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. R

    Tangential Acceleration of Object moving in cylindrical wall

    Homework Statement An object slides along the ground at speed v at the base of a circular wall of radius r. The object is in contact with both the wall and the ground, and friction acts at both contacts. The wall is vertical and provides no force in the vertical direction. (i) Show that the...
  2. beer

    Refesher Part Duex - Rectangular -> Cylindrical -> Spherical

    I'm at it again today. Helping the same friend (plus another) study for their final calculus exams; it's a good refresher for me as well. (I'm a senior industrial engineering major so I'm "done" with calculus, and it isn't used much in our upper level classes nor professionally to the best of...
  3. karush

    MHB Volume about x axis using cylindrical shells

    Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis. $x=1+{y}^{2}$, $x=0$, $y-1$, $y=2$ https://www.physicsforums.com/attachments/4237 The answer is $\frac{21\pi}{2}$ but I couldn't get it using...
  4. F

    Cylindrical tank vs conical tank

    Hey everyone, I'm new to this site and I figured this would be the best place to ask this question. We've been using maple to solve two specific problems on the time it would take two tanks to drain. One being cylindrical, and the other conical. They have the same height, the same volume...
  5. Calpalned

    Spherical vs cylindrical notation

    Homework Statement Plotting a point in spherical coordinates means using the format ##(\rho, \theta, \phi)## in place of ##(x, y, z)##. Taking a triple integral means replacing ##dV## with ##\rho ^2 sin(\phi) d\rho d\theta d\phi ## As you can see, ##\rho, \theta, \phi ## are all in the same...
  6. Calpalned

    Triple integral in cylindrical coordinates

    Homework Statement Evaluate ## \int \int \int_E {x}dV ## where E is enclosed by the planes ##z=0## and ##z=x+y+5## and by the cylinders ##x^2+y^2=4## and ##x^2+y^2=9##. Homework Equations ## \int \int \int_E {f(cos(\theta),sin(\theta),z)}dzdrd \theta ## How do I type limits in for...
  7. B

    E-field of cylindrical conductor above infinite ground plane

    Homework Statement Find the electric field between the conductor and ground. The conductor is at: Potential = +V0, radius a distance d from the ground plane. Homework Equations I used image theory to create a conductor at -V0 at distance -d from the ground plane. Laplace's equation: ∇2V = 0...
  8. Alex_Neof

    Infinitely long cylindrical shell (magnetic field at centre)

    Homework Statement An infinitely long hollow cylinder of radius (a) carries a constant current (i). Use Biot - Savart's law and show that the magnetic field at the centre of the cylinder is zero. Also show, using symmetry arguments and Ampere's law, the magnetic field is zero in any point...
  9. D

    Cylindrical cavity resonator problem

    Homework Statement Q. A cylindrical cavity resonator has diameter of 24 mm and length 20 mm. The dominant mode and the lowest frequency band are operated as ? I am providing a picture of problem to show the options given to me. I solved the problem by calculating resonant frequency for cavity...
  10. S

    Expressing electric field in cylindrical coordinates.

    Hi everyone, I am new to the physics forums and I need your help :) I understand that depending on the symmetry of the problem, it may be easier to change the coordinate system you are using. My question is, how would I convert the electric field due to a point charge at the origin, from...
  11. M

    MHB Cylindrical coordinates - Orthonormal system

    Hey! :o Using cylindrical coordinates and the orthonormal system of vectors $\overrightarrow{e}_r, \overrightarrow{e}_{\theta}, \overrightarrow{e}_z$ describe each of the $\overrightarrow{e}_r$, $\overrightarrow{e}_{\theta}$ and $\overrightarrow{e}_z$ as a function of $\overrightarrow{i}...
  12. N

    Cylindrical Charge distribution with dielectric shell

    Homework Statement A cylindrical distribution of charge ρ = α/sqrt(r) where α = 2 µC/m^(5/2) extends from 0 cm to 9.3 cm (has radius 9.3 cm). Concentric with this is a dielectric shell with k = 5.44 of inner radius 16.6 cm and outer radius 24.9 cm. What is the electric field at 3.53 cm, 12.6...
  13. A

