What is Cylindrical: Definition and 821 Discussions

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. F

    Cylindrical Coordinate Inequalities: Half-Cylinder and Quarter Cone/Paraboloid

    cylindrical cordinace?? Homework Statement this is a two part question and is multiple choice part 1 Determine the type of the solid described by the given inequalities. 0 ≤ r ≤ 4, - pi≤ θ ≤ pi, -sqrt(16 − r^2) ≤ z ≤ sprt(16 − r^2) a half-cylinder a cylinder a...
  2. P

    Electric field from a cylindrical shell

    Homework Statement Consider a uniformly charged thin-walled right circular cylindrical shell having total charge Q, radius R, and height h. Determine the electric field at a point a distance d from the right side of the cylinder as shown in the figure below. Homework Equations E =...
  3. K

    What dimension is the surface of a cylindrical shell

    Hello there, i wanted to know what is the difference between a surface in R^2 and a surface in R^3 in an xyz cordiante system. More specifically how do they look like? an example please. Is this different from a 2 dimensional surface and a 3 dimensional surface respectively. Also what...
  4. R

    Cylindrical Capacitor

    Homework Statement Hey guys, My prof asked us to find the radius of a cylinder within a cylindrical capacitor with 2 radii a and b. I know we use the Capacitance formula for a cylinder but I can't seem to get pass the q that shows up when I plug it into the 1/2 c*V^2 EDIT: He wants us to find...
  5. Pengwuino

    Cylindrical potential problem using Bessel functions

    Jackson 3.12: An infinite, thin, plane sheet of conducting material has a circular hole of radius a cut in it. A thin, flat disc of the same material and slightly smaller radius lies in the plane, filling the hole, but separted from the sheet by a very narrow insulating ring. The disc is...
  6. D

    Magnetic field expansion in cylindrical coordinate

    Homework Statement Dear all, i am figuring the taylor expansion for magnetic field in cylindrical coordinate (r,theta,z). The taylor expansion is simple, however if i want to express the magnetic field in just z direction, i don't know to start. It is because i seen some books...
  7. P

    Transform vector to Cylindrical Coordinates

    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...
  8. E

    Charge on cylindrical capacitor

    Homework Statement A cylindrical air capacitor with a length of 12.2 m stores an amount of energy equal to 3.00E-8 J when the potential difference between the conductors is 4 V. Calculate the magnitude of the charge on each conductor. Homework Equations...
  9. T

    Resonances of Cylindrical Shells with uniform radial pressure

    I have picked up "Roark's Formulas for Stress and Strain" and "Mechanical Vibrations" and have been unable to reach resolution on a particular problem. I am interested in the behavior of a uniform cylindrical shell (cylinder diameter >> wall thickness) rigidly clamped at both ends wherein...
  10. S

    Stokes Theorem in cylindrical coordinates

    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...
  11. 1

    Charge Inside A Non-Conductive Charged Spherical or Cylindrical Shell

    Hey Guys, I wanted to clarify something I'm not too sure about. The charge inside (in the center not actually in the shell) of a charged non-conductive spherical or cylindrical shell is zero, am I wrong? The reason being the geometry within the shell cancels all the charges within. Any...
  12. K

    Solving by using cylindrical shell method

    Homework Statement Evaluate using the cylindrical shell method, the volume of the solid of revolution obtained by rotating the region enclosed by the curves y=x^3, y=-x and y=1 around the line y=-1. The attempt at a solution The answer is suppose to be 127(pi)/42 but I keep getting...
  13. N

    Power dissipated in a cylindrical cavity due to a current carrying filament

    Homework Statement A cylindrical cavity oriented along z axis with length of 2 m has a filament in it upon which a current of 10 A is impressed. Cavity is perfectly conducting whereas it is filled with lossy dielectric. Electric field on the cavity is given as: E=-z(i+j). One has to...
  14. M

    Line Integral in Cylindrical Coordinates

    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...
  15. E

    What Is the Capacitance Between Two Long Parallel Cylindrical Wires?

