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. E

    Electric Field due to a charged conducting finite cylindrical shell.

    Hi everyone. I'm having a bit of trouble with finding an electric field. Basically, I'm trying to understand the formula for a cylindrical capacitor, so the method involves integrating the field between two conducting cylindrical shells. Firstly can Gauss's law be used in this case, because the...
  2. J

    How Do You Determine the Limits for r and θ in a Cylindrical Coordinate System?

    What are the r and θ limits for the triple integral of y where there's a parabloid cylinder x=y^2 and planes x+z=1 and z=0? I rearranged x+z=1 to get z=1-x => so 1-rcosθ; 0 ≤ z ≤ 1-rcosθ but I don't know how to get the limits for θ or r. How do I do this?
  3. V

    Radial Acceleration in cylindrical coordinates

    Hey guys, Been given this formula for radial acceleration, I am not sure how they derived it. I have tried but the only forumla I know is a(radial) = v^2/r A_{r} = \ddot{r} - r\dot{\theta}^{2}EDIT - should be minus not plus
  4. N

    Laplace equation, cylindrical 2D

    [SOLVED] Laplace equation, cylindrical 2D Homework Statement I am given the Laplace eq. in cylindrical coord. (2D), and I am told that we can assume the solution u(rho, Phi) = rho^n * Phi(phi). Find the general solution. The Attempt at a Solution My teacher says that the general...
  5. A

    Vector Cross Product Formula in Spherical & Cylindrical Coordinates

    Hello all, it might be funny! but i am stuck to it! what is the vector cross product formula in spherical and cylindrical coordinates?! I know for Cartesian coordinate we have that nice looking determinant. but what about the other coordinates. I had looks to all the math books (like...
  6. S

    Magnetic Fields: I don't understand cylindrical current systems

    ...||==|| .||...|| ||... 0...|| ..||...|| ...||==|| This is a really bad picture, but it should kind of give the idea. How do I deal with a system where a current is running in a cylinder surrounded by a cylindrical shell? I know this sounds like a homework question, and it is related to...
  7. T

    Field of long cylindrical shell conductor

    [SOLVED] Field of long cylindrical shell conductor Homework Statement Shown above is the cross-section of a long cylindrical shell conductor of inner radius a=4.00 cm and outer radius b=7.00 cm which carries a current into the page. The current density J (current/area) is uniform across the...
  8. P

    Laplace Cylindrical Coordinates (Separation of variables)

    Hello, The following equation: \frac{\partial^2 u}{\partial r^2}+\frac{1}{r} \cdot \frac{\partial u}{\partial r}+ \frac{\partial^2 u}{\partial z^2} = 0 is solved by separation of variables assuming a solution of the form: u=R(r)Z(z) In other cases the assumed solution is of the...
  9. E

    Converting to cylindrical and then taking div and curl

    Homework Statement Change to cylindrical coordinates and find the divergence F = <x, y, 0>/(x^2 + y^2) Homework Equations \nabla . F = \frac{1}{\rho}\frac{\partial\rho F}{\partial\rho}+\frac{1}{\rho}\frac{\partial F}{\partial\theta}+\frac{\partial F}{\partial z} The Attempt at...
  10. G01

    Laplace's Equation in Cylindrical Coordinates

    Homework Statement A long copper pipe, with it's axis on the z axis, is cut in half and the two halves are insulated. One half is held at 0V, the other at 9V. Find the potential everywhere in space.Homework Equations \nabla^2V=0The Attempt at a Solution Alright. This is a laplace's equation...
  11. B

    Breakdown Potential of a Cylindrical Capacitor

    Homework Statement You are asked to construct a capacitor having a capacitance near 1 nF and a breakdown potential in excess of 13000 V. You think of using the sides of a tall plastic drinking glass as a dielectric (with a dielectric constant 5.2 and dielectric strength 12 kV/mm), lining the...
  12. H

    What Is the X-Component of the Electric Field in Coaxial Cylindrical Conductors?