    Acceleration and cylindrical coordinates

    Homework Statement The question and my attempt are attached as pics Homework EquationsThe Attempt at a Solution I can't seem to find r¨ and θ¨. Assuming I already got r˙ and θ˙ (the answers are written after the question). The idea I tried was to get the acceleration equation in cylindrical...
  14. Philethan

    A ball rolls without slipping in a cylindrical trough

    Homework Statement A solid sphere sphere (radius = R) rolls without slipping in a cylindrical trough (radius = 5R) as shown in the following figure. Show that, for small displacements from equilibrium perpendicular to the length of the trough, the sphere excuses simple harmonic motions with a...
  15. R

    Electric Field above a cylindrical shell w/ charge density

    Homework Statement [/B] We need to use the equation for the E field of a ring to set up the integral for calculating the E field of a cylindrical shell with a charge density of σ and a radius of R and a height of H, at a point P that is D distance away from the cylinder.Homework Equations [/B]...
  16. C

    Index of Refraction Through a Cylindrical Tube

    Hello All, I would like to start learning how to ray trace but the tracing through a tube with a thickness of t has got me stumped. If I have an n1 (outside tube), n2 (Tube), and n3 (inside tube). n1≠n2≠n3. Knowing Θ1 (the angle of incidence in relation to the normal), I can calculate Θ2 from...
  17. D

    What are new ways to open a cylindrical pressure vessel?

    I am currently helping one of my old physics professors and his Phd student designing a pressure vessel for ultra-sciencey detector (still figuring out the theory behind it all). So far we have the general vacuum tank that opens on the ends, with the pressure difference holding the ends on...
  18. B

    Finding flux through ellipsoid in Cylindrical Coordinates

    Homework Statement Using Cylindrical coordinates, find the total flux through the surface of the ellipsoid defined by x2 + y2 + ¼z2 = 1 due to an electric field E = xx + yy + zz (bold denoting vectors | x,y,z being the unit vectors) Calculate ∇⋅E and then confirm the Gauss's Law Homework...
  19. K

    Gauge symmetry of cylindrical rod

    A twisted cylindrial rod has the cross sectional symmetry so that it's not posible to tell whether it is twisted or not without knowing if there is any torsional energy. now drawing a line on the surface of it can tell us whether or not it's twisted. It might not be a straight line.. there are...
  20. P

    Converting arbitrary Cartesian vector to cylindrical

    Hello PF, I have a problem to solve in the following form: Given a vector with Cartesian components, V={Vx,Vy,Vz}, find its components in circular cylindrical coordinate. Given the actual vector components, it'd be very easy to convert. But I have no idea where to start on this. Any guide to...
  21. allamsetty

    Need 2D plot of plane wave, cylindrical & spherical wave

    plane wave is represented as exp (ik.r) and the cylindrical wave as 1/sqrt(r) *exp(ik.r) and the spherical wave as 1/r*exp(ik.r) Have anyone tried to plot these waves? How to do it? Attempt: in Matlab assuming k=1 >> x=linspace(-1,1,100); >> for(ii=1:100) fp(ii)=exp(i*x(ii)); end >>...
  22. P

    Cylindrical coordinate of Galilean transformation

    r\rightarrow r-2qz and \psi\rightarrow\psi+q\cdot(r-qz), I don't know how to derive it, anybody know? This question results from the book "Optical Solitons: From Fibers to Photonic Crystals [1 ed.]" section 6.5
  23. R

    MHB Vector Calculus - Cylindrical Co-ordinates

    I have a question, to use cylindrical coordinates to find the volume of the ellipsoid ${R}^{2}+{3z}^{2}=1$. I know for cylindrical coordinates the Jacobian is $r$ so I have some integral: $$\iiint (r)dzdrd\theta$$ However I am struggling to work out the bounds of the integral for $z,r,\theta$...
  24. G

    Finding the magnetic field of an infinite cylindrical wire.

