Cylindrical coordinates Definition and 225 Threads

Homework Statement Let S be the part of the cylinder of radius 9 centered about z-axis and bounded by y >= 0; z = -17; z = 17. Evaluate \iint xy^2z^2 Homework Equations The Attempt at a Solution So I use the equation x^2 + y^2 \leq 9, meaning that r goes from 0 to 3 Since y...

In my physics textbook we have d\vec{l}=\hat{z}dz and then it says d\vec{l}\times \hat{R}=\hat{\phi}\sin \left (\theta \right )dz How so? What is \hat{z}\times\hat{R}? If it is \hat{\phi} then where does the sine come from?

Homework Statement Use cylindrical coordinates to describe the line through the point (1,1,0) and parallel to the z-axis. Homework Equations How does one go about this? Even my course book was unclear about this. Any general overview about how to do such a question will be helpful. The...

Homework Statement Find the volume of the solid that lies between z=x2+y2 and x2+y2+z2=2 Homework Equations z=r2 z=√(2-r2) The Attempt at a Solution So changing this into cylindrical coordinates, I get z goes from r2 to √(2-r2) r goes from 0 to √2 theta goes from 0...

hello i am solving heat equation in cylindrical coordinator. i am using MATLAB "pdepe" solver to solve the partial differential equation. can anyone suggest me how to choose the initial condition?

Hi all, Del = i ∂/∂x + j ∂/∂y + k ∂/∂z in x y z cordinate similarly I require to see the derivation of del in other coordinates too. Please give me a link for the derivation.

Large, cylindrical bales of hay used to feed livestock in the winter months are D = 2 m in diameter and are stored end-to-end in long rows. Microbial energy generation occurs in the hay and can be excessive if the farmer bales the hay in a too-wet condition. Assuming the thermal conductivity of...

Homework Statement Find the volume of the solid that the cylinder r = acosθ cuts out of the sphere of radius a centered at the origin.Homework Equations Cylindrical coordinates: x = rcosθ, y = rsinθ, z=z, r2 = x2+y2, tanθ = y/xThe Attempt at a Solution So I know that the equation for the sphere...

Homework Statement Consider the interated integral I=∫∫∫ρ^3 sin^2(∅) dρ d∅ dθ -the bounds of the first integral (from left to right) are from 0 to pi -the bounds of the second integral are from 0 to pi/2 -the bounds of the third integral are from 1 to 3 a)express I as an interated...

There has been a few times when I switch from Cartesian to cylindrical coordinates to integrate I would get the wrong because I used the wrong substitution. For instance I would use x = rcos(θ) and y = rsin(θ) where r and θ are variable when I was suppose to leave r as a constant. Question...

Homework Statement I'm trying to get to grips with Godel's 1949 Paper on Closed Time-like Curves (CTCs). Currently I'm trying to confirm his transformation to cylindrical coordinates using maple but seem to keep getting the wrong answer. Homework Equations The line element in cartesian...

Homework Statement Let W= {(x,y,z)| x^2 + y^2 ≤ 1, -1 ≤ z ≤ 1} (W is a bounded cylindrical region) Evaluate the triple integral f(x,y,z)= z^2 x^2 + z^2 y^2 over W. Use cylindrical coordinates Homework Equations i don't see any relevant equations besides the obvious cylindrical...

From this equation x2 + y2 = 2y I was wondering how in the solutions manual it was decided that 0≤z≤1 ? Edit: Don't read... I was looking at a solution to a different problem

Homework Statement The surface is x^2/y*z=10. Put this into cylidrical coordinates. in the form r=f(theta,z) Homework Equations No clue The Attempt at a Solution No clue

Homework Statement As a part of bigger HW problem, I need to calculate the integral: \oint[\hat{r}+\hat{z}]d\phi Homework Equations The Attempt at a Solution In cylindrical coordinates: =[\hat{r}+\hat{z}] \ointd\phi =2∏[\hat{r}+\hat{z}] On the other hand if I convert it to...

Hey Guys, Does anyone know where I can find a derivation of the laplace operator in spherical and cylidrical coordinates?

Homework Statement https://dl.dropbox.com/u/64325990/cylindrical.PNG The Attempt at a Solution Okay so I found r = 2.24 and z = -3. However I am stuck at finding theta. I think I just don't understand what the question means when it says "In addition, the line defined by theta = 0 in...