    Homework Statement tow long cylindrical conducting wire ,each of radius a and length l parallel and separated by d , and between the centers of the wires , d>>a ,and the surface charge densities is uniformly,then the total electris potential is the sum of each wire . the effect between them...
  16. M

    Cylindrical vs. spherical coordinates

    Hi everyone! There's a question bothering me about the two coordinate systems - cylindrical and spherical: Consider the two systems, i.e. (r, \theta, \phi)\rightarrow\left(\begin{array}{c}r\sin\theta\cos\phi\\r\sin\theta\sin\phi\\r\cos\theta\end{array}\right) and...
  17. N

    Electric field in a cylindrical configuration

    Homework Statement Immediately outside a very long, cylindrical wire of radius R1=0.6mm, the electric field is 50 kV/m directed towards the wire's surface. The wire is in air. What is the charge per unit along length the wire? (take care with sign) What is the field at R2=3.0mm? (i.e. 2.4mm...
  18. L

    Wave equation, general solution, cylindrical symmetry

    I was interrested in the general solutions to the wave equation depending on only one spatial coordinate. For one linear coordinate, the general solution is: a f(x-ct) + b g(x+ct) For one radial spherical coordinate, the general solution is: a f(r-ct)/r + b g(r+ct)/r I thought that...
  19. E

    Electric Flux on a Cylindrical Gauss Surface

    Homework Statement A cylinder of length L and radius R is centered on the z-axis in a region where there is a uniform electric field of E i. Determine the flux for the fourth of the cylindrical surface where x > 0 and y > 0. Homework Equations \phi = \int E dS The Attempt at a...
  20. M

    Coriolis forse and cylindrical co-ordinates

    Pseudo forses arising in a frame are defined as the negative of mass times acceleration of the frame used. now in cylindrical coordinate system if we compute acceleration, we should be able to know completely the corilis and centripetel forses. However my problem is I don't understand...
  21. M

    Helical Pathway Movement Using Vectors, Spherical & Cylindrical Coordinates

    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.
  22. P

    Air vibrating in a cylindrical cavity

    The diagram accompanying this post shows a cylindrical column bored at right angles to a flat surface. Let’s say the material is a block of brass with a hole drilled in it. The arrow represents a fast moving stream of compressed air. As the air passes over the top of the column a high pitched...
  23. N

    Elliptic Cylindrical Coordinates

    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
  24. H

    Del Operator for Cylindrical Coordinate

    http://img208.imageshack.us/img208/5153/12802868.png Why is the del operator for cylindrical coordinate the upper one and not the lower one? How does the 1/r term arises?
  25. Z

    What is the Centroid of a Cylindrical Cone?

    Homework Statement Determine the centroid of volume for a right circular cone with base diameter of 100mm and an altitude of 200mm. Homework Equations I know that if the my xy-plane is parallel to the base of the cylindrical cone then the x and y coordinates of the centroid must be...
  26. W

    Total induced charge of an infinite cylindrical conductor

    Homework Statement calculate total induced charge on a charged cylinder. where the surface charge density is given by sigma= 2eEo cos(phi) Homework Equations the total induced charge on the cylinder is Integral of (sigma) da can u calculate this integral fo me ... it very...
  27. W

    Cylindrical optimization problem

    A closed cyliindrical container has a volume of 5000in^3. The top and the bottom of the container costs 2.50$in^2 and the rest of the container costs 4$in^2. How should you choose height and radius in order to minimize the cost? v=pi(r)^2 Unfortunately my attempt at this problem is...
  28. J

    Cylindrical fishing reel problem using moment of inertia

    Homework Statement A cylindrical fishing reel has a mass of 0.85 kg and a radius of 4.5 cm. A friction clutch in the reel exerts a restraining torque of 1.6 N·m if a fish pulls on the line. The fisherman gets a bite, and the reel begins to spin with an angular acceleration of 66 rad/s2. a)...
  29. J

    Graphing the Surface y^2 + z^2 = 1 in Cylindrical Coordinates

    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...
  30. J

    What is the equation of the resulting surface in cylindrical coordinates?

    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...
  31. B

    What are the Limits for Computing the Volume of a Cylinder Inside a Sphere?

    Hi Guys, I have been given the coordinates of a cylinder inside a sphere and want to convert to Cylindrical coordinates to compute the volume of the cylinder. Can you please check the limits and integral I have? The cylinder is x^2+y^2= 4 sphere = x^2+y^2+z^2= 9 As its a cylinder...
  32. M

    How did the author determine the range of x for this problem?

    y=x^4, y=sin(pix/2); about x=-1 the solution is attached . how he determinate it to be from 0 to 1 ...? as I know , we usually put for example the expression of y1 = y2 and solve it for zero but in this case is not easy to do it,so how did he do it...?? note: my english is...
  33. N

    When to use spherical and cylindrical coordinates?

