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. Vigardo

    Weird (or not) issues in thin-walled cylindrical shell buckling modes

    Dear FEA experts, I’m trying to analyse* some finite elements model of a thin walled cylinder with variable cross-section, but I’m observing four weird issues in the buckling modes. The structure is vertically (along z-axis) and horizontally (along y-axis) loaded on top. Would you help me to...
  2. H

    A Crank-Nicholson solution to the cylindrical heat equation

    Hi, I am solving the radially symmetric heat equation with an internal heat source(this is meant to model the heating of a cylindrical battery). It's meant to model heat in a cylinder with conduction to the environment, so my outer boundary condition is Newton's law of cooling. The $T$ in the...
  3. physics_CD

    A cart with two cylindrical wheels connected by a rod

    Firstly I only consider one of the wheels. This wheel consists of a big wheel (black) with mass M and radius R and inside it a circular region with a negative mass (-m) and radius R/2. (I assume they have same mass density but with opposite signs. I do this because I don't know where the center...
  4. V

    Inlet and outlet design for a cylindrical tank

    I am designing an inlet tube and a screened outlet for a cylindrical tank with a top opening hole (which determines the water level). I hope I could receive some suggestions and advice on the approach or some texts/equations I should check out. I am still in the process of learning fluid...
  5. tworitdash

    A Dirichlet and Neumann boundary conditions in cylindrical waveguides

    The book of Balanis solves the field patterns from the potential functions. Let say for TE modes, it is: F_z(\rho, \phi, z) = A_{mn} J_m(\beta_{\rho}\rho) [C_2 \cos(m\phi) + D_2 \sin(m\phi)] e^{-j\beta_z z} There is no mention of how to solve for the constant A_{mn} . Then, from a paper...
  6. P

    Understanding Gauss's Law in Cylindrical Shells of Non-Infinite Length

    My question is going to be rather specific. I am trying to understand how Gauss's law applies to this scenario. I know if a cylindrical shell is infinitely long, and there is an external electric field, the inside of the shell will have an electric field of zero everywhere. I am wondering...
  7. CptXray

    Ideal gas in a cylindrical container

    It looks more like a computational obstacle, but here we go. Plugging all of these to the partition function: $$Q = \frac{1}{N! h^{3N}} \int -\exp(\frac{1}{2m}(p^2_{r}+p^2_{\phi}/r^2+p^2_{z})+gz)d\Gamma=$$ $$= \frac{1}{N! h^{3N}} \int \exp{(\frac{-1}{2m}p^2_{r})}dp_{r_{1}}...dp_{r_{N}}...
  8. Z

    Find the electric field of a cylindrical charge

    I begin by calculating the flux to be the flux of the cylinders lateral surface, which equals E*2*pi*p*h (p is the radius) The other two surfaces have E ortogonal to dA, so their flux is 0. Using Gauss law together with the calculated flux above, I get Flux = Q/e Flux = E*2*pi*p*h Solve for E...
  9. S

    I Godel metric in a cylindrical chart

    Can someone express the Godel metric line element in cylindrical coordinates? I keep looking for this line element, but no source clearly gives it to me. Can you please express it using the (- + + +) signature and while retaining all c terms? Thanks. Here is the line element in Cartesian...
  10. P

    Measuring Magnetic Field Strength of a Cylindrical Magnet

    Hello, Today I am wondering if anyone can help me quantify the strength of the magnetic field created by a permanent cylindrical magnet. I have been able to find equations online for the strength of the field within the z axis, (ie. the longitudinal length) but I would like to know the strength...
  11. M

    Convert cylindrical coordinate displacement to Cartesian

    Summary: I can't figure out how the solver carries out the conversions from cartesian to cylindrical coordinates and vice-versa. I have a set of points of a finite element mesh which when inputted into a solver (ansys) gives the displacement of each node. I can get the displacement values of...
  12. Luke Tan

    I Transforming Vector Fields between Cylindrical Coordinates

    In dealing with rotating objects, I have found the need to be able to transform a vector field from cylindrical coordinate systems with one set of coordinate axes to another set. For eg i'd like to transform a vector field from being measured in a set of cylindrical coordinates with origin at...
  13. O

