Cylindrical Definition and 821 Threads

A cylinder (from Greek κύλινδρος – kulindros, "roller", "tumbler") has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. It is the idealized version of a solid physical tin can having lids on top and bottom.
This traditional view is still used in elementary treatments of geometry, but the advanced mathematical viewpoint has shifted to the infinite curvilinear surface and this is how a cylinder is now defined in various modern branches of geometry and topology.
The shift in the basic meaning (solid versus surface) has created some ambiguity with terminology. It is generally hoped that context makes the meaning clear. Both points of view are typically presented and distinguished by referring to solid cylinders and cylindrical surfaces, but in the literature the unadorned term cylinder could refer to either of these or to an even more specialized object, the right circular cylinder.

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  1. T

    Cylindrical coordinates question

    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...
  2. O

    Iterative procedure for potential distribution of a cylindrical problem?

    Hi there, I arrived at the solution for a electric potential problem for a semi-infinite cylinder (there was a potential distribution given for the boundary conditions but that's not important here). http://i210.photobucket.com/albums/bb283/DidgeFrank/Cylinder_pot.jpg The solution is...
  3. R

    Stokes theorem in a cylindrical co-ordinates, vector field

    Homework Statement given a vector field v[/B=]Kθ/s θ (which is a two dimensional vector field in the direction of the angle, θ with a distance s from the origin) find the curl of the field and verify stokes theorem applies to this field, using a circle of radius R around the origin Homework...
  4. U

    Calculating Volume of a Cylindrical Wedge

    Homework Statement The problem is attached in the picture. The Attempt at a Solution What bothers me is that they say the wedge is bounded by x + z = a. Doesn't this imply that the calculated volume should only be half of what is written in the answers? I'm aware that the plane x +...
  5. N

    Volume of the solid using a cylindrical cross section

    Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Homework Equations y = \sqrt{x-1} , y = 0, x = 5; about y = 3 The Attempt at a Solution I already completed graphing it, but not really sure how...
  6. P

    Forces on a cylindrical vacuum chamber

    If a cylindrical vacuum chamber's diameter is increased, then the inward force on the two ends will increase because the area is increased. However, if the length of the chamber is increased, while keeping diameter constant, will that increase the net inward force on the chamber? Or does...
  7. J

    Images formed by cylindrical lens

    Cylindrical lenses focus light rays onto a line instead of a point. Is that means several images will be formed from a point object aftering passing through the lens? (please see the attached files 1 and 2) If I am correct, can anyone explain to me,when you add water to a tall water...
  8. A

    To find vectors in cylindrical system

    is there any way to find vector in cylindrical system without converting the variable of cylindrical system to Cartesian system? advanced thanks
  9. G

    Calculating Time of Impact of Pendulum Bob on Cylindrical Bar

    Homework Statement A cylindrical metal bar of length L hangs by two strings in a horizontal position. The metal bob of a simple pendulum hits one end of this metal bar in a direction perpendicular to the crossection of the bar. Find an expression for the time t of contact during the impact...
  10. 5

    Heat transfer in a cylindrical tube

    Homework Statement I don't really understand something in my textbook. It says the heat Resistor (how to say that in English? I hope it's alright like this...) trough a cylindrical tube (from the inside to the outside or revers) would be: R(heatrisistor)=1/2∏Lλ * ln (R1/R2) And then my...
  11. B

    Cylindrical capacitor with varying dielectric

    Homework Statement Consider a long cylindrical coaxial capacitor with an inner conductor of radius a, and outer conductor of radius b, and a dielectric with a relative electric permittivity or dielectric ε(r), varying with the cylindrical radius. The capacitor is charged to the voltage V...
  12. W

    Insulating Cylindrical Shell, Potential at edge

    Homework Statement A long cylindrical insulating shell has an inner radius of a = 1.37 m and an outer radius of b = 1.60 m. The shell has a constant charge density of 2.70 10−9 C/m3. The picture shows an end-on cross-section of the cylindrical shell. What is the magnitude of the electric...
  13. P

    Concentric cylindrical insulator and conductor

    Homework Statement A line charge λ is surrounded by a long cylindrical insulator with a linear charge density 2λ and radius a. This is surrounded by a concentric conductor cylinder of radius b. Use Gauss’s Law to find the charge density on the surface per unit length at r = a just inside...
  14. T

    Triple integral for cone in cylindrical coordinates.

    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...
  15. Z

    Integral in cylindrical coordinates

    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...
  16. Z

    Cylindrical Co-ordinate Question

    Homework Statement In a textbook it states: How do they conclude this? Thank you. Homework Equations The Attempt at a Solution
  17. C

    Mathematica How to Plot in Cylindrical Coordinates in Mathematica?

