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. U

    Force between cylindrical capacitors

    Homework Statement Homework Equations The Attempt at a Solution I'm not sure what is being varied here, radial separation between capacitors x = (b-a) or whether the capacitors can slide up and down so as to change the length L of the capacitor..
  2. A

    Principal Virtual Work Theories - Cylindrical Pipe Application

    Dear All, I did post this issues in the physics forum, however there is somebody ask me to post it in the engineering forum. With this I re-post it here. Does anyone here familiar with a theory called Principal Virtual Work (Equilibrium theory) ? I read somewhere that with this theory, i...
  3. A

    Principal Virtual Work Theories - Cylindrical Pipe Application

    Dear All, Does anyone here familiar with a theory called Principal Virtual Work (Equilibrium theory) ? I read somewhere that with this theory, i could relate(for pipeline application - collapse & buckling) the components for ovalisation, external pressure and hoop strain. Appreciate if...
  4. M

    Magnetic Fields from Currents in a Wire and a Cylindrical Shell

    1. Homework Statement [/b] A solid cylindrical conducting shell of inner radius a = 4.9 cm and outer radius b = 6.1 cm has its axis aligned with the z-axis as shown. It carries a uniformly distributed current I2 = 7.4 A in the positive z-direction. An inifinte conducting wire is located along...
  5. R

    Ampere's Law: Cylindrical conducter with varying current

    Homework Statement The current density of a cylindrical conductor of radius R varies as J(r) = J0e−r/R (in the region from zero to R). Express the magnitude of the magnetic field in the regions r < R and r > R. (Use any variable or symbol stated above along with the following as necessary...
  6. W

    Cylindrical coordinates of line through a point?

    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...
  7. C

    Calculating Resistance for Cylindrical Shell Resistor

    Homework Statement A copper resistor has the shape of a cylindrical shell. What is the resistance of this resistor if its length is 1m, its inner radius is 0.1cm, and its outer radius is 0.2 cm? What is the radius of a solid wire of circular cross section with the same length and the same...
  8. G

    Calculating Bx for Two Coaxial Cylindrical Conductors

    Homework Statement Two very long coaxial cylindrical conductors are shown in cross-section above. The inner cylinder has radius a = 2 cm and caries a total current of I1 = 1.2 A in the positive z-direction (pointing out of the screen). The outer cylinder has an inner radius b = 4 cm, outer...
  9. G

    Rotating cylindrical spaceship

    Is the energy of a rotating cylindrical spacecraft conserved when a point-like astronaut climbs up a spoke connecting the walls with the center of the cylinder? If so, when I calculate the fractional change in apparent gravity at the walls when the astronaut reaches the middle I get different...
  10. M

    Concentric Cylindrical Conducting Shells

    Homework Statement The picture of the problem can be found here: http://www.2shared.com/photo/U_JIkDks/Capture.html The questions that I'm having trouble with are: (a) The magnitudes of the charge densities on the inner and outer shells are now changed (keeping λinner = -λouter) so that...
  11. B

    Net electrical flux on a cylindrical Gaussian Surface

    Homework Statement a cylindrical solid of charge q, radius R, and length H. The Gaussian surface S is a cylindrical shell of radius r and length h, with r < R. Determine the net electric flux given that q = -48Q, R = 4L, H = 3L, r = 2L, and h = 2L (type the integer value, along with the sign...
  12. L

    Triple integral in cylindrical coordinates

    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...
  13. J

    Compressible flow in cylindrical coordinate

    Hi, could anyone tell me a reference on Navier-Stokes equation for the COMPRESSIBLE flow in CYLINDRICAL coordinate? Just can't find a good reference book. Thanks in advance. Jo
  14. M

    MATLAB Solving Heat Equation in Cylindrical Coordinates with MATLAB's pdepe

    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?
  15. M

    Cylindrical pipe holding up a screen (real world project)

    This is a real world project. I'm building a giant roll-up window shade to be used for a special effects green screen. The first real model attempt (without math) failed. See the two pictures of the tube structure being held up by chairs. The only axle was about 3ft of 1.5" pipe at each...
  16. K

    Cracking the Code: Solving Cylindrical Shells with Gauss's Law

    Homework Statement "A cylindrical shell of length 230 m and radius 6 cm carries a uniform surface charge density of σ = 14 nC/m^2. What is the total charge on the shell? Find the electric field at the end of a radial distance of 3 cm from the long axis of the cylinder." Homework Equations...
  17. dexterdev