    I Radius vector in cylindrical coordinates

    I am starting to learn classical physics for my own. One exercise was, to calculate the vector r (see picture: 1.47 b). The vector r is r=z*z+p*p. I don’t understand this solution. My problem is: in a vector space with n dimensions there are n basis vectors. In the case of cylindrical...
  14. K

    Square wire in a cylindrical magnetic field

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  15. R

    Circulation of water in a cylindrical reservoir

    Fig1: Fig2: We haven't covered this topic yet, but they expect us to solve it and I'm not 100% sure what I'm doing. a) ##C_r =\oint{\vec{v}*\vec{dl}} = \int{\omega*r*dl} = \omega*\int{r*r*d\phi} = \omega*r^2*2pi## b) Now here I begin to struggle. If v is constant, can I simply pull it out of...
  16. Np14

    What is the angular acceleration of this cylindrical system?

    PART B ONLY: The cylinder undergoes torque when the mass m2 is removed: τNET = Iα = FNETr = 45α = FT(0.5) FT = 90α, therefore msystem = 90 kg After this step, I am not sure what to do. τ = ΣF = Fg - Ft = ma = (20 kg)(9.8 m/s2) - (90α) = 196 -...
  17. F

    What is the Magnetic Field Inside a Cylindrical Coaxial Cable?

    I have no idea where to start.
  18. G

    Surface temperature of a Cylindrical heated rod

    How can I calculate the surface temperature of a Cylindrical Heating rod after some time interval? There is internal heat generation in the rod and convective heat transfer to the surroundings.
  19. maxd23

    A neutral conducting cylindrical shell

    Homework Statement A neutral conducting cylindrical shell with inner radius b and outer radius c surrounds a charged insulated cylinder of radius a at its center whose volume charge density varies radially away from the center as ρ(r) = ρ0 (1− r / a) . A cross-sectional view is shown. (a)...
  20. CharlieCW

    Potential inside a cylindrical shell with a line charge

    Homework Statement Find the electric potential of an infinitely long cylinder shell of radius ##R## whose walls are grounded, when in its interior a line charge, parallel to the cylinder, is placed at ##r=a## (with ##a<R##) and that has a lineal charge density ##\lambda##. Homework Equations...
  21. Z

    Kinematics in Cylindrical Coordinates

    Homework Statement A small bead of mass m slides on a frictionless cylinder of radius R which lies with its cylindrical axis horizontal. At t = 0 , when the bead is at (R,0), vz = 0 and the bead has an initial angular momentum Lo < mR sqrt(Rg) about the axis of the cylinder where g is the...
  22. Mason Smith

    Cylindrical coordinates: unit vectors and time derivatives

    Homework Statement Homework EquationsThe Attempt at a Solution I have found expressions for the unit vectors for cylindrical coordinates in terms of unit vectors in rectangular coordinates. I have also found the time derivatives of the unit vectors in cylindrical coordinates. However, I am...
  23. F

    Shell in a cylindrical capacitor

    Homework Statement There is a capacitor (llenght ##L##) made of a conductor (cylinder of radius ##R_1##) and a cylindrical surface (radius ##R_2##). It is charged with a potential ##V_0##, then it is isolated. (There is vacuum between ##R_1## and ##R_2##) Now we insert a cylindrical...
  24. Q

    Cylindrical Coordinates: Line Integral Of Electrostatic Field

    Homework Statement An electrostatic field ## \mathbf{E}## in a particular region is expressed in cylindrical coordinates ## ( r, \theta, z)## as $$ \mathbf{E} = \frac{\sin{\theta}}{r^{2}} \mathbf{e}_{r} - \frac{\cos{\theta}}{r^{2}} \mathbf{e}_{\theta} $$ Where ##\mathbf{e}_{r}##...
  25. M

    I Converting from spherical to cylindrical coordinates

    I have the coordinates of a hurricane at a particular point defined on the surface of a sphere i.e. longitude and latitude. Now I want to transform these coordinates into a axisymmetric representation cylindrical coordinate i.e. radial and azimuth angle. Is there a way to do the mathematical...
  26. F

    I Proof that the E field inside a cylindrical resistor is constant

    I am reading a proof for this statement and I don't understand one of the steps. It is stated that since the surrounding medium is nonconductive the flow of charge at the surface has no component along the normal of the surface. From this the conclusion is drawn that the E field along the normal...
  27. S

    Cartesian to Cylindrical coordinates?

