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. H

    Estimating the FOV of a thin sliced plano-convex cylindrical lens

    I've scoured the internet, books I have available, and forums, but I can't seem to find any information regarding the field of view of a plano-convex cylindrical lens. The lens in question would be a 1/4" slice from something like a 26x13mm lens. The dimensions would then become 6.35x13mm...
  2. B

    Schrodinger equation in cylindrical coordinates.

    Hi guys! For nuclear case, I need to write an Schrodinger equation in cylindrical coordinates with an total potential formed by Woods-Saxon potential, spin-orbit potential and the Coulomb potential. Schrodinger equation can be written in this form: $$[-\frac{\hbar^2}{2m}(\frac{\partial...
  3. Andy Resnick

    Q: cantilevered cylindrical shell

    I'm trying to find a decent reference that discusses the (static) deformation of a cantilevered cylindrical shell under a transverse load- for example, how a horizontal cantilevered pipe will deform due to gravitational loading. Everything I can find either discusses axial loading or considers...
  4. JTC

    I Coordinate systems vs. Euclidean space

    Good Morning I am having some trouble categorizing a few concepts (I made the one that is critical to this post to be BOLD) Remote parallelism: the ability to move coordinate systems and frames around in space. Euclidean Space Coordinate systems: Cartesian vs. cylindrical I am aware that if...
  5. I

    How to express velocity gradient in cylindrical coordinates?

    Homework Statement The vlasov equation is (from !Introduction to Plasma Physics and Controlled Fusion! by Francis Chen): $$\frac{d}{dt}f + \vec{v} \cdot \nabla f + \vec{a} \cdot \nabla_v f = 0$$ Where $$\nabla_v$$ is the del operator in velocity space. I've read that $$\nabla_v =...
  6. S

    Cylindrical Vector Field Equation Convsersion to Cartesian

    Homework Statement I have been given a changing magnetic field in cylindrical coordinates. The equation is: \begin{equation} B(r,\phi,z) = - \frac {B_1} {2} r \hat{r} + (B_0 + B_1z)\hat{z} \end{equation} I need to be able to find the magnetic field as a function of x, y, and z. Homework...
  7. K

    Electric field model using a cylindrical capacitor

    Homework Statement In a lab experiment we measured the potential at different points within a cylindrical capacitor electric field modeling plate thing (apparently that's the best I could do to translate that into English). The positive electrode was connected in the middle and the negative...
  8. Y

    Water Filling a Cylindrical Container with a Scale Under It

    Homework Statement A scale is adjusted so that when a large, shallow pan is placed on it, it reads zero. A water faucet at height h = 4.0 m above is turned on and water falls into the pan at a rate R = 0.20 kg/s. A) Determine a formula for the scale reading as a function of time t if at the...
  9. K

    Cartesian unit vectors in terms of cylindrical vectors

    How do I express ex,ey,ez in terms er,eθ,eZ? r=(x^2+y^2)^1/2,θ=arctan(y/x),Z=z A(r,θ,z) ∂A/∂x=x/(x^2+y^2)^1/2er+(-y)/(x^2+y^2)eθ=cosθer-(sinθ/r)eθ ex=(∂A/∂x)/|∂A/∂x| I should get ex as cosθer-sinθeθ, but I don't get ex correctly. am i doing this wrong?
  10. Draconifors

    Triple integral using cylindrical coordinates

    Homework Statement The first part of the question was to describe E the region within the sphere ##x^2 + y^2 + z^2 = 16## and above the paraboloid ##z=\frac{1}{6} (x^2+y^2)## using the three different coordinate systems. For cartesian, I found ##4* \int_{0}^{\sqrt{12}} \int_{0}^{12-x^2}...
  11. RJLiberator

    Volume Charge Density in Spherical and Cylindrical Coordinat

    Homework Statement Consider a ring of radius R placed on the xy-plane with its center at the origin. A total charge of Q is uniformly distributed on the ring. a) Express the volume charge density of this configuration ρ(s,Φ,z) in cylindrical coordinates. b) Express the volume charge density of...
  12. C

    A Cylindrical Poisson equation for semiconductors

    In a cylindrical symmetry domain ## \Phi(r,z,\alpha)=\Phi(r,z) ##. Does anyone can point me what can be found in literature to solve, even with an approximate approach, this equation? \nabla^2 \Phi(r,z)=-\frac{q}{\epsilon} \exp(-\frac{\Phi(r,z)-V}{V_t}) Where ## q, \epsilon, V ## and ## V_t ##...
  13. T