    Derivation of Del Operator in Spherical & Cylindrical Coordinates

    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.
  18. E

    Heat Equation in cylindrical coordinates

    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...
  19. E

    Cylindrical / Spherical Coordinates

    I'm trying to convert the below Cartesian coordinate system into cylindrical and spherical coordinate systems. For the cylindrical system, I had r,vector = er,hat + sint(e3,hat). While I do have a technically correct answer for the spherical coordinate system, I believe, I was wondering if there...
  20. O

    Cylindrical coordinates, finding volume of solid

    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...
  21. J

    Which Coil Shape is Better for Eddy Current Measurements?

    Hi, I'm currently in a dead spot of my mini-project where I've to decide upon the coil shape. I can't find adequate definition of both coils by the means of: - size - losses - frequency range - inductance - skin depth which makes it impossible to argue which one would be better...
  22. C

    Concentric infinite conducting cylindrical shells, outer one grounded

    Homework Statement The figure (found here) shows a cross-sectional view of two concentric, infinite length, conducting cylindrical shells. The inner shell has as an inner radius of a and an outer radius of b. The electric field just outside the inner shell has magnitude E0 and points radially...
  23. B

    Converting a triple integral from spherical to cartesian, cylindrical coordinates

    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...
  24. M

    Cartesian to cylindrical coordinates (integration question)

    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...
  25. T

    Solving Poisson-Boltzmann equation in Cylindrical and Spherical Coordinates

    Homework Statement I don't have a specific problem in mind, it's more that I forgot how to solve the particular equation from first principles. \nabla^{2} \Phi = k^{2}\Phi Places I've looked so far have just quoted the results but I would like the complete method or the appropriate...
  26. fluidistic

    Solving Schrödinger's Equation for Cylindrical Boundaries

    Homework Statement I must get the first eigenvalues of the time independent Schrödinger's equation for a particle of mass m inside a cylinder of height h and radius a where ##h \sim a##. The boundary conditions are that psi is worth 0 everywhere on the surface of the cylinder. Homework...
  27. O

    Transformation from cartesian to cylindrical coordinates

    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...
  28. J

    Converting a DISPLACEMENT vector in Cartesian to Cylindrical Corrdinates

    Hi all, I was wondering how would one go about converting a displacement vector in cartesian coordinates to cylindrical. I am getting a bit confused on how to deal with the unit vectors; converting a point in space is a simple task, but when it's a vector it just confuses me. I am specifically...
  29. Saitama

    Intensity by cylindrical light source

    Homework Statement The intensity produced by a long cylindrical light source at a small distance r from the source is proportional to a)\frac{1}{r^2} b)\frac{1}{r^3} c)\frac{1}{r} d)None of these Homework Equations I=\frac{dF}{dω} I is the intensity, dF is the luminous flux of the...
  30. C

    Log transform on cylindrical coordinates

    Homework Statement I'd like to do a log transform on the radius variable of the heat conservation equation: qr - qr + Δr= ΔE/Δt where qr= -kA(dT/dr) My solution for this equation in cylindrical coordinates is: Tt+Δt=Tt+(Δt*k)/(ρ*c*Δr^2)* [(Tt-1-Tt)/(ln(rt/rt-1) - (Tt-Tt+1)/(ln(rt+1/rt)]...
  31. R

    Calc Height Dielectric Oil Coaxial Cylinder Tubes

    Homework Statement Fromm Griffiths Two long coaxial cylindrical metal tubes (inner radius a, outer radius b) stand vertically in a tank of dielectric oil (susceptibility \chi_{epsilon}, mass density \rho. The inner one is maintained at potential V, and the outer one is grounded. To what...
  32. 3

    What is the triple integral of z^2(x^2 + y^2) over a bounded cylindrical region?