    Homework Statement I want to convert R = xi + yj + zk into cylindrical coordinates and get the acceleration in cylindrical coordinates. Homework Equations z The Attempt at a Solution I input the equations listed into R giving me: R = i + j + z k Apply chain rule twice: The...
  28. C

    I Force fields in curvilinear coordinate systems

    I am trying to solve problems where I calculate work do to force along paths in cylindrical and spherical coordinates. I can do almost by rote the problems in Cartesian: given a force ##\vec{F} = f(x,y,z)\hat{x} + g(x,y,z)\hat{y}+ h(x,y,z)\hat{z}## I can parametricize my some curve ##\gamma...
  29. W

    I Curl in cylindrical coordinates

    So, let me derive the curl in the cylindrical coordinate system so I can showcase what I get. Let ##x=p\cos\phi##, ##y=p\sin\phi## and ##z=z##. This gives us a line element of ##ds^2 = {dp}^2+p^2{d\phi}^2+{dz}^2## Given that this is an orthogonal coordinate system, our gradient is then ##\nabla...
  30. T

    ∇ x E in Cylindrical Cordinates

    Homework Statement I would like to re-write equation according to polar coordinates. ∇ x E = determinant of Polar coordinates. My question is how can i write determinant of polar coordinates? Homework Equations Maxwell Equations. (Faraday) The Attempt at a Solution E(x,y,z)= e(x,y) e^jβz...
  31. M

    Convert a spherical vector into cylindrical coordinates

    Homework Statement Convert the vector given in spherical coordinates to cylindrical coordinates: \vec{F}(r,\theta,\varphi) = \frac{F_{0}}{arsin\theta}\bigg{[}(a^2 + arsin\theta cos\varphi)(sin\theta \hat{r} + cos\theta \hat{\theta}) - (a^2 + arsin\theta sin\varphi - r^2 sin^2\theta)...
  32. sams

    I A Question about Unit Vectors of Cylindrical Coordinates

    I wrote the equations of the Nabla, the divergence, the curl, and the Laplacian operators in cylindrical coordinates ##(ρ,φ,z)##. I was wondering how to define the direction of the unit vector ##\hat{φ}##. Can we obtain ##\hat{φ}## by evaluating the cross-product of ##\hat{ρ}## and ##\hat{z}##...
  33. C

    I Cylindrical Microwave Cavity Resonator: Speed of Light Dependency?

    Does the operation of a cylindrical microwave cavity resonator as described here, https://en.wikipedia.org/wiki/Microwave_cavity, depend on the speed of light being isotropic along the cylinder axis?
  34. Gene Naden

    I Connection forms and dual 1-forms for cylindrical coordinate

    I ran across exercise 2.8.4 in Oneill's Elementary Differential Geometry. It says "Given a frame field ##E_1## and ##E_2## on ##R^2## there is an angle function ##\psi## such that ##E_1=\cos(\psi)U_1+\sin(\psi)U_2##, ##E_2=-\sin(\psi)U_1+\cos(\psi)U2## (where ##U_1##, ##U_2##, ##U_3## are the...
  35. pobro44

    Converting Coordinate Systems: Exploring the Force on a Semicircular Conductor

    1. The problem statement, all variables and given/known dana I was revisiting University physics textbook and came across this problem. We learned new coordinate systems in classical mechanics classes so I wanted to see if I can apply this to the problem of force on semicircular part of the...
  36. Z

    Potential of N Cylindrical Conductors of Infinite Length

    The electric field of an infinite conductor of net charge Q along the x-y plane is easily found using Gauss's Law: $$ \vec E(x, y) = \frac {\lambda} {2\pi \epsilon}\frac {[(x-x_c)\hat x + (y-y_c)\hat y]} {[(x - x_c)^2 + (y - y_c)^2]^3}, $$ where ##x_c## and ##y_c## mark the location of the...
  37. G

    Magnetic energy stored in a cylindrical conductor

    Homework Statement So I came across with following problem: > Consider a cylindrical conductor of infinite length and circular section of radius a and that is traversed by a stationary current I. What is the magnetic energy stored in the conductor. Homework Equations 3. The Attempt at a...
  38. T