    Volume of a sphere in cylindrical coordinates

    Homework Statement A sphere of radius 6 has a cylindrical hole of radius 3 drilled into it. What is the volume of the remaining solid. The Attempt at a Solution [/B] I am able to solve this using cylindrical coordinates but I'm having trouble when I try to solve it in spherical coordinates...
  14. JTC

    A Understanding Metric Tensor Calculations for Different Coordinate Systems

    Good Day, Another fundamentally simple question... if I go here; http://www-hep.physics.uiowa.edu/~vincent/courses/29273/metric.pdf I see how to calculate the metric tensor. The process is totally clear to me. My question involves LANGUAGE and the ORIGIN LANGUAGE: Does one say "one...
  15. C

    Resistance of a cylindrical resistor

    Homework Statement Homework EquationsThe Attempt at a Solution Can someone tell me what formula to use? Is it p=RA/L? but what about the mass? Thanks~
  16. akkex

    MHB Change from cartesian coordinates to cylindrical and spherical

    Hello, I have 6 equations in Cartesian coordinates a) change to cylindrical coordinates b) change to spherical coordinate This book show me the answers but i don't find it If anyone can help me i will appreciate so much! Thanks for your time1) z = 2...
  17. L

    Volume of a Solid using Cylindrical Shells

    Homework Statement Find the volume of the region bounded by the curves y=3x-2, y=6-x, and the x-axis when the region is rotated around the y-axis. Homework Equations Volume using cylindrical shells: 2π∫r(x)h(x)dx The Attempt at a Solution I graphed the curves and then found the x-intercept...
  18. C

    A Laplace Eq. in Cylindrical coordinates (no origin)

    Hi, I need to solve Laplace equation:##\nabla ^2 \Phi(x,r)=0## in cylindrical domain ##r_1<r<r_2##, ##0<z<+\infty##. The boundary conditions are: ## \left\{ \begin{aligned} &\Phi(0,r)=V_B \\ & -{C^{'}}_{ox} \Phi(x,r_2)=C_0 \frac{\partial \Phi(x,r)}{\partial r}\rvert_{r=r_2} \\ &\frac{\partial...
  19. C

    A Laplace Eq. in Cylindrical coordinates

    Hi, I need to solve Laplace equation:## \nabla ^2 \Phi(x,r)=0 ## in cylindrical domain ##0<r<r_0##, ##0<x<L## and ##0<\phi<2\pi##. The boundary conditions are the following ones: ## \left\{ \begin{aligned} &C_{di}\Phi(x,r_0)=\epsilon \frac{\partial \Phi(x,r)}{\partial r}\rvert_{r=r_0} \\...
  20. L

    A Relation between Vector Norms in Cylindrical and Cartesian Coordinates

    Relations between vectors in cylindrical and Cartesian coordinate systems are given by \vec{e}_{\rho}=\cos \varphi \vec{e}_x+\sin \varphi \vec{e}_y \vec{e}_{\varphi}=-\sin \varphi \vec{e}_x+\cos \varphi \vec{e}_y \vec{e}_z=\vec{e}_z We can write this in form \begin{bmatrix}...
  21. M

    Shell balances in cylindrical coordinates

    I have a question regarding writing a shell balance for a cylindrical system with transport in one direction (in any area of transport phenomena). When we set up the conservation equation(say steady state), we multiply the flux and the area at the surfaces of our control volume and plug them...
  22. Mark Hamil

    MCNP Cylindrical Phantom Calculation Help

    I'm new to mcnp and trying to perform this calculation, if anyone can provide some feedback to see if I'm even going in the right direction that would be much appreciated. The geometry is correct with only 1 transverse, the issue I am having is making sure my data block is correct and how I am...
  23. W

    Cylindrical rod velocity profile

    Homework Statement Homework Equations 0=viscous forces 0=in-out+sum of forces(0) 2*pi*r*L*τrz evaluated at r-2*pi*r*L*τrz evaluated at r+ΔR (eq1) Dividing by volume and taking limit as δr->0 in eq1 I get : (δτrz)/(δr) =0 My question is, how did they in solution got (rδτrz)/(δr) =0, how do...
  24. Alanay

    Can magnets on a cylindrical object be used for projectiles?