Homework Statement Find limits of integration for volume of upside down cone with vertex on origin and base at z=1/sqrt(2). Angle at vertex is pi/2. Do this in cylindrical coordinates. Homework Equations None. The Attempt at a Solution My inner integral conflicts with the books...

I recently did an integral of the form: ∫∫1/ρ dρρdθ the extra ρ between dρ and dθ is the cost of switching to cylindrical coordinates. Now I want to know, do you carry out the integration in ρ, keeping the ρ outside the integration (since it's technically a scaling factor that belongs to...

I am trying to work the following problem; A rigid body is rotating about a fixed axis with a constant angular velocity ω. Take ω to lie entirely on th z-axis. Express r in cylindrical coordinates, and calculate; a) v=ω × r b)∇ × v The answer to (a) is v=ψωρ and (b) is ∇ × v = 2ω...

Homework Statement In cylindrical coordinates, sketch the surface defined by z=6 The hand drawn sketch shown in the answer I have appears to be a rectangular or square plane at z=6 Should the plane be square/rectangular or should it be circular? To illustrate, the blue plane in the diagram...

Homework Statement I need to calculate the integral where the region is given by the inside of x^2 + y^2 + z^2 = 2 and outside of 4x^2 + 4y^2 - z^2 = 3 Homework Equations The Attempt at a Solution So far, I think that in cylindrical coordinates (dzdrdtheta): 0 <= theta <= 2pi sqrt(3)/2 <=...

I can find the metric tensor in cylindrical coordinates to be [1,-1,-1/r^2,-1] but how about the electromagnetic field tensor and thus the energy stress tensor? Is it just change the Ex,Ey,Ez to Eρ,Eθ,Ez? Is FσρFσρ still equal to 2(B^2-E^2)

For fluid with viscosity \mu our stress strain relationship takes the form \sigma_{ij} = -p \delta_{ij} + 2 \mu u_{ij}. I was wondering how to express this in cylindrical coordinates. The strain tensor I can calculate in cylindrical coordinates (what I get matches eq 1.8 in [1]). But how...

find the geodesics on a cylinder, where R^2 = x^2 + y^2 ---------------------------- so the goal is to find a function F, that gives the minimum distance between any two points on the cylinder. in cylindrical coordinates, dl = sqrt( ds^2 +(sdθ)^2 +dz^2 ) since we are on the surface...

Consider the attached picture, where they express the unit vectors in cartesian coordinates with the unit vectors in a cylindrical coordinate system: The questions might be a bit loose, but try to get what I mean and answer as well as you can please :) 1) I find the expression for i, j and k a...

Homework Statement If the scalar electric potential v in some region is given in cylindrical coordinates by [SIZE="4"] v (r, \phi, z) = r^2 sin \phi e^{\frac{-3}{z}} , what is the electric field \vec{E} in that region? Homework Equations E = -\nabla v The Attempt at a Solution...

Homework Statement .. Here is the question; In cylindrical coordinate system , (a) If r = 2 meters , \varphi = 35° , z = 1 meter , what are x,y,z? (b) if (x,y,z) = (3,2,4) meters, what are (r, \varphi, z) Homework Equations x = r cos \varphi y = r sin \varphi z = z r =...

I'm trying to understand this one derivation but this one part keeps messing me up; theta = tan^-1 (y/x) r^2 = x^2 + y^2 d theta/ d x = y/ (x^2 + y^2) how did they get this line?

Homework Statement When you are doing a triple integral and convert it to cylindrical co ordinates, how do you find the new ranges of integration? I understand the new range of z, if z is between f(x,y) and g(x,y), you just sub in x = r cos θ and y = r sin θ to find the new functions...

Are spherical and cylindrical coordinate systems only a physical tool or is there some mathematical motivation behind them? I assume that they can be derived mathematically, but multivariable calculus texts introduce them and state their important properties without much background information...

Hello everyone, Sorry if this is in the wrong sub-forum, I wasn't sure exactly where to place it. I was wondering if there is an orthogonality relationship for the Legendre polynomials P^{0}_{n}(x) that have been converted to cylindrical coordinates from spherical coordinates, similar to...

Homework Statement i just want to know how to visualize in spherical and cylindrical coordinates I am really having a rough time doing that for example why is that when we keep r constant we get a sphere and θ constant a cone why?? Homework Equations The Attempt at a Solution

Homework Statement Use cylindrical coordinates to find (a) the volume and (b) the centroid of the solid S bounded above by the plane z=y and below by the paraboloid z=x2+y2. Homework Equations V= ∫∫∫dv x= r cos θ, y=sin θ, z=z The Attempt at a Solution For the first integral I got...

