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. M

    Particulate matter in a cylindrical bin

    Hello :) I am currently confused about the forces acting on particulate matter in a cylindrical bin. It is apparently widely accepted that the vertical forces acting on an elemental slice of particulate solids in a cylindrical bin are: The pressure difference between the bottom and the...
  2. T

    Transformation from cylindrical 2 cartisian

    it's not homework but it's something I can't make any sense with it why when we transform from cylindrical 2 cartisian or the inverse we take the unit vector in our consideration and transform it also not just transform the function and relate it to the other unit vectors ??. for example ...
  3. Y

    How Do You Solve the Cylindrical Heat Equation with Non-Constant Coefficients?

    I have tried to solve the cylindrical case of the heat equation and reached the second order differential equation for the function R(r): R'' + (1/r)*R' + (alfa/k)*R = 0 (alfa, k are constants) I couldn't find material on the web for non-constant coefficients, does anyone know how to...
  4. U

    Minimum Volume of a Hom., Bare Cylindrical Reactor

    Just trying to do a problem to find the minimum volume for a homogeneous, bare cylindrical reactor, and my main question is if the radial and axial bucklings are equal to one another at min. V or if there is some other condition that would be helpful. Thanks.
  5. fluidistic

    Vector field, cylindrical coordinates

    Homework Statement Describe the following vector field: \bold v (\bold x)=\frac{\bold a \times \bold x}{(\bold a \times \bold x)(\bold a \times \bold x)} with \bold a = \text{constant}. Calculate its divergence and curl. In what region is there a potential for \bold v? Calculate it. Hint...
  6. A

    Cylindrical Capacitors Questions

    Homework Statement An isolated cylindrical capacitor consists of two concentric conducting cylinders of length L and radii a and b. The inner and outer conductors carry +Q and -Q, respectively. a. Determine the electric field between the conductors. b. Determine the electric potential...
  7. R

    Electric Field in a cylindrical Coaxial Capacitor

    Homework Statement Two infinite coaxial metal cylindrical tubes of radius a and b (a < b) are charged with charge per unit length (unit [C/m]) \lambda and -\lambda respectively. Calculate the electric field between the tubes (i.e. for a < r < b) Where \epsilon_{0} is the permittivity...
  8. V

    Need help coming up with dl in cylindrical coords.

    The whole problem consists of several parts, but my issue is to come up with a dl for the piece of wire shown. Im trying to find the force on the wire due to a magnetic field produced by another wire running along the x-axis (not shown in pic). \vect{B} = \frac{\mu_0I}{2\pi s}\hat{\phi}...
  9. Z

    Solid of revolution question: given height of a cylindrical core in a sphere

    Homework Statement A hole is drilled through the center of a ball of radius r, leaving a solid with a hollow cylindrical core of height h. Show that the volume of this solid is independent of the radius of the ball. Homework Equations V = \int_{a}^{b} 2\pi x (f(x) - g(x))...
  10. P

    Local stress on thin cylindrical shell

    Hello I have a local stress acting radial on a thin cylindrical plate (see illustration), how can I calculate if the plate will deform/bend? I can only find equations for uniform external pressure (Marcel Dekker), but will it be okay when the stress is only local?
  11. H

    Triple Integral Using Cylindrical Coordinates

    Homework Statement A conical container with radius 1, height 2 and with its base centred on the ground at the origin contains food. The density of the food at any given point is given by D(r) = a/(z + 1) where a is a constant and z is the height above the base. Using cylindrical polar...
  12. C

    Electric field / net charge on a cylindrical shell

    Homework Statement A cylindrical shell of radius 8.1 cm and length 247 cm has its charge density uniformly distributed on its surface. The electric field intensity at a point 20.3 cm radially outward from its axis (measured from the midpoint of the shell ) is 41800 N/C. Given: ke =8.99×10^9...
  13. S

    Electrostatic Potential for Two Concentric Cylindrical Shells

    Homework Statement Two very long hollow conducting cylindrical shells are situated along the x-axis. The shells are concentric and have negligible thickness. The inner shell has a radius a and a linear charge density +lambda, while the outer shell has a radius b and a linear charge density...
  14. K