    What I mean is if I have 2 cylinder objects made out of a light wood for example with 6 or so magnets on either face spread evenly and another magnet behind it causing it to spin could it generate a good amount of torque to shoot a small projectile between the two cylinders. To give you a better...
  25. R

    Length and Area of Cylindrical Nichrome Resistor

    Homework Statement You must complete the circuit of (Figure 1) in such a way that it draws a current of 0.450 A from the battery. The battery maintains a potential difference of 10.0 V with no load, but has an internal resistance of Rbatt = 15.0 Ω . The only material you have is 20.0 mm^3 of...
  26. J

    Can I design a horizontal cylindrical hollow turbine blade

    Hello everyone, I need the following but I am not sure if it is possible or not? I don’t have mechanical engineering background. Please advise me on feasibility of this project and any suggestion would be greatly appreciated. I am looking to design a horizontal cylindrical hollow turbine...
  27. jlmccart03

    Find ratio of diameter of two Cylindrical Resistors?

    Homework Statement Two cylindrical resistors are made from the same material and have the same length. When connected across the same battery, one(A) dissipates twice as much power as the other(B). Find ratio of dA/dB. Homework Equations P = VI = V2/R = I2R Area of cylinder = 2πrh + 2πr2 The...
  28. B

    Recast a given vector field F in cylindrical coordinates

    Homework Statement F(x,y,z) = xzi Homework Equations N/A The Attempt at a Solution I just said that x = rcos(θ) so F(r,θ,z) = rcos(θ)z. Is this correct? Beaucse I am also asked to find curl of F in Cartesian coordinates and compare to curl of F in cylindrical coordinates. For Curl of F in...
  29. B

    Flux Density, B, of a Cylindrical Magent

    Hi, I'm trying to calculate the flux density of a magnet, I can get all but one of the values needed to calculate it. Does anyone know how/where to get the z(distance from a pole face on the symmetrical axis) value?
  30. F

    Conversion vectors in cylindrical to cartesian coordinates

    Homework Statement It's just an example in the textbook. A vector in cylindrical coordinates. A=arAr+aΦAΦ+azAz to be expressed in cartesian coordinates. Start with the Ax component: Ax=A⋅ax=Arar⋅ax+AΦaΦ⋅ax ar⋅ax=cosΦ aΦ⋅ax=-sinΦ Ax=ArcosΦ - AΦsinΦ Looking at a figure of the unit vectors I...
  31. Toby_phys

    Understanding Cylindrical Capacitors: Charged vs. Disconnected

    Homework Statement Normally this style of question wouldn't be too bad, however the 2 different parts confused me. Surely once set to a potential V, it would stay at that potential - it doesn't need to stay connected How are the 2 parts any different from each other?
  32. J

    How can I find this surface integral in cylindrical coordina

    Homework Statement A vector field $\vec F$ is defined in cylindrical polar coordinates $\rho , \theta , z$ by $\vec F = F_0(\frac{xcos (\lambda z)}{a}\hat i \ + \frac{ycos(\lambda z)}{a}\hat j \ + sin(\lambda z)\hat k) \ \equiv \frac{F_0 \rho}{a}cos(\lambda z)\hat \rho \ + F_0sin(\lambda...
  33. H

    Potential of Concentric Cylindrical Insulator and Conducting

    Homework Statement An infinitely long solid insulating cylinder of radius a = 4.3 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 28 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner...
  34. Ian Baughman

    Heat transfer through a cylindrical shell

    Homework Statement An infinitely long cylindrical shell has an inner radius a and outer radius b. If the inside is maintained at a temperature Ta and the outside at a temperature Tb, determine the rate of heat flow per unit length between inner and outer surfaces assuming the shell has a...
  35. L

    A Laplacian cylindrical coordinates

    Laplacian in cylindrical coordinates is defined by \Delta=\frac{\partial^2}{\partial \rho^2}+\frac{1}{\rho}\frac{\partial}{\partial \rho}+\frac{1}{\rho^2}\frac{\partial^2}{\partial \varphi^2}+\frac{\partial^2}{\partial z^2} I am confused. I I have spherical symmetric function f(r) then \Delta...
  36. Hannibal247

    One-dimensional steady state conduction in Cylindrical coordinates

    Hello, Im having some issues with my task. 1. Homework Statement The heat generation rate of a cylindrical fuel (D=0.2 m and 1 m long) is 160 kW. The thermal conductivity of the fuel is 100 W/mK and its surface temperature is maintained at 283 K. Determine the temperature at the axis...
  37. Vitani11

    Electric field everywhere for a hollow cylindrical conductor?

    Homework Statement An infinitely long, hollow, conducting cylinder has a inner radius a and outer radius b and carries a linear charge density λ along its length. What is the electric field everywhere? Homework Equations ∫E⋅dA = Qenc/∈ Variables ∈ = permittivity constant a = inner radius b =...
  38. G

    I How to write a Vector Field in Cylindrical Co-ordinates?