    Homework Statement Two coaxial cylindrical conductors are shown. The inner cylinder has radius a = 2 cm, length 10 m, and carries a total charge of Q inner = +8nC. The outer cylinder has an inner radius b = 6 cm, outer radius c= 7 cm, length 10 m, and carries a total charge of Q outer =...
  13. M

    Volume of gas in a cylindrical vessel on which a piston has been placed

    [SOLVED] volume of gas in a cylindrical vessel on which a piston has been placed Homework Statement A cylindrical vessel with a tight but movable piston is placed in a vertical position so that the piston, whose area is 60 cm2, is subject to atmospheric pressure. When the gas in the vessel...
  14. S

    Cylindrical transverse oscillation

    Hi all. Picture a series of strings around a circle, oscillating with fixed ends. Now picture a these strings as being in a pseudo-cylinder. Akin to a "breathing" tube, expanding and contracting in on itself. I'm trying to identify just how that'd work for an idea that I have about an IPMC...
  15. G

    From 1D to cylindrical co-ordinates in PDEs

    Hi all, I have another post on here relating to Fick's law of diffusion, but before I asked that I really should have started with this question: How do you go from a one dimensional version of the diffusion equation to a cylindrical co-ordinate system of the same equation? I have found...
  16. D

    Why Does Cylindrical Wave Amplitude Vary Inversely with Radius?

    does anyone know why, in order to conserve flux, the amplitude of a cylindrical wave varies inversely with its radius? I know the equation for a cylindrical wave is \frac{A}{\rho^{1/2}}e^{i(k\rho\pm\omega t)} , but how does this relate to conserving the flux? The main reason for my...
  17. G

    Fick's second law in cylindrical co-ordinates

    Hi all, Having some trouble understanding/finding the derivation of Fick's second law of diffusion in cylindrical co-ordinates. I have attached the solution which describes the refilling of a laser cleaned spot via surface diffusion. So basically i would like to know the intermediate...
  18. Q

    Volume Calculation Using Cylindrical Shells

    Consider the given curves to do the following. x = 3 + (y-2)**2, x = 4 Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. V = ?? **************** I set up the problem like this... V...
  19. L

    TORQUE A cylindrical fishing reel has a mass of 0.65 kg and a radius of 4.3 cm .

    TORQUE A cylindrical fishing reel has a mass of 0.65 kg and a radius of 4.3 cm... Homework Statement A cylindrical fishing reel has a mass of 0.65 kg and a radius of 4.3 cm. A friction clutch in the reel exerts a restraining torque of 1.3 N·m if a fish pulls on the line. The fisherman gets...
  20. A

    Cylindrical Rotation Volume Help

    Homework Statement The region R enclosed by the coordinate axes and the graph of y = k(x-2)^2 is shown above. When this region is revolved around the y - axis, the solid formed has a volume of 8*pi cubic units. What is the value of k? A) 1 B) 4/3 C) 3/pi D) 2 E) 3 Homework...
  21. K

    What is the work done in emptying a half-full cylindrical tank through a pipe?

    A storage tank is a right circular cylinder 20ft long and 8 ft in diameter with its axis horizontal. If the tank is half full of olive oil weighing 57 lb/ft^3, find the work done in emptying it through a pipe that runs from the bottom of the tank to an outlet that is 6 ft above the top of the...
  22. X

    How Do You Model Brunelleschi's Dome in Cylindrical Coordinates?

    Homework Statement In cylindrical coordinates write a function which describes the surface of the dome (brunelleshci's dome) whose center is not on the central axis but rather one-fifth of the way from the edge. the sides form a shape called quinto acuto, span of base of dome is 143 find...
  23. P

    Magnetic Field Inside Cylindrical Conductor

    why is the magnetic field just inside a cylindrical conductor with inner radii a, and outer radii b carrying a uniform current I distributed throught it's croos section just 0 inside the conductor. I used ampere's law and that surely doesn't give 0
  24. P

    Drag/friction on cylindrical surface

    First some backstory...having graduated quite a few years ago and going to work directly out of school (SolidWorks VAR) I feel as though I might be brain dead for having to ask this but I'm absolutly stuck now that I'm back in the "real world" and even my reference materials at home don't seem...
  25. E

