Cylindrical coordinates Definition and 225 Threads

Homework Statement Use cylindrical coordinates to find volume... Homework EquationsInside: x2+y2+z2=16 Outside: z=sqrt(x2+y2) The Attempt at a Solution Cylindrical coordinates have always been a problem for me, so I initially tried to put them into spherical and then convert them over, but...

Homework Statement do we only use spherical and cylindrical coordinates for triple integrals? or for double too? thanks for your replies in advance

Hi there, I'm trying to determine the radial component of a velocity vector in a disk. The vector doesn't (necessarily) start from the centre of the disk and can be pointed in any direction. I've attached a .pdf with the schematics - it seems like a simple problem but it has me stumped...

Consider cylindrical coordinates p = (x^2 + y^2)^.5  angle = arctan(y=x). Consider your curve to be specified by z(p). Write down a (first order) differential equation governing z(p) please help!

Homework Statement I have been given the problem of finding the potential of a dipole in cylindrical coordinates. The only way that comes to my mind is to extract the dipole term from the multipole expansion of the potential of an arbitrary charge distribution in cylindrical coordinates. But I...

Homework Statement Integrate the function f(x,y,z)=−4x+3y over the solid given by the figure below, if P = (5,1,0) and Q = (-5,1,2). [PLAIN]http://img259.imageshack.us/img259/958/sfig1681g1.gif Homework Equations x=rcos(\theta) y=rsin(\theta) r=sqrt(x^2+y^2)The Attempt at a Solution i...

Homework Statement Calculate the divergence of the vector function f = a/s^2 (s hat) where s is the radial distance from the z axis, expressed in cylindrical coordinates. Homework Equations The Attempt at a Solution Using the divergence theorem I relate the volume integral of...

Homework Statement This seems like a trivial question (because it is), and I'm just not sure if I'm doing it right. I have vector in cartesian coordinate system: \vec{a}=2y\vec{i}-z\vec{j}+3x\vec{k} And I need to represent it in cylindrical and spherical coord. system Homework...

Homework Statement A gun can fire shells in any direction with the same speed v0. Ignoring air resistance and using cylindrical polar coordinates with the gun at the origin and z measure vertically up, show that the gun can hit any object inside the surface z = \frac{v_{0}^{2}}{2g} -...

Homework Statement A gun can fire shells in any direction with the same speed v_{0}. Ignoring air resistance and using cylindrical polar coordinates with the gun at the origin and z measured vertically up, show that the gun can hit any object inside the surface z = \frac{v^{2}_{0}}{2g} -...

Homework Statement Hi there. Hi have in cylindrical coordinates that \theta=\displaystyle\frac{\pi}{3}, and I must make the graph, and take it into cartesian coordinates. How should I do? I've tried this way: \begin{Bmatrix}x=r\cos\displaystyle\frac{\pi}{3}\\y=r\sin\displaystyle\frac{\pi}{3}...

Hi, I'm trying to find the Hamiltonian for a system using cylindrical coordinates. I start of with the Lagrangian L=\frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2+\dot{z}^2)-U(r,\theta,z) From that, using H=\sum p\dot{q}-L...

Has to convert B6-1 into B6-2 Source Transport Phenomenon 2nd ed -

I'm trying to solve the homogeneous heat equation of a semi-infinite cylinder in cylindrical coordinates for a semi-infinite cable (no theta dependence): \frac{\partial U}{\partial t}=D\left(\frac{\partial^{2} U}{\partial r^{2}}+\frac{1}{r}\frac{\partial U}{\partial r}+\frac{\partial^{2}...

I wish I knew how to type this out with the proper symbols but here it goes. It says to change the following to cylindrical coordinates and evaluate (x^2 + y^2)^(1/2) dz dy dx where -3<=x<=3, 0<=y<=(9-9x^2)^1/2, 0<=z<=9-x^2-y^2Homework Equations The Attempt at a Solution I got 162pi/5 Would...

Just a question. Say you have a function, which in cylindrical coordinates it gives that \int\int\int \sqrt{x^2 + y^2} dx dy dz which is \int\int\int r^2 dr d/theta dz i want to find in cylindrical coordinates, in the area limited by the functions : x^2 + y^2 = z^2 z is greater or equal than...

So I'm trying to find out what the procedure is to convert a cartesian unit vector to a cylindrical unit vector. Any thoughts?

Use cylindrical coordinates to evaluate the triple integral , sqrt(x^2+y^2) where the region integrated is the solid bounded by the circular paraboloid z=9-16(x^2+y^2) and the xy-plane. I'm having trouble deciding what the bounds for r would be.