    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...
  34. 0

    Beam emergence from cylindrical lens

    if a cylindrical lens is put in the path of a laser beam what is expected to be seen at its focal plane? how will the beam look like after emerging from it?
  35. Zarlucicil

    Triple Integration of a Sphere in Cylindrical Coordinates

    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...
  36. S

    Need help in build a cylindrical arm robotfinal project

    I am a student at ungku omar polytechnic.i want to ask someone that is good in engineering robot.i want to know how to make the cylindrical robot,do i have to used ball screw or belting as an actuator.I want to a build a small robot only about 550mm long and 650 mm hight.It can pull load of...
  37. 0

    Understand Cylindrical Lens Imaging & Refs

    can anyone help me in understanding the concept of a cylindrical lens ? how is the imaging by a cylindrical lens different from that of a sphericaL lens? how does one decide to use a particular lens or a system of lenses for image formation? please suggest some good reference for this .. thanx
  38. somasimple

    Cylindrical Capacitor Computation

    Hi All, from this page (Cylindrical Capacitor) => http://www.phys.uri.edu/~gerhard/PHY204/tsl105.pdf What happens when L is <= b? Does the computation change? and from this page http://www.physics.umd.edu/perg/abp/TPProbs/Problems/E/E52.htm The capacitor is simplified to a plane...
  39. J

    Transforming divergence from cartesian to cylindrical coordinates

    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...
  40. W

    PDE Cylindrical and Spherical Symmetry

    Homework Statement Show that the solution u(r,theta) of Laplace's equation (nabla^2)*u=0 in the semi-circular region r<a, 0<theta<pi, which vanishes on theta=0 and takes the constant value A on theta=pi and on the curved boundary r=a, is u(r,theta)=(A/pi)[theta + 2*summation ((r/a)^n*((sin...
  41. S

    Circle to cylindrical coordinates

    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...
  42. E

    Converting Cylindrical Coordinates to Rectangular: A Helpful Hint

    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...
  43. F

    Ampére's Law Cylindrical Conductor with Hole

    Homework Statement A long circular rod of radius R, made of conducting material, has a cylindrical hole of radius a bored parallel to its axis and displaced from the centre of the rod by a distance d. The rod carries a current I distributed uniformly over its cross-section. Consider the...
  44. M

    Solving Spherical and Cylindrical Capacitors for Inner Radii

    Homework Statement I have two homework problems, both of which require me to solve the equation for the capacitance of a capacitor for the inner radius of the capacitor (one cylindrical, one spherical). This shouldn't be a problem, but I think my algebra is screwy. a = inner radius b = outer...
  45. A

    Setting up triple integral in cylindrical coords (looking to check my answer)

    Homework Statement set up an integral in cylindrical coords to compute the volume of the solid S bounded by the sphere x^2+y^2+z^2=12 and the cone 3z^2=x^2+y^2 where z>=0 The Attempt at a Solution i will post my answer here. please let 'I' stand for integral: i get, I[0,2pi]...
  46. I

    Electric potential in cylindrical coordinates using separation of variables

    Hi, I am new to the forum. I've encountered a couple problems with separation of variables in cylindrical coordinates. Problem #1: a clindrical surface of radius R is oriented along the z-axis, and is split into two conducting half-cylinders. The potential satisfies the...
  47. B

    Gauss's Law with a Cylindrical Shell

    Homework Statement A cylindrical shell of radius 7.00 cm and length 24.0 cm has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0cm radially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C. Find (a) the...
  48. N

    Cylindrical Symmetry - Gauss's Law

    I am having trouble understanding the concept of cylindrical symmetry in an infinitely long line. Please picture a finite Gaussian cylinder enclosing a portion of the length of the line, parallel to the line. My book states that there cannot be any component of E perpendicular to the...
  49. J

    Infinitely Long Cylindrical Surface Problem

    Homework Statement Here is my problem. I don't fully understand Gauss' law so any assistance there would be greatly appreciated Charge is distributed uniformly throughout the volume of an infinitely long cylinder of radius R = 4.00×10-2 m. The charge density is 1.00×10-2 C/ m3. What is the...
  50. C

    Calc 2 using washer meathod v.s cylindrical shells

    What are the reasons for using washer meathod v.s cylindrical shells? Cylindrical shells are much easier but there has to be some reason we can always use them Thanx
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