    Homework Statement An infinite cylindrical wire of radius ##R## carries a current per unit area ##\vec{J}## which varies with the distance from the axis as ##J(s)=ks^2\hat{z}## for ##0<s<R## and zero otherwise where k is a constant. Find the magnetic field ##\vec{B(s)}## in all space. Homework...
  25. N

    Electric field in a cylindrical conductor

    Homework Statement Problem 1c from here: http://web.phys.ntnu.no/~ingves/Teaching/TFY4240/Exam/Exam_tfy4240_Dec_2013.pdfHomework Equations Maxwell's equations The Attempt at a Solution According to the solutions, the electric field is ZERO everywhere because it's "magnetostatics" and because...
  26. M

    Finding this volume without cylindrical shells

    This is not a homework problem this is just a problem I was thinking about whether or not it would be possible to solve without cylinderical shells The region bounded by y=1/(x^2) x=e x=e^3 and the x-axis Rotated around y axis.. I did cylindrical shells and got 4pi and then wondered if I...
  27. R

    2D cylindrical heat equation

    Hello friends, I am new for numerical methods and programming. i have been trying to devolop a program in 2D poisson heat equation in cylinder (r,angle) by finite difference method ∂2u/∂r2 + 1/r * ∂u/∂r + 1/r2 * ∂2u/∂θ2 = Q(u,θ)discritized equation :- ui+1,j − 2uij + ui−1,j/(∆r)2 + 1/ri *...
  28. R

    Short Cylindrical Vacuum Chamber

    I seek to build a vacuum chamber for shipping radon contamination sensitive samples. The cylinder will have a height of approximately 2 inches, and needs an inner diameter of 10 inches. The plan is to weld stainless steel pipe to a plate on the bottom, and to have a lid bolt on to the pipe with...
  29. E

    Proper way to graph xy = 1 for a cylindrical shell problem

    Homework Statement Proper way to graph xy = 1 for a Cylindrical Shell problems. Homework Equations V = ∫^b_a 2πy f(y) dy The Attempt at a Solution I am rotating around the x-axis, so I am integrating with respect to y, but should I choose x = 1/y, or y = 1/x to solve my problem? How are...
  30. V

    Laplace's Equation in Cylindrical Coordinates (Potential)

    Homework Statement A hollow cylinder with radius ##a## and height ##L## has its base and sides kept at a null potential and the lid on top kept at a potential ##u_0##. Find ##u(r,\phi,z)##. Homework Equations Laplace's equation in cylindrical coordinates...
  31. K

    Transform Cylindrical coordinates into Cartesian Coordiantes

    I've learned that a vector in coordinate system can be expressed as follows: A = axAx+ayAy+azAz. ai, i = x, y, z, are the base vectors. The transformation matrix from cylindrical coordinates to cartesian coordiantes is: Ax cosΦ -sinΦ 0 Ar Ay = sinΦ cosΦ...
  32. C

    Cartesian unit vectors expressed by Cylindrical unit vectors

    please someone explain me the following expression for Cartesian unit vectors expressed by the cylindrical unit vectors: http://web.mit.edu/8.02t/www/materials/modules/ReviewB.pdf at page B-8 line B.2.4 i would like to know which steps led to it. thanks, Chen
  33. R

    Potential of concentric cylindrical insulator & conducting shell. Stuck on 2nd question

    An infinitely long solid insulating cylinder of radius a = 5.2 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 23 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 14.2 cm, and...
  34. R

    Solving Laplace Equation in Cylindrical Coordinates - Potential Outside Cylinder

    The potential on the side and the bottom of the cylinder is zero, while the top has a potential V_0. We want to find the potential outside the cylinder. Can I use the same boundary conditions as for case of inside cylinder potential? What is different?
  35. A

    Calculating Current in a Cylindrical Region

    Homework Statement (a)The current density across a cylindrical region of radius R varies according to the equation: J=J0(1-r/R), where r is the distance from the axis of the cylinder. The current density is the maximum J0 at the axis r=0 and decreases linearly to zero at the surface r=R...
  36. M

    Where Can I Find a 7-Position Rotating Cylinder Switch for My Prototype Device?