Homework Statement Let W be the region between the paraboloids z = x^2 + y^2 and z = 8 - x^2 - y^2 Homework Equations The Attempt at a Solution for each domain, 0 ≤ z ≤ 8 0 ≤ r ≤ 2 0 ≤ θ ≤ 2\pi So... \int^{2\pi}_{0}\int^{2}_{0}(8-2r^{2})r drdθ

Homework Statement Set up intergral expression for center of mass of a cone using cylindrical coordinates with a given height H and radius R Homework Equations rdrddθdz is part of the inter grand. M/V=D volume of cone is 1/3π(r^2)H The Attempt at a Solution dm=Kdv dv=drdθdx K...

Homework Statement Evaluate the integral, where E is the solid in the first octant that lies beneath the paraboloid z = 9 - x2 - y2. ∫∫∫(2(x^3+xy^2))dV Homework Equations x=rcosθ y=rsinθ x^2+y^2=r^2 The Attempt at a Solution θ=0 to 2π, r=0 to 3, z=0 to (9-r^2)...

Hi all, I have been struggling (really) with this and hope someone can help me out. I would just like to compute the gradient of a tensor in cylindrical coordinates. I thought I got the right way to calculate and successfully computed several terms and check against the results given by...

Hello, In Godel's paper: an example of a new type of cosmological solutions of einstein's field equations of gravitation, he passes from his original metric to cylindrical coordinates by giving some transformation formulas. Can someone tell me how is this transformation obtained, or at least...

This is calculus question, but I don't think calculus really cover this topic in either multi-variables or even vector calculus classes. This is really more common problem in electrodynamics. Let R be position vector that trace out a circle or radius a with constant velocity. In rectangular...

Homework Statement I took a picture of the problem so it would be easier to understand. All I need to know is what the bounds are. Homework Equations In cylindrical: x=rcos(theta) y=rsin(theta) z=z The Attempt at a Solution I don't know why we should change this to...

Homework Statement Hi there. I haven't used iterated integrals for a while, and I'm studying some mechanics, the inertia tensor, etc. so I need to use some calculus. And I'm having some trouble with it. I was trying to find the volume of a cone, and then I've found lots of trouble with such a...

Homework Statement Question 3 (a)A long metal cylinder of radius a has the z-axis as its axis of symmetry.The cylinder carries a steady current of uniform current density J = Jzez. Derive an expression for the magnetic field at distance r from the axis,where r<a. By resolving the...

How would I go about working out the Electric Field E(X) in cylindrical coordinates? The question is, Suppose pho = pho(r) find E^pho. Suggestion to use Greens & Gauss theorem

1. Homework Statement +attempt at solution+equations In Cartesian coordinates, x translate into x=r \cos \theta into cylindrical coordinates, y=r \sin \theta and z=z . However dx=\cos \theta dr - r \sin \theta d\theta. This is what I don't understand. Since x is a function of both...

Homework Statement Find the volume of the solid bounded by the paraboloids z=x^2+y^2 and z=36-x^2-y^2. Answer is: 324\pi \\ Homework Equations r^2=x^2+y^2 x=rcos0 y=rcos0 The Attempt at a Solution 36-x^2+y^2=x^2+y^2\\ 36=2x^2+2y^2 18=x^2+y^2 r^2=18 V=\int_{0}^{2\pi} \int_0^{3\sqrt{2}}...

Homework Statement A cam has a shape that is described by the function r = r_0(2 - cos \theta), where r_0 = 2.25 ft. A slotted bar is attached to the origin and rotates in the horizontal plane with a constant angular velocity (\dot{\theta} dot) of 0.85 radians/s. The bar moves a roller...

This is something I have zero familiarity with. Anyways, I was given the equation: r=2asin(theta)+2bcos(theta) and had to prove that it was a circle, and then state its center in cartesian and cylindrical coordinates. After making the appropriate substitutions and completing the square...

Homework Statement Not really a homework question, but more of a concept question which I'm unfamiliar with. So as we know, equations can be in any coordinate, but how do you convert them from one to another? For example, a few equations from fluid mechanics. the first equation is the vector...

Hello everybody! Although this may sound like a homework problem, I can assure you that it isn't. To prove it, I will give you the answer: 40pi. So.. I'm self-studying some electrodynamics. I'm using the third edition of Griffiths, and I have a quick question. For those who own the book and...