Homework Statement Describe the following vector field: \bold v (\bold x)=\frac{\bold a \times \bold x}{(\bold a \times \bold x)(\bold a \times \bold x)} with \bold a = \text{constant}. Calculate its divergence and curl. In what region is there a potential for \bold v? Calculate it. Hint...

Homework Statement A conical container with radius 1, height 2 and with its base centred on the ground at the origin contains food. The density of the food at any given point is given by D(r) = a/(z + 1) where a is a constant and z is the height above the base. Using cylindrical polar...

Can anyone please explain the stress fields in cylindrical coordinates? What is the difference between \sigma_{rz} and \sigma_{\theta z}? What is the difference between stress in the r axis and stress in the \theta axis? Thanks

Homework Statement Plate in the shape of the circular halo (inner radius a, outer radius b>a), the inner edge is being kept at a constant temperature T_0, and the outer at the temperature given by the function f(\phi)=T_0\cos(2\phi). Find the equilibrium distribution of the heat everywhere...

Homework Statement In cyclindrical coordinates we can represent points as (\rho,\phi,z) We define a vector in cyclindrical coordinates as follows A = A\rhoa\rho + A\phia\phi + Azaz I'm having some problem with subscripts. Anyway I don't understand this. If I am given a point say ( 5, 20...

Evaluate by changing to cylindrical coordinates \int from 0 to 1 \int from 0 to (1-y^2)^1/2 \int from (x^2+y^2) to (x^2+y^2)^1/2 (xyz) dzdxdy I came to an answer of integral from 0 to pi integral from 0 to 1 integral from r^2 to r (rcos\thetarsin\thetaz) r dzdrd\theta Is this the correct answer?

Hi all! I was trying to figure out how to find the volume of a cone with radius R and height h using integration with cylindrical coordinates. I first tried to set the the integral as: \int_{0}^{2\pi}\int_{0}^{h}\int_{0}^{R}\rho d\rho dz d\phi ...but I think that this is setting up the...

Can anyone help with the solution of the Laplace equation in cylindrical coordinates \frac{\partial^{2} p}{\partial r^{2}} + \frac{1}{r} \frac{\partial p}{\partial r} + \frac{\partial^{2} p}{\partial z^{2}} = 0 with Neumann no-flux boundaries: \frac{\partial p}{\partial r}...

Homework Statement Use cylindrical coordinates to evaluate the triple integral \int\int\int \sqrt{x^2+y^2} dV in region E where E is the solid bounded by the circular paraboloid z=9-(x^2+y^2) and the xy-plane. Homework Equations knowing that x = rcos\theta y= rsin\theta z=z...

i need help transforming this equation into cylindrical coordinates... w = omega i = i hat j = j hat k = k hat r is a vector r(t) = Asin(wt)i + Bsin(wt)j + (Ct - D)k where w, A, B, C and D are constants. i, j, and k are throwing me off...i know they are components of x, y and z...and i know...

Homework Statement A vector field A is in cylindrical coordinates is given. A circle S of radius ρ is defined. The line integral \intA∙dl and the surface integral \int∇×A.dS are different. Homework Equations Field: A = ρcos(φ/2)uρ+ρ2 sin(φ/4) uφ+(1+z)uz (1) The Attempt at...

Homework Statement Find the value of the (surface) integral \int curl \textbf{A} \bullet \textbf{a} if the vector \textbf{A}=y \textbf{i}+z \textbf{j}+x \textbf{k} and S is the surface defined by the paraboloid z=1-x^2-y^2 Homework Equations x=s\cos\phi y=s\sin\phi...

would anybody like to discuss how to accurately follow a particle moving in a HELICAL PATHWAY using vectors, spherical and cylindrical coordinates? I'm not sure how to follow a geometric helical pathway using linear and parametric equations.

Is there a cylindrical coordinate system that is centered about the foci of an ellipse. It would include (r,theta,z) just like cylindrical coordinates only for an ellipse. If this coordinate system exists, what is the laplacian? Chris

Homework Statement Identify and sketch the graph of the surface y^2 + z^2 = 1. Show atleast one contour perpendicular to each coordinate axis Homework Equations The Attempt at a Solution for the yz plane z = (1-y^2)^1/2 a circle of radius 2 centered at the origin xy, set z=0...

Homework Statement z = 4y^2, x = 0, is rotated about the z axis. write the equation of the resulting surface in cylindrical coordinates Homework Equations The Attempt at a Solution not really sure what the x = 0 means so i ignored it i solved for y because that would be my...