    Rolling without slipping on a cylindrical surface - need clarification

    Hi, The following is a general question which doesn't have to do with any particular problem. (therefore I am not including the template). I understand that when a circular object (e.g: a hoop) rolls on a *flat* surface without slipping with angular speed \omega, its contact point, and thereby...
  15. K

    Voltmeter cylindrical shell help

    Homework Statement A very long insulating cylindrical shell of radius 6.00 cm carries charge of linear density 8.90*10^-6 C/m spread uniformly over its outer surface. *What would a voltmeter read if it were connected between the surface of the cylinder and a point 4.70 above the surface...
  16. K

    Calculating Voltage Difference in a Cylindrical Shell

    .A very long insulating cylindrical shell of radius 6.00 cm carries charge of linear density 8.90*10^-6 C/m spread uniformly over its outer surface. *What would a voltmeter read if it were connected between the surface of the cylinder and a point 4.70 above the surface. and What would a...
  17. S

    Capacitance of a cylindrical capacitor

    Homework Statement A coaxial cable used in a transmission line has an inner radius of 0.15 mm and an outer radius of 0.65 mm. Calculate the capacitance per meter for the cable. Assume that the space between the conductors is filled with polystyrene. (Also assume that the outer conductor is...
  18. L

    Stress field in cylindrical coordinates

    Can anyone please explain the stress fields in cylindrical coordinates? What is the difference between \sigma_{rz} and \sigma_{\theta z}? What is the difference between stress in the r axis and stress in the \theta axis? Thanks
  19. H

    Calculating Electric Field of Cylindrical Rod and Shell

    Homework Statement An infinitely long conducting cylindrical rod with a positive charge lambda per unit length is surrounded by a conducting cylindrical shell (which is also infinitely long) with a charge per unit length of -2 \lambda and radius r_1, as shown in the figure. What is E(r)...
  20. R

    Applying Guass' Law to Cylindrical Symmetry

    OK, having some trouble wrapping my head around this so would appreciate some clarification. Let us say I had a long, thin wall metal tube of radius R with a uniform charge per unit length. Would there be some magnitude of E of the electric field at a radial distance of R/2? I understand...
  21. C

    Setting up a triple integral using cylindrical & spherical coordinates

    Homework Statement Inside the sphere x2 + y2 + z2 = R2 and between the planes z = \frac{R}{2} and z = R. Show in cylindrical and spherical coordinates. Homework Equations \iiint\limits_Gr\,dz\,dr\,d\theta \iiint\limits_G\rho^{2}sin\,\theta\,d\rho\,d\phi\,d\theta The Attempt at a...
  22. S

    Conversion to cylindrical co-ordinates

    Conversion to cylindrical co-ordinates...please help I came a across the following problem in William Hayt book. 1.) Expresss in cylindrical componenets:(a) vector from C ( 3,2,-7) to D (-1,-4,2) The following is the solution in the solution manual of that book: a) the vector from C(3, 2,−7)...
  23. D

    Equilibrium heat equation in 2D cylindrical coordinates

    Homework Statement Plate in the shape of the circular halo (inner radius a, outer radius b>a), the inner edge is being kept at a constant temperature T_0, and the outer at the temperature given by the function f(\phi)=T_0\cos(2\phi). Find the equilibrium distribution of the heat everywhere...
  24. S

    How Do You Find the Field Inside a Polarized Cylinder?

    Homework Statement This problem is at Griffiths 4.13. A very long cylinder of radius a with a uniform polarization perpendicular to the axis. The question is to solve for the field inside the cylinder. Homework Equations \rho_b=P\cdot\hat{n} and \sigma_b=-\nabla\cdot P The Attempt...
  25. J

    Choosing the Right Variable for Radius of Shell in Cylindrical Shell Method

    Im new to finding volume using the cylindicral shell method so what should i do. I know I will eventually plug equations into the integral 2piX(f(x)-g(x))dx x=y x+2y=3 and y=0 revolve about the x axis
  26. M

    Cylindrical Triple Integral: Evaluating Over a Bounded Solid

    Homework Statement Use cylindrical coordinates to evaluate the triple integral (over E) sqrt(x^2+y^2) dV , where E is the solid bounded by the circular paraboloid z=9−16(x^2+y^2) and the xy plane. The Attempt at a Solution This is really bugging me... Is this the correct setup for the...
  27. T

    How Are Stresses Calculated in Non-Standard Shaped Pressure Vessels?