    I Del operator in a Cylindrical vector fucntion

    Hi there I'm having a hard time trying to understand how come ∂r^/∂Φ = Φ^ ,∂Φ/∂Φ = -r^ -> these 2 are properties that lead to general formula. I've been thinking about it and I couldn't explain it. I understand every step of "how to get Divergence of a vector function in Cylindrical...
  39. Remixex

    Stress and Strain tensors in cylindrical coordinates

    Homework Statement I am following a textbook "Seismic Wave Propagation in Stratified Media" by Kennet, I was greeted by the fact that he decided to use cylindrical coordinates to compute the Stress and Strain tensor, so given these two relations, that I believed to be constitutive given an...
  40. R

    Viewing Particle P in a Cylindrical Vessel - 40 cm Height Needed

    I1. Homework Statement A cylindrical vessel whose diameter and height both are equal to 30 cm is placed on a horizontal surface and a small particle p is placed in it at a distance of 5 cm from the centre. An eye is placed at a position such that the edge of the bottom is in the plane of...
  41. U

    Formula for Magnetic Field of Cylindrical Magnet | R,L Values

    Hi, I am looking for the formula of the magneti field along the axis of a axially magnetized cylindrical magnet. Unfortunately, there are quite different answers on Internet. Is the uploaded formula (where R is the magnet radius and L its length) correct?
  42. J

    Air resistance: cylindrical rotor in stator with air gap

    Hello, I am currently doing research on the aerodynamic properties of a rotating cylinder in a cylindrical housing. The cylinder represents a rotor in a electric motor. The air gap between rotor and stator is about 0.5mm. I'm looking for a theoretical analysis and calculation on the...
  43. Samnolan1031

    Gauss Law- Conducting and Non-conducting cylindrical shells

    Homework Statement Below is a diagram of an infinitely long non-conducting rod of radius, R, with a uniform continuous charge distribution. The uniform linear charge density of this line is lamba1. The rod is at the center of an infinitely long, conducting pipe. The linear charge density of...
  44. niaz

    Cylindrical rotor generator power under loss of excitation

    Hello all, I want to know about turbo alternator real power producing capability under loss of excitation condition. Normally in salient pole rotor have capability to supply real power under field current=0 condition, as there is reluctance power developed. But what about non salient pole...
  45. F

    Cylindrical Coordinates Triple Integral -- stuck in one place

    Homework Statement Use cylindrical coordinates to evaluate triple integral E (sqrt(x^2+y^2)dv where E is the solid that lies within the cylinder x^2+y^2 = 9, above the plane z=0, and below the plane z=5-y Homework EquationsThe Attempt at a Solution So i just need to know how to get the bounds...
  46. Perodamh

    What is the diameter of the cylindrical rod

    Homework Statement A cylindrical rod of copper (E = 110GPa) having a yield strength of 240MPa is to be subjected to a load of 6660N. If the length of the rod is 380mm, what must be the diameter to allow an elongation of 0.5mm. Homework Equations E = stress/ strain stress = Force/Area ; Area =...
  47. E

    Showing E.dl is 0 - Why cylindrical coordinates?

    Homework Statement A point charge +Q exists at the origin. Find \oint \vec{E} \cdot \vec{dl} around a circle of radius a centered around the origin. Homework EquationsThe Attempt at a Solution The solution provided is: \vec{E} = \hat{\rho}\frac{Q}{4\pi E_0a^2} \vec{dl}=\hat{\phi}\rho d\phi...
  48. T

    Radial Heat Conduction through a Cylindrical Pipe

    Homework Statement A 1.75m long PVC pipe with a thermal conductivity of 0.19 W/mK has an internal diameter of 3mm and an external diameter of 5.5mm. Inner temperature is 298K and outer temperature is 273K. Calculate the heat transfer rate through the pipe and thus the decrease in the inner...
  49. M

    Distribution of ions in a cylindrical container

    Homework Statement In a cylindrical container of radius ## R ## and height ## h \ll R ##, with long axis ## \hat{z} ##, in the presence of gravity acceleration ## \vec{g} = - g \vec{z} ## is contained a neutral ionized gas, whose ions can be described as material points with electric charge ##...
  50. M

    Change integration limits for cylindrical to cartesian coord

    Homework Statement I want to change the integration limits of an integral in cylindrical to cartesian coordinates. For example the integral of function f(r) evaluated between b and R: ∫ f(r)dr for r=b and r=R (there is no angular dependence). For write de function in cartesian coordinates...
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