    Easy question about divergence in cylindrical coordinates

    Consider a cylindrical shell so that the cross sectional radius is some constant a. In the first term of the divergence expression in cylindrical coordinates: \frac{1}{r}\frac{\partial}{\partial r}(rA_{r}) When I multiply the radial component by r, do I go ahead and substitute r=a...
  26. N

    Second moment of area of a hollow cylindrical arc

    Homework Statement I need to find the second moment of area for a hollow cylindrical arc. When I searched the web, they had formulas for several shapes but I couldn't find this one The profile of my part is a little unusual as follows: R: Outer Radius = 35.089" r: Inner Radius = 35.050"...
  27. C

    Why Does Grounding the Inner Shell Affect Cylindrical Capacitor Capacitance?

    Why is the theoretical capacitance for a cylindrical capacitor (given here http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capcyl.html) equal to the value measured on the outer shell with the inner grounded using a L-C meter? I'm stuck.
  28. S

    Divergence in cylindrical coordinate system

    I am trying to understand the derivation of the divergence formula in cylindrical coordinates. www.csupomona.edu/~ajm/materials/delcyl.pdf paper does a good job of explaining it but I don't understand 2 things that the author does. \frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi} and...
  29. P

    Green's Fucntions in Cylindrical coordinates

    Hey everyone, first time poster. I am looking for a general solution to poisson's equation in a cylindrical geometry for the electrostatic field. By general, I am thinking of two concentric, grounded, hollow cylinders of finite height, and the solution for the field using the green's function...
  30. P

    Can Green's Function Solve Poisson's Equation in Cylindrical Geometry?

    Hey everyone, first time poster. I am looking for a general solution to poisson's equation in a cylindrical geometry. By general, I am thinking of two concentric hollow cylinders of finite height, and the solution for the field using the green's function in between the two cylinders. With...
  31. A

    Cylindrical general differential equation of conduction

    Homework Statement Desperate help needed on the derivation of the differential equation on conduction on a clyinder, i have come close to the answer and working with the co-ordinates scale of T(r,0,z). I am sure that i have made a simple mistake but am blind to it right now, i have...
  32. C

    How Do E-Field Lines Behave Between Finite Coaxial Cylindrical Conductors?

    Homework Statement What would the equipotential or e-field lines look like when staring down the axis of the two finite cylinders? Will the E-field lines be radial or are they different because the cylinders aren't infinite?
  33. N

    Fluid cylindrical bucket Question

    A cylindrical bucket, open at the top has height 27.0 cm and diameter 13.0 cm. A circular hole with a cross-sectional area 1.49 cm^2 is cut in the center of the bottom of the bucket. Water flows into the bucket from a tube above it at the rate of 2.28×10−4 m^3/s my work let 1 denote the top...
  34. W

    Electric Field of an Insulating Cylindrical Shell

    Homework Statement A long cylindrical insulating shell has an inner radius of a = 1.38 m and an outer radius of b = 1.61 m. The shell has a constant charge density of 4.80 C/m3. 1. What is the magnitude of the electric field at a distance of 1.87 m from the axis? 2. What is the magnitude...
  35. K

    Need help in designing cylindrical robot arm

    I'm currently designing the mechanism for a basic cylindrical robot arm. It must be capable of lifting max 2kg of item. The robot arm looks like ST Robotic R19 model. It moves in X and Z direction plus rotation at base and arm. The robot should looks like the attachment below. Can u please...
  36. V

    Two cylindrical tanks, connecting pipe and outlet pipe - Differential Equation

    Homework Statement Two vertical cylindrical tanks, each 10 meters high, are installed side-by-side. Their bottoms are at the same level. The tanks are connected at their bottoms by a horizontal pipe 2 meters long which has an internal diameter of 0.03 meters. The first tank is full of oil and...
  37. M

    Calculating Rotational Kinetic Energy of a Falling Ball-Rod System

    Homework Statement A cylindrical rod 36.4 cm long has mass 0.655kg and radius 1.1cm. A 18.5kg ball of diameter 11.4cm is attached to one end. The arrangement is originally vertical with the ball at the top and is free to pivot about the other end. After the ball-rod system falls a quarter...
  38. K