    Are there standard algorithms for calculating stresses (axial, radial) in pressure vessels? I have found pages detailing circular cylindrical, thin- and thick-walled pressure vessels. However, what about other shapes? Are there some equations I can use to integrate to find stresses for e.g...
  28. J

    Converting a Vector Field from Cartesian to Cylindrical Coordinates

    Homework Statement I have a rather complicated vector field given in cartesian coordinates that I need to evaluate the line integral of over a unit square. I know to use Stoke's Theorem to do this, and I suspect that the integral would be greatly simplified if it were in cylindrical...
  29. D

    Globular clusters cylindrical polar coordinates

    Homework Statement Two globular clusters A and B have cylindrical polar coordinates relative to the centre of the galaxy (r, z, Ø) given by A = (5,2,15°) and B= (4.6,65°), where the r and z coordinates are in kiloparsecs. Homework Equations Find a and b the position vectors of each...
  30. D

    What Is the Maximum Pressure a Reinforced Cylindrical Tank Can Withstand?

    the cylinder in the picture below has a maximum shear strength of 90Mpa and a maximum normal strength of 150Mpa the tank has a wire tightly wrapped around it so that the wire has a tensile stress of 250Mpa when the tank is empty, what is the stress the tank feels due to the wire...
  31. ╔(σ_σ)╝

    Integration in cylindrical coordinates

    Homework Statement In cyclindrical coordinates we can represent points as (\rho,\phi,z) We define a vector in cyclindrical coordinates as follows A = A\rhoa\rho + A\phia\phi + Azaz I'm having some problem with subscripts. Anyway I don't understand this. If I am given a point say ( 5, 20...
  32. T

    Principle stresses and maximum shearing stress in a cylindrical shaft. Pl help

    Homework Statement Nevermind the rough picture, the shaft is cylindrical. Knowing that the post has a diameter of 60mm, determine the principle stresses and the maximum shearing stress at point K. Homework Equations These are equations for your reference: \sigma = My/I \tau = Tc/J Where...
  33. S

    Volume of Cylindrical Shells: y = 4x - x^2, y = 3; about x = 1

    Homework Statement Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. Sketch the region and a typical shell. y = 4x - x^2, y = 3; about x = 1 Homework Equations ? The Attempt at a...
  34. K

    Calculating Intensity of Coherent Radiation in Cylindrical Filter

    Hello, All. I'm a student. I have a problem. I need numerically calculate of the intensity distribution of the full coherent radiation in the spatial filter(cylindrical geometry) (Katron's scheme). Input data: Focal length of lenses F = 1 (m) Length of the wave of radiation Lambda = 10-6...
  35. Z

    Why the term cylindrical functions for the states in LQG?

    Why the term "cylindrical functions" for the states in LQG? I just can't find a any reference that explain the why of the term "cylindrical" for the states in LQG. Thanks in advance for any comment. Z.
  36. M

    Area of Solid/Convert to Cylindrical and Spherical

    Homework Statement Convert to Cylindrical Coordinates from Cartesian 1st int(-2 to 2), 2nd int(-sqrt(4-x2) to sqrt (4-x2)), 3rd int((x2+y2) to 4) X dz dy dx. I changed the integrals to Cylindrical 1st int(0 to pi), 2nd int(-2 to 2), 3rd int(r2 to 4) and the X to r cos(theta). r dz dr...
  37. C

    Conducting wire with cylindrical hole, Please help

    Homework Statement The conductor is cylindrically shaped with a radius of R. The hole on the inside is also cylindrically shaped with a radius of R/2. If a cross-section of this conductor is placed on an x-y coordinate plane, the hole would be centered on the x-axis at a distance of R/2 from...
  38. F

    Magnetic repulsion force between two cylindrical magnets

    I'm doing an investigation where I am trying to find the repulsion force of cylindrical magnets. For this I have two ferromagnetic disk magnets on their sides, so that the curved sides face each other. In the investigation I push one of the magnets with a constant force towards a stationary one...
  39. C

    Find Speed of Cylindrical Shell on Incline-Loop

    Homework Statement http://img688.imageshack.us/img688/5277/loopb.jpg A cylindrical shell is released from rest and rolls down an incline without slipping. Find speed of shell at the top of the loop. h(incline) = 2.0m h(loop) = 1.3m The Attempt at a Solution vf = sqrt(g * yi)...
  40. L

