's just that. I know if it says in the first quadrant that it's pi/2 and 0 but that's a really basic one, everything...

Homework Statement Homework Equations r=sinx r= cosx Ok , i need help how to properly select the integral to evaluate the area they make. Can someone please show me how , i know how to evaluate it just having hard times with integrals The Attempt at a Solution

Were on the conic section. I need help how to choose the right interval to evaluate the arc lengh. x=5cost-cos5t and y=5sint-sin5t . I don't get how to choose the inverval to evaluate this, can someone pleasse tell me how. I just don't grasp this.

Homework Statement A.Using polar coordinates, evaluate the improper integral of e^(-10(x^2+y^2))dxdy B. use part A to integrate from negative infinity to positive infinity of e^(-10x^2)dx 2. Homework Equations [/b] The Attempt at a Solution i got part A to be pi/10, but for...

So I've calculated the polar coordinates of a planet, with the sun at the origin and the x-axis being the striped line going from the sun towards point P. Now I have to convert these polar coordinates to heliocentric ecliptic coordinates. To do this, I have to convert to cartesian...

Ok, I have been given the steady state diffusion equation in 1d spherical polar coordinates as; D.1/(r^2).'partial'd/dr(r^2.'partial'dc/dr)=0 I know that the solution comes in the form c(r) = A+B/r where A and B are some constants. I just don't know how to get from here to there. I...

Homework Statement When dealing with an integral integrated with respect to dxdy, I can convert this to polar coordinates, and then integrate with respect to dr d\theta. But I have to multiply with a "r" before integrating. If I am dealing with an integral with respect to dydz, I can...

I'm looking at the proof for the Gaussion integral in polar coordinates and I don´t understand why theta reaches from 0 to 2pi in the integral since you can´t get a negative value out of an exponential function (and therefor the exponential function is never in the 3rd and fourth quadrant, which...

If we have as a manifold euclidian R^2 but expressed in polar coordinates... Do any circle centered at the origin constitute a geodesic? Because I think it parallel transport its own tangent vector.

Homework Statement The velocity field for a line source in polar coordinates (r,theta) is given by: V=m/(2(pi)r) (in the "e" little r vector direction) convert to cartesian and calculate the strain rate tensor. Homework Equations R=Sqrt(x2+y2); Theta=ArcTan(Y/X); Cartesian...

Homework Statement The angle is 59.1, which is in the second quadrant. Give the angle from the positive x-axis. Homework Equations The Attempt at a Solution 180-59.1=120.9 Does that look right? Thank you very much

[SOLVED] conic sections in polar coordinates Homework Statement write a polar equation of a conic with the focus at the origin and the given data. i know it's an ellipse with eccentricity 0.8 and vertex (1, pie/2) The Attempt at a Solution my question is: how do I find the...

Homework Statement A cameraman standing at A is following the movement of a race car traveling at a speed of 30 m/s. Determine the angular rate (theta dot) at which the man must turn to keep the camera directed on the car at theta = 30 degrees...

Homework Statement change the following equation into polar form: y=x^2 The Attempt at a Solution r*sin(t) = r^2 * cos(t)^2 stuck after this... my friend suggested that I cancel an r, but won't that get rid of one of the solutions? I'm not really sure how to proceed

Okay I have no idea where to start on this example problem: Use polar coordinates to evaulate the double integral e^((x^2)+(y^2))dydx [frist (inner) integal lower limit y= -sqrt(4-x^2) upper limit y=0)] [second (outer) lower limit x=0 upper limit x=2] When I start doing the integral...

[SOLVED] Double integration and polar coordinates Homework Statement Find the area inside both circles r = 1, and r = 2 sin \theta by double integration in polar coordinates. Homework Equations None The Attempt at a Solution The way the problem is worded sounds a bit...

Alright, the problem here is that I seem unable to grasp an example given in class. I am not sure if this is due to not copying it down correctly, or if there's something I am just missing. Either way, I know I am not the only one who has had a bit of trouble with this. I'm hoping that someone...

[SOLVED] Area of Polar Coordinates Homework Statement Find the area of the region bounded by r=6-4sin\Theta Homework Equations A=(1/2)\int r^{2} d\Theta The Attempt at a Solution I'm not sure what the bounds are but I thought they were 0 to 2pi. Am I wrong if so how then do you go...

Homework Statement Find the area of the region bounded by r=8cos10\Theta Homework Equations The Attempt at a Solution I set r=0 to find \Theta, which i used for my bounds \Theta=pi/20, 3pi/20 A= \int(1/2)64cos^2(10\Theta) d\Theta

Homework Statement Convert the following integrals into polar coordinates and then calculate them. a) int(0 , 2^(1/2)) int(y, [(4-y^2)^1/2]) xydxdy . Homework Equations x = rcostheta y = rsintheta r = (x^2 + y^2)^(1/2) The Attempt at a Solution Would it simply be: int(0...

Homework Statement My book says if you write a plane curve in polar coordinates by p = p(?), a<=?<=b then the arc length is ??(p^2+(p')^2)d? (the integral is from a to b). It doesn't tell me how they got this equation though and I can't figure it out myself. what does the equation p(?) mean...

Hi, I was wondering how to go about converting a homogeneous ODE of the form M(x,y)dx+N(x,y)dy=0 (where, by definition of a homogeneous ODE, M(tx,ty)=(t^a)M(x,y) and N(tx,ty)=(t^a)N(x,y) ) to polar coordinates. I wan to do this because using substitution of y/x=u and dy/dx=u+xdu/dx to make the...

Homework Statement A car P travles along a straight road with a constant speed v = 65mi/hr. At the instant when the angle theta = 60 degrees, determine the values of r (with dot above) in ft/sec and theta (with dot above) in deg/sec. (r = 100ft) The picture has a car on highway and radius...