    I'm looking for a function to plot things in 3D using cylindrical coordinates but apparently Mathematica doesn't have one?
  18. C

    Charged sphere place within a cylindrical capacitor

    Homework Statement The outer conductor (radius b, length l) of a long cylindrical capacitor is earthed. The inner conductor (radius a, length l) is hollow, insulated and uncharged. A sphere of radius R is charged to a potential V far from any other bodies and is inserted inside the inner...
  19. A

    Calculate electric field for cylindrical charge distributions

    (2.16) A long coaxial cable carries a uniform volume charge density ρ on the inner cylinder (radius a) and a uniform surface charge density on the outer cylindrical shell (radius b). This surface charge is negative and just the right magnitude so that the cable as a whole is electrically...
  20. J

    Heat Flow across cylindrical surface

    Homework Statement The temperatur at the point (x,y,z) in a substance with conductivity K=6.5 is u(x,y,z)=2y2+2z2. Find the rate of heat flow inward across the cylindrical surface y2+z2=6, 0≤x≤4. Homework Equations F=-k∇u -k∫∫s∇u*ds The Attempt at a Solution So F=-6.5(0,4y,4z) I...
  21. S

    Hydrostatics and Cylindrical Tank

    Homework Statement I fill a cylindrical tank of length 50 ft and diameter 90 ft with water (to the brim). What is the force the bottom 1 ft band of water exerts on the lining? Homework Equations The Attempt at a Solution My main doubt is whether i should integrate from 0 to 1 and...
  22. D

    Triple Integral in Cylindrical Coords

    Homework Statement Construct a triple integral in cylindrical coords to find the volume of the cone r=z, where the height (z value) is limited by z=L. Should be in the form => {int[b,a] int[d,c] int[f,e]} (r) {dr dtheta dz} (Sorry for weird formatting above, brackets purely to make terms...
  23. A

    Magnitude and Direction of Induced Current on a wire around a cylindrical volume

    Homework Statement A uniform magnetic field B is confined to a cylindrical volume of radius 0.080m. B is directed into the plane of the paper and is increasing at a constant rate of (delta)B/(delta)t=0.300 T/s. Calculate the magnitude and direction of the current induced in a circular wire...
  24. 9

    Gravity of a Rotating Cylindrical Space Station: Confirmation Needed

    A cylindrical space station of radius r with thin walls and mass M rotates at angular velocity ω such that the apparent gravity on the inner surface of the cylinder is equal to g. 1) Radial spokes of negligible mass connect the cylinder to the centre of motion. An astronaut of mass m climbs a...
  25. N

    Force between two cylindrical magnets

    Hello, I'm a high school senior and I'm trying to find an equation to calculate the force in the x direction between two identical N35 Neodymium magnets given a certain position relative to one another (see attached .jpg). N35 cylinder magnets Dimensions: 4.5 mm (height) 5 mm...
  26. N

    Converting Spherical to Cylindrical Coordinates for a Velocity Expression

    Homework Statement Hi I have an expression on the form df(v, \theta, \phi) = v e^{-v^2/C}\cos(\theta)v^2\sin(\theta)\,dv\,d\theta\,d\phi and I am trying to write it in cylindrical coordinates. Note that θ runs from 0..π, v is a velocity and C a real constant. So I wish to write it in terms...
  27. L

    Continuum Mechanics - Bernouilli's Equation in a Cylindrical Tank

    Homework Statement A large cylindrical tank of radius R is full of water to a height h(t). This drains under gravity out of the bottom of the tank through a small hole of radius r. The acceleration due to gravity is g. The pressure of the air can be assumed to be the same at the top and at...
  28. G

    Vector product question in cylindrical coordinates

    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...
  29. F

    How does an image formed by a cylindrical lens look like?

    Hello forum, I have been trying to understand how a cylindrical lens (plano cylindrical) forms images. The images are blurred, smeared, only in one direction. I know that this type of lens focuses parallel rays to a focal line instead of to a focal point... So the smearing occurs along...
  30. R

    Calculating the Volume of a Cylindrical Wedge Using Calculus and Geometry

    Homework Statement Find the volume of the enclosed by the surfaces z=qx z=0 and x²+y²=2ax Homework Equations This is meant to be done with calculus but can verify my answer with simple geometry - should be \pi a^3q The Attempt at a Solution So the top of the wedge will be when x=2a...
  31. Z

    Sketch in Cylindrical Coordinates for z=6

    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...
  32. R

    Integral in cylindrical coordinates

    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 <=...
  33. C

    EMF/Eddy Currents Induced in a Hollow Cylindrical Conductor

    I'm attempting to figure out the total current induced in a hollow metal tube as a result of the EMF due to a constantly varying magnetic flux through its cross-section. Faraday's law of induction states that for an infinitely thin loop of wire in such varying magnetic flux has induced EMF...
  34. S

    Finding the volume of the cone using cylindrical polar coordinates?