    Let's say we have a vector field that looks similar to this. Assume that the above image is of the x-y plane. The vector arrows circulate a central axis, you can think of them as tangents to circles. The field does not depend on the height z. The lengths of the arrows is a function of their...
  39. PhotonSSBM

    Potenital of a cylindrical, linear dialectric in a E-Field

    Homework Statement A very long cylinder of linear dialectric material is placed in an otherwise uniform electric field ##E_0##. Find the resulting field within the cylinder. (The radius is ##a##, the susceptibility ##X_e##, and the axis is perpendicular to ##E_0##) Homework Equations Boundary...
  40. C

    Masses Over a Uniform Cylindrical Pulley

    ηϖ1. Homework Statement Homework Equations I=½MR2 PE=mgh The Attempt at a Solution The first thing that jumped out at me was "uniform cylinder" so I went ahead and calculated the moment of inertia for the cylinder and got I=½(4.4)(.4)2 = .352 and held onto that. Then, I calculated the...
  41. N

    The magnetic field within cylindrical hollow conductor

    Hi, While studying the coaxial cable, i noticed that the magnetic field of the inner conductor can pass through the hollow conductor (can be calculated in the region 3). However, the boundary condition of the magnetic field at the surface (between dielectric and perfect conductor) of a perfect...
  42. Z

    Energy per unit length of a cylindrical shell of charge

    Homework Statement "An infnitely long hollow cylinder of radius ##a## has surface charge density ##σ_a##. It is surrounded by a coaxial hollow cylinder of radius ##b## with charge density ##σ_b##. The charge densities are such that the total confguration is electrically neutral. Using whatever...
  43. nysnacc

    Rewrite Cartesian in Cylindrical form

    Homework Statement Homework Equations Cartesian to Cylindrial The Attempt at a Solution What I was doing is that, I changed the limits of z, and the function.
  44. P

    Imaging by cylindrical concave mirror

    Consider an upright cylindrical concave mirror with a point source located at the focal point of the mirror. By upright I mean that the mirror is plane in the vertical direction and a concavity in the horizontal plane. Now it seems likely that you would see a virtual image of the point source...
  45. A

    Conversion of a vector from cylindrical to cartesian

    (mentor note: thread moved from general to here hence no template) Hi, I need some help with converting this cylindrical vector: $$\vec A = \vec a_r(3*cos(\phi)-\vec a_{\phi}*2r+\vec a_z5$$ into the cartesian: I have found these: where $$A_x =3cos^2(\phi)+2sin(\phi)*r\\...
  46. M

    A Wave equation in cylindrical coordinates - different expression?

    Hello to everybody, I am solving some examples related to wave equation of shear horizontal wave in cylindrical coordinates (J.L Rose: Ultrasolic Waves in Solid Media, chapter 6), which is expressed as follows: ∇2u=1/cT2⋅∂2u/∂t2 The Laplace operator in cylindrical coordinates can can be...
  47. toforfiltum

    Sketching surfaces described in cylindrical coordinates

    Homework Statement The surface is described by the equation ## (r-2)^2 + z^2 = 1 ## in cylindrical coordinates. Assume ## r ≥ 0 ##. a) Sketch the intersection of this surface with the half plane ## θ= π/2 ## Homework Equations ## r= psin φ ## ## p^2 = r^2 + z^2 ## The Attempt at a Solution...
  48. N

    Triple integral in cylindrical coordinates

    1. Homework Statement I am trying to solve a triple integral using cylindrical coordinates. This is what I have to far . But I think I have choosen the limits wrong. Homework EquationsThe Attempt at a Solution [/B]
  49. RaulTheUCSCSlug

    I CMA (Cylindrical Mirror Analyzer)

    I'm supposed to be working with a CMA (Cylindrical Mirror Analyzer), but I'm more interested in the physics behind it. This is the instrument in question that we are looking to get: http://www.rbdinstruments.com/products/micro-cma.html We want it to look at different eV levels of different...
  50. DavideGenoa

    I Integral: magnetic field inside infinite cylindrical current

    Let ##V\subset\mathbb{R}^3## be an infinitely high solid cylinder, or a cylindrical shell of radii ##R_1<R_2##, whose axis has the direction of the unit vector ##\mathbf{k}##. For any point of coordinates ##\boldsymbol{r}\notin \bar{V}## external to ##V## the Lebesgue integral (which is...
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