For example with a paraboloid, which do i use? I am also slightly confused with the limits in the integral. If doing a triple integral with drdθdΦ i understand the limits of the dr integral but when it comes to dθ and dΦ i don't understand why sometimes its 0 to 2π or 0 to π etc. For example...

Homework Statement The problem was to find the volume enclosed by a sphere of radius "a" centered on the origin by crafting a triple integral and solving for it using cylindrical coordinates. Homework Equations x^{2}+y^{2}+z^{2}=a^{2} : Equation for a sphere of radius "a" centered on...

Homework Statement Compute the divergence in cylindrical coordinates by transforming the expression for divergence in cartestian coordinates. Homework Equations F = F_x i + F_y j + F_z k div F = ∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z ... (divergence in Cartesian coordinates) I need to...

Homework Statement Transform to cylindrical coordinates: x^{2}+y^{2}=R^{2} Doesn't look like a problem at all first... :smile: Homework Equations .. after all I know that is a circle (2d) and we can forget the z-axis (=0) and transform it to just polar coords. Also I know, that for...

Convert r=2cos(theta) from cylindrical coordinates to rectangular coordinates I have tried squaring both sides so that it will be equal to x squared plus y squared, and then solving for a variable. No matter what I do though I am left with two variables so I feel like I am taking the...

So we just were given some formulas and I am confused about this simple question Find the differential length or distance between the two points. P(2,pi/2,-1) and Q(5,3pi/2,5)I know this for cylindrical dL = dp (ap) + p dphi (aphi) + dz (az) So i would integrate I have a few questions...

Homework Statement \int\int_{Q}\int(x^4+2x^2y^2+y^4)dV where Q is the cylindrical solid given by \{(x,y,x)| x^2+y^2 \leq a^2, 0\leqz\leq\frac{1}{\pi}\}Homework Equations When I convert to cylindrical I get f(r,\theta,z) = r^4\cos^2\theta + 2r^4\cos^2\theta\sin^2\theta + r^2\sin^2\theta, but I...

Homework Statement Use Cylindrical Coordinates. Find the volume of the solid that the cylinder r=acos\theta cuts out of the sphere of radius a centered at the origin. Homework Equations Sphere = x2+y2+z2=a3 The Attempt at a Solution I think that the limits are from -pi/2 to...

Homework Statement This is my last question about triple integrals in cylindrical coordinates. Evaluate the integral by changing to cylindrical coordinates: \int _{-3}^3\int _0^{\sqrt{9-x^2}}\int _0^{9-x^2-y^2}\sqrt{x^2+y^2}dzdydx Homework Equations In cylindrical coordinates...

Homework Statement Find the mass and center of mass of the solid S bounded by the paraboloid z=4x^2+4y^2 and the plane z=a\;\;(a>0) if S has constant density K. Homework Equations In cylindrical coordinates, x^2+y^2=r^2. The Attempt at a Solution In order to find the mass, I tried...

Homework Statement Evaluate \int \int \int_E x^2 \, dV where E is the solid that lies within the cylinder x^2+y^2=1, above the plane z=0, and below the cone z^2=4x^2+4y^2.Homework Equations In cylindrical coordinates, x^2+y^2=r^2 and x=r\cos{\theta}.The Attempt at a Solution I tried \int...

Revised question is below.

Could someone tell me what I'm doing wrong? thanks! Homework Statement Write the equation is cylindrical coordinates 7x2 + 7y2 = 2y r = ? (has to be in the r = ? format) Homework Equations r2 = x2 +y2 x = rcos(θ) y = rsin(θ) The Attempt at a Solution 7x2 + 7y2 = 2y...

Homework Statement Transform the vector below from Cartesian to Cylindrical coordinates: Q\,=\,\frac{\sqrt{x^2\,+\,y^2}}{\sqrt{x^2\,+\,y^2\,+\,z^2}}\,\hat{x}\,-\,\frac{y\,z}{x^2\,+\,y^2\,+\,z^2}\,\hat{z} Homework Equations Use these equations...

Homework Statement Set up triple integrals for the volume of the sphere rho = 2 in (a) spherical, (b) cylindrical, and (c) rectangular coordinates. Homework Equations Volume in cylindrical coordinates: Triple integral of dz r dr d(theta) over region D. Volume in spherical coordinates...

My question is about vector addition in cylindrical coordinates: Let A = 2x + y, B = x + 2y. In rectangular coordinates, AB = B-A = -x+y In cylindrical coordinates, x=rcosθ + θsinθ, y=rsinθ + θcosθ A =Axx + Ayy, B =Bxx + Byy Ar = Ax(x.r) + Bx(y.r)=2.236, Aθ = 0. So A = 2.236r Br =...