    Calculating the Torque of a Cylindrical Flywheel

    Our air motor has 2 cylinders and is a low rpm device. It therefore needs a flywheel to store enough torque to get the crankshaft past the dead spots at 10 degrees before and after top dead center and 10 degrees before and after bottom dead center. My question is how to calculate the...
  39. S

    Vector potential in cylindrical coordinates

    Homework Statement What current density would produce the vector potential, A = k \hat{\phi} where k is a constant, in cylindrical coordinates? Homework Equations \nabla^2 A = -\mu_{0} J In cylindrical coordinates for radial and z symmetry \nabla^2 t = \frac{1}{s^2}...
  40. B

    Meters of water are in a cylindrical cumulus cloud

    Please help me! Homework Statement A cubic centimeter in a typical cumulus cloud contains 50 to 500 water drops, which have a typical radius of 10 µm. For that range, give the lower value and the higher value, respectively, for the following. (a) How many cubic meters of water are in a...
  41. O

    Behavior of a cylindrical magnet

    I noticed when I stick a cylindrical magnet on a smooth metal surface (longways) and roll the magnet along the surface, it does not roll smoothly. Instead, it seems to resist movment, then 'pop' forward into another position. It is almost as if the magnet has a preference on which side sticks...
  42. C

    Derivation of Energy Equation in Cylindrical Coordinates

    So, I have searched the globe to find the derivation of the conservation of energy equation in 3D cylindrical coordinates. I have looked in about every heat transfer, thermodynamic, thermofluid books in the library. I have spent about 4 hours on the internet trying to find something, but no...
  43. S

    Converting Cartesian Coordinates to Cylindrical Coordinates

    Homework Statement Say I have line, y = - 5 in cartesian coordinates. How do I express this in cylindrical coordinates? Also, if I have a point (0,-5) in cartesian coordinates, how to I express this position vector in cylindrical coordinates? Homework Equations y = r sin (phi)...
  44. A

    Cylindrical conductor with an off center cavity

    I have a quick question. I recently did an E&M problem in which I was given a cylindrical conducting wire of radius a, in which someone bores an off-center cylindrical cavity of radius b (the center of the smaller circle is offset from the center of the wire by distance d). I'm asked to find...
  45. T

    Position of Floating Cylindrical Disk in Water

    A cylindrical disk has volume 8.99 × 10-3 m3 and mass 8.07 kg. The disk is floating on the surface of some water with its flat surfaces horizontal. The area of each flat surface is 0.633m2. (a) What is the specific gravity of the disk? (b) How far below the water level is its bottom surface? (c)...
  46. I

    How Do You Apply the Cylindrical Shell Method for y=x^2, y^2=x About x=-1?

    How to solve this problem and how to graph it? Please help... y=x^2, y^2=x, about x=-1
  47. J

    Derivation of Continuity Equation in Cylindrical Coordinates

    Help! I am stuck on the following derivation: Use the conservation of mass to derive the corresponding continuity equation in cylindrical coordinates. Please take a look at my work in the following attachments. Thanks! =)
  48. S

    Cylindrical Shells and Gauss' Law

    Homework Statement An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density sigma = 12 nC/m^2. The electric field at r = 5.9 cm is approximately a.0.81 kN/C b.zero. c.1.3 kN/C. d.12 kN/C. e.0.56 kN/C...
  49. B

    Find Volume Using Cylindrical Coordinates

    Can someone explain to me how to find the volume of the following? I am asked to use cylindrical coordinates to find the volume of the solid enclosed by the sphere r^2+a^2 = a^2 and by the cone z = r cot φ where φ is some fixed angle between 0 and pi/2? I would have thought that the volume...
  50. 7

    C/C++ Verifying Cost of Cylindrical Containers Production

    Hi, could some one please verify that I successfully completed the objective of my programming homework? This is my first assignment and I'm just being extra cautious that I did everything right. So the user provides measurements in inches but the program must then convert them into...
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