    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...
  33. A

    Electric potential at the center of a cylinder enclosed in a cylindrical shell

    Homework Statement A solid metal cylinder of radius R and length L, carrying a charge Q, is surrounded by a thick coaxial metal shell of inner radius a and outer radius b. The shell carries no net charge. Find the potential at the center, using r=b as the reference point. Homework...
  34. S

    Rotate a Circle Around the X/Y Axis - Cylindrical Shells

    Homework Statement Rotate the region bound by the given curve by about the x and y axis. Find the volume through the cylindrical method. x^2 + (y-1)^2 = 1 Homework Equations Cylindrical method: ∫2∏xf(x)dx Slice Method: ∫A(x)dx The Attempt at a Solution x^2 + (y-1)^2 = 1 x =...
  35. M

    Surface of 2 rotating fluids in a cylindrical container

    Homework Statement In a cylindrical container (with radius R) there are 2 fluids (separated like water and oil, fluid 1 lies under fluid 2) with given volumes V_i, given densities ρ_i. You let them rotate with respective angular frequencies ω_i. There is no friction. Find the functions of...
  36. N

    Going from cylindrical to cartesian coordinates

    Homework Statement Hi The expression for the magnetic field from an infinite wire is \boldsymbol B(r) = \frac{\mu_0I}{2\pi}\frac{1}{r} \hat\phi which points along \phi. I am trying to convert this into cartesian coordinates, and what I get is \boldsymbol B(x, y) =...
  37. N

    Circular vs. Cylindrical Charge Distribution

    I recently had a problem set with two questions that seemed to give very similar answers. I'm not asking how to do this, so I don't think this post belongs in the homework section. Rather, I'm asking if the similarity I think I see has any deeper meaning in the physics of electric fields...
  38. A

    Solution of laplace eqn in cylindrical coordinate

    Homework Statement A infinite long hollow cylinder has a narrow lengthwise cut and the potential on the cylinder is given by v(r,θ) = vo(θ/(2*pi)) Homework Equations V(s,theta) = Ao + Ʃ (n AnSnSin nθ + BnSn Cos nθ) The Attempt at a Solution boundary condition V(r,0)= 0 gives...
  39. G

    Velocity of flow in cylindrical coordinates

    An infinitely long cylindrical bucket with radius a is full of water and rotates with constant angular velocity \Omega about its horizontal axis. The gravity is in the vertical direction. The velocity of the flow in cylindrical coordinates (whose z axis is the horizontal axis of the bucket) is...
  40. C

    Findind Area element in Cylindrical Coordinate System

    Hi I would like to know is there any way except using graph to find area element in cylindrical ( or Spherical) coordinate system? Thanks.
  41. I

    Finding material thickness on cylindrical shells

    I have been tasked to find the material thickness needed for a cylindrical shell with open ends. I have been given the internal pressure, the cylinder inside diameter, the Poisson's ratio and the allowable tensile strength. I have used Birnie's equation to solve (see attached file in thread...
  42. M

    Cylindrical coordinates

    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
  43. C

    Describe the surface in cylindrical coordinates?

    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
  44. V

    Simple integral in cylindrical coordinates

    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...
  45. K

    Radii in Cylindrical Shells

    Homework Statement Hi, I'm having a tremendous amount of difficulty with finding the radii in problems using cylindrical shells. Here's the question: find the volume of the solid found by rotating the region bounded by the given curves: x = y2+1, x = 2, about y = -2 I got 2 -...
  46. T

    Derivation of Laplace Operator in Spherical and Cylindrical Coordinates

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

    Charge from field, cylindrical symmetry

    The problem states: From the field with a radial cylindrical component only given by the following equations: E(r)= (ρ0*r3)/(4 * ε0*a2) for r<=a E(r)= (ρ0*a2)/(4*ε0*r2) for r > a obtain the corresponding charge distribution in free space in which the equation is: ρ(r) = ρ0*(r2/a2)...
  48. T

    Cylindrical and Spherical Coordinates Changing

    Homework Statement Convert the following as indicated: 1. r = 3, θ = -π/6, φ = -1 to cylindrical 2. r = 3, θ = -π/6, φ = -1 to cartesian The Attempt at a Solution I just want to check if my answers are correct. 1. (2.52, -π/6, 1.62) 2. (-2.18, -1.26, 1.62)
  49. J

    Change of Variable for a Vector from Rectangular to Cylindrical

    Homework Statement 1.21 Express in cylindrical components: (a) the vector from C(3, 2,−7) to D(−1, −4, 2); (b) a unit vector at D directed toward C; (c) a unit vector at D directed toward the origin. I just want to know (a). And the solution from the book is attached, too...
  50. A

    Expressing Spherical coordinates in terms of cylindrical

    Homework Statement I'm trying to express spherical coordinates in terms of cylindrical and vice versa. I would appreciate it if someone could give me some feedback on my attempt at a solution. Thanks for the help! The Attempt at a Solution Spherical(cylindrical) r=(ρ^2+z^2)^(1/2)...
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