The function u(r,\theta) satisfies Laplace's equation in the wedge 0 \leq r \leq a, 0 \leq \theta \leq \beta with boundary conditions u(r,0) = u(r,\beta) =0, u_r(a,\theta)=h(\theta) . Show that u(r,\theta) = \sum_{n=0}^\infty A_nr^{n\pi/\beta}sin(\frac{n\pi\theta}{\beta})...

Homework Statement "Find the area of the region described: The region that is enclosed by the rose r=4cos3[theta]" Homework Equations A= [integral] (1/2)r^2 d[theta] The Attempt at a Solution I'll use Q as [theta].. I'm not really sure, but I set up (1/2) [integral] (16(cos^2)3Q) dQ ...

Car B is driving straight toward the point O at a constant speed v. An observer, located at A, tracts the car with a radar gun. What is the speed |r(dot)[SIZE="1"]B/A| that the observer at A records? --I've attached a crude version of the example picture. By the way, the angle of the line from...

Homework Statement Find all points of intersection of the two graphs r=sin \theta and r=cos 2 \theta The Attempt at a Solution sin \theta = cos 2 \theta I use the trigonometric identity cos 2x = (cosx)^2 - (sinx)^2 but it doesn't take me any further.

I'd like to understand how to calculate the components of Newtonian tidal accelaration tensor in polar coordinates. Is any available Internet source which clearly explains the technique with details? Reading James B. Hartle "Gravity" textbook I stumbled on the following Example from...

I don't know where have I gone wrong... I converted Cartesian coordinates to polar coordinates: \frac{\partial^2\Psi}{\partial x^2} +\frac{\partial^2\Psi}{\partial y^2}= \frac{1}{2}(\frac{\partial^2}{\partial x^2}+\frac{\partial^2 }{\partial y^2})\Psi^2 - \Psi(\frac{\partial^2}{\partial...

Hey I am trying to compute the volume of the region under the plane z=7 x + 4 y + 34 and over the region in the xy -plane bounded by the circle x^2+y^2=4 y. i can't seem to get it... like i i know that the circle is x^2+(x-2)^2=4 so 0<r<2 and 0<theta<2pi this is what i try double integral of...

I'm well out of school, and brushing up on math/physics as a hobby. My question is if there is an intuitive explanation for the exp(I*theta) factor? From Shankar, dz = (dr+ir*d(theta))*exp(I*theta) Here's a good derivation of CR equations in polar...

The problem is to find the area of r = 4cos3θ. I know the formula for finding the area in polar coordinates is ∫ (from α to β) ½r²dθ. I substituted into this formula the given equation and got: A = ½ ∫ (from 0 to 2π) (4cos3θ)²dθ = ½ ∫ (from 0 to 2π) (16cos²9θ)dθ = 8 [(9/2)θ +...

if i have a system that I'm describing using polar coordinates, do i need to have an additional term for rotational kinetic energy? it would seem like this is covered since my velocity is in terms of the r and theta basis vectors. (i.e. i will have a term that covers the rotational movement ala...

I'm a little puzzled with the work of a force considering rectangular and polar coordinates. In rectangular coordinates we have: (1) [F]=(Fx [i] + Fy [j]) is the force vector. (2) [dr]=(dx [i] + dy [j]) is small displacement. Then the work is: (3) W = [F] [dr] = (Fx dx + Fy dy) In...

http://i10.tinypic.com/3ztgdx2.jpg Consider a pasture bordering on a straight river. At 2m from the river, a goat is tied to a pole with a 4m long rope. What is the area of grass that the goat can graze? The answer i got is about 40.4383m^2 Am i correct?

Find the surface area of the surface z=cosh(sqrt(x^2+y^2)) above the region in the xy plane given in polar coordinates: r is between 0 and theta theta is between 2 and 4 Ok. I used the formula: Surface area equals the square root of the partial derivative of x squared plus the partial...

I am having trouble with this seemingly easy problem. Evaluate the double integral (sin(x^2+y^2)) , where the region is 16=<x^2+y^2=<81. I find the region in polar coordinates to be 4=<r=<9 0=<theta=<2pi I find the expression to be sin(rcos^2theta+rsin^2theta) r dr dtheta , which is...

Hey everyone, my lecture has given me this question, I am unsure where to start with it. Express the Cartesian point (3, 3) in polar coordinates. Do i need to use the sin and cos on my calc. Any help would be very helpful lakitu

I'm a bit unclear about the description of orbital motion in a plane by using the polar coordinates (r,\theta). This coordinate system changes its orientation in the inertial reference frame, that it is rotating as the orbiting object moves along its path. In the derivation of the equations of...

Bit of a problem with polar coordinates. (Only trig knowledge needed.) Right. So, in this problem, I'm given the polar coordinate point (rad2, 4.39) -- "rad2" being, naturally, short for radical 2. I'm to find the rectangular coordinates of the point, using the formulas: x = r cos Theta...

Heres where I am struggling, I can't seem to change equations from rectangular to polar and vice versa an example x^2+y^2-2ax=0 heres what I got when I tried r=2a cos theta and that's a graph of a rose curve, I think, I am about 10% sure on that answer heres an example of one I...

Ok, so I've been given a curve in polar coordinates. I came up with a parameterisation: x(t)=rcos(theta) y(t)=rsin(theta) But now I have to plot the graph using MATLAB and I have no idea. Theta lies between 0 and 2pi. This is what I put in and got back in matlab: >> t=[0:pi/50:2pi]...

how do you change the schrodinger's equation into the spherical polar coordinates?