    I'm working on a prototype device, and I'm currently figuring out the form factor. On the turn indicator of my car, there is a ring with several positions that will control the lights. I'm thinking that something similar would work well on the handle of my device, and I'm looking to purchase...
  37. J

    How to design a vertical cylindrical Water tank

    I Need to design a Vertical cylindrical water tank to be build by Fiberglass. I need to calculate the tank also for 7.5 m bar pressure and 2.5 m bar vacuum pressure. Tank Dimensions to be 4m Dia, 5 m High (60000 Liters). I have Fiberglass laminate of 6 mm Thk and Modules is 1470000 psi. I have...
  38. J

    Why liquids transported in cylindrical or elliptical cylindrical

    on road? and why not cuboidal ones?
  39. W

    2-Plane Distribution in Cylindrical Coords.

    Hi all, I am trying to describe/understand how to define a 2-plane distribution in R^3 , i.e., an assignment of a 2-plane at each tangent space, when the distribution is given in terms of the basis of a plane in (R^3, cylindrical). It has just been a while since I have worked with cylindrical...
  40. N

    Plano-convex vs Double-convex (fly's eye) cylindrical microlens array

    I am trying to find out if I could substitute a Plano-convex cylindrical microlens array with a Double-convex (fly's eye) cylindrical microlens array for laser beam homogenization in 1 dimension. Assuming that the lens parameters are the same, how would the quality of performance be affected...
  41. T

    "Potential of Concentric Cylindrical Insulator and Conducting Shell"

    Homework Statement An infinitely long solid insulating cylinder of radius a = 2.5 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 30 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of...
  42. J

    Double dot product in Cylindrical Polar coordinates

    Hello, I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows: 2W = σijεij Where σ and ε are symmetric rank 2 tensors. For cartesian coordinates it is really easy because the metric is just the identity matrix, hence: 2W = σxxεxx +...
  43. D

    2D quantum harmonic oscillator in cylindrical coordinates (radial part

    Dear kind helpers, actually I am not 100% sure whether this is the right place to post, as it is not a homework in the sense of an exercise sheet. But I think it could be because it feels pretty basic and that I should be able to solve it. Though I really searched for a solution but could not...
  44. G

    Discretization in cylindrical coordinates, unit thickness for azimuth?

    I am setting up a numerical simulation from a 2D discretization of the heat equation in cylindrical coordinates. my spatial variables are radius (r), height (z), and azimuth (ø). The assumption is that there is no gradient along the azimuth direction (if temperature is T then dT/dø = 0)...
  45. M

    Capacitance of cylindrical shells

    I know the capacitance of cylindrical shell formula if both cylinder length is same.If cylinders length differs between which the dielctric is sandwitched what is the formula to calculte the capacitance?
  46. S

    Poisson's Equation in Cylindrical Coordinates

    Homework Statement Homework Equations Possions Equation and boundary conditions... The Attempt at a Solution First Part that I think is right... However when I try and apply the boundary conditions ie V(a)=V(r)=0... I can't get the answer! And for the last...
  47. M

    Electric Field of a charged sphere with cylindrical gaussian surface

    So the problem statement is: A conducting solid sphere (R = 0.167 m, q = 6.63·10–6 C) is shown in the figure. Using Gauss’s Law and two different Gaussian surfaces, determine the electric field (magnitude and direction) at point A, which is 0.00000100 m outside the conducting sphere. (Hint: One...
  48. tristanm

    Electric Fields of Cylinders and Cylindrical Shells

    Homework Statement 1. Use Gauss' Law to calculate the electric field at a radius of 5.0cm from the z-axis 2. Use Gauss' Law to calculate the electric field at a radius of 8.0cm from the z-axis 3. What is the surface charge density σmetal on the outer surface of the metal cylinder...
  49. PsychonautQQ

    Question about cylindrical Coordinates

    I'm confused why when using cylindrical coordinates three unit vectors are needed. My book says that the three unit vectors are one for the radial direction which is bound to the xy plane and then a unit vector in the z direction. It goes on to say that there is another unit vector associated...
  50. C

    Linear Actuator (Solenoid pushing a cylindrical magnet)

    I am working on a home made electromechanical actuator to replace the vacuum actuator on the front axle of my Jeep Cherokee. The vacuum actuator isn't the greatest and I have replaced it and the system lines few times. SO I figure, I know what force the vacuum actuator is putting out, I...
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