    Cylindrical tank w/ water flowing out of small tube near bottom

    1. A cylindrical open tank needs cleaning. The tank is filled with water to a height meter, so you decide to empty it by letting the water flow steadily from an opening at the side of the tank, located near the bottom. The cross-sectional area of the tank is square meters, while that of the...
  41. J

    If a cylindrical tank of radius 1m rests on a platform 5m above the

    If a cylindrical tank of radius 1m rests on a platform 5m above the ground. Initially the tank is filled with water up to a height 5m. A plug whose area is 10-4m2 removed from an orifice on the side of the tank at the bottom.(density of water = 103kg/m3, g= 10m/s2). i wanted to ask what would...
  42. A

    A cylindrical rod of 380mm long and 10mm in diameter

    A cylindrical rod of 380mm long and 10mm in diameter is subjected to a tensile load of 25kN. If the rod is to allow neither plastic deformation nor an elongation of more than 0.9 mm, select a suitable material for the rod from the table below. Justify your choice(s) with full calculations and...
  43. C

    Convert to cylindrical coordinates

    Evaluate by changing to cylindrical coordinates \int from 0 to 1 \int from 0 to (1-y^2)^1/2 \int from (x^2+y^2) to (x^2+y^2)^1/2 (xyz) dzdxdy I came to an answer of integral from 0 to pi integral from 0 to 1 integral from r^2 to r (rcos\thetarsin\thetaz) r dzdrd\theta Is this the correct answer?
  44. J

    Volume of a cone using cylindrical coordinates and integration

    Hi all! I was trying to figure out how to find the volume of a cone with radius R and height h using integration with cylindrical coordinates. I first tried to set the the integral as: \int_{0}^{2\pi}\int_{0}^{h}\int_{0}^{R}\rho d\rho dz d\phi ...but I think that this is setting up the...
  45. T

    Help Rectangle to Cylindrical coordinate question

    Homework Statement evaluate : \int\int\int_{E} e^z DV where E is enclosed by the paraboloid z = 1 + x^2 + y^2 , the cylinder x^2 + r^2 = 5 I just need help setting this up. I know that theta is between 0 and 2pi Now is z between 0 and 1 + r ? and r is between 0 and sqrt(5)...
  46. T

    Rectangle to Cylindrical coordinate question

    Homework Statement can you explain this conversion, I am not sure. Rectangle coord : \int^{2}_{-2}\int^{sqrt(4-x^2)}_{-sqrt(4-x^2)}\int^{2}_{sqrt(x^2 + y^2 )} F(x) dzdydx = cylindrical coord : \int^{2\pi}_{0}\int^{2}_{0}\int^{2i}_{r} r*dzdrd\theta I see that x^2 + y^2...
  47. fluidistic

    Cylindrical capacitor with a dielectric

    Homework Statement I must calculate the capacitance of the following capacitor : A cylindrical capacitor made of 2 shells (not sure if shell is the right word in English. Made of 2 cylinders maybe), one of radius a and the other of radius b>a. It has a length of L. We introduce entirely...
  48. A

    Laplace equation in cylindrical coordinates

    Can anyone help with the solution of the Laplace equation in cylindrical coordinates \frac{\partial^{2} p}{\partial r^{2}} + \frac{1}{r} \frac{\partial p}{\partial r} + \frac{\partial^{2} p}{\partial z^{2}} = 0 with Neumann no-flux boundaries: \frac{\partial p}{\partial r}...
  49. J

    Comparing Bound Charges on Cylindrical Dielectric Surfaces

    Homework Statement A conducting wire carrying a charge \lambda per unit length is embedded along the axis of the cylinder of Class-A dielectric. The radius of the wire is a; the radius of the cylinder is b. Show that the bound charge on the outer surface of the dielectric is equal to the...
  50. M

    Triple integral with cylindrical coordinates

    Homework Statement Use cylindrical coordinates to evaluate the triple integral \int\int\int \sqrt{x^2+y^2} dV in region E where E is the solid bounded by the circular paraboloid z=9-(x^2+y^2) and the xy-plane. Homework Equations knowing that x = rcos\theta y= rsin\theta z=z...
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