    The cone centre is the z-axis and has base ρ=1 and height z=1, I'm looking at the lecture notes and it says the limit φ=0 to 2pi, z=0 to 1, ρ=0 to (1-z). Could someone tell me where the (1-z) comes from please? Why is it not 0 to 1?
  35. S

    Vector Fields in Cartesian and Cylindrical Coordinates, The Curl

    All necessary information is attached except the answer in Cartesian coordinates, which is -ix-jy+2kz and my work converting back from cylindrical to Cartesian, which I used WolframAlpha for, as the trig is a mess (that is, if the way I am doing this is correct)...
  36. S

    Vector Fields in Cartesian and Cylindrical Coordinates, The Curl

    All necessary information is attached except the answer in Cartesian coordinates, which is -ix-jy+2kz and my work converting back from cylindrical to Cartesian, which I used WolframAlpha for, as the trig is a mess (that is, if the way I am doing this is correct)...
  37. N

    Convert tensor from cartesian to cylindrical coordinate

    Homework Statement Given the tensor F_{\mu \nu }= \left[ \begin{array}{cccc} 0 & -E_{x} & -E_{y} & -E_{z} \\ E_{x} & 0 & B_{z} &-B_{y} \\E_{y} & -B_{z} & 0 & B_{x} \\E_{z} & B_{y} & -B_{x} & 0 \end{array} \right] F^{\mu \nu }F_{\mu \nu }=2(B^2-\frac{E^2}{c^2}) and metric tensor n_{\mu \nu...
  38. E

    Electric field of a cylindrical capacitor

    Homework Statement Calculate the electric field of a cylindrical capacitor comprised of a smaller cylindrical conductor of radius ##a## enclosed within a larger cylindrical conductor of radius ##b## where ##b>a##. The smaller cylinder has charge ##+Q## and the larger cylinder has charge...
  39. N

    Electromagnetic tensor in cylindrical coordinates

    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)
  40. T

    Vector transformation, cylindrical to Cartesian

    Homework Statement I have a result which is in the form (cylindrical coordinates): $$ A\boldsymbol{e_{\theta }}=kr\boldsymbol{e_{\theta }} $$ And I have to provide the answer in cartesian coordinates.Homework Equations I know that the unit vectors: $$ \boldsymbol{\hat{\theta}...
  41. H

    Eddy current in an infinitely long cylindrical conductor in an solenoid

    Problem: Calculating the eddy current distribution inside an infinitely long cylindrical conductor inside a straight and infinitely long solenoid energized by an alternating sinusoidal current. The problem has a perfect summery and we know that magnetic field and the eddy current depend on...
  42. Peeter

    Fluid stress tensor in cylindrical coordinates?

    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...
  43. G

    Cylindrical shell- electric potential problem

    A very long insulating cylindrical shell of radius 6.40 cm carries charge of linear density 8.90μC/m spread uniformly over its outer surface. What would a voltmeter read if it were connected between the surface of the cylinder and a point 4.00 cmabove the surface? λ=dq/dr V=k∫dq/r...
  44. V

    Finding the B field in a long cylindrical hole in a long wire

    So, I'm trying this problem and just want to make sure my attack is correct. We have an infinitely long cylindrical hole in an infinitely long cylindrical wire, like in this picture: (Here, they call the radius of the hole 'a'. I'm going to call it r.) There's an electric current I in...
  45. J

    Eulers equation in cylindrical coordinates

    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...
  46. Biosyn

    How to Find Volume by Cylindrical Shells?

    Homework Statement Rotate around the y-axis the region above the graph of y=x3 that is bounded by the lines x=1 and y=8 Homework Equations dV= (2pix)(y)(dx) The Attempt at a Solution dV = (2pix)(y)dx dV = (2pix)(x^3) dx = 2pix^4 I integrated from y = 1 to y=8 and I...
  47. A

    What are the differences between cylindrical and cartesian coordinates?

    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...
  48. J

    Computing for Electric Field given cylindrical coordinates of v.

    Homework Statement If the scalar electric potential v in some region is given in cylindrical coordinates by 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 So...
  49. D

    Concentric Cylindrical Conducting Shells and Capacitors

    Homework Statement An infinitely long solid conducting cylindrical shell of radius a = 3.1 cm and negligible thickness is positioned with its symmetry axis along the z-axis as shown. The shell is charged, having a linear charge density λinner = -0.49 μC/m. Concentric with the shell is another...
  50. C

    Finding electric potential given a cylindrical configuration

    Homework Statement You have two concentric cylinders. The inner cylinder has radius a and the external cylinder has radius b. Find the electric potential in the region between the cylinders. [Hint: The final equation takes the form V(r) = constant1 - constant2 ln(something) ]...
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