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. Y

    Derivative in cylindrical coordinates.

    This is calculus question, but I don't think calculus really cover this topic in either multi-variables or even vector calculus classes. This is really more common problem in electrodynamics. Let R be position vector that trace out a circle or radius a with constant velocity. In rectangular...
  2. A

    Stress-energy tensor in static cylindrical case

    I have some problems using this definition, maybe because it's not valid in every coordinate system: T^{\mu\nu} = (\epsilon + p) \frac{dx^{\mu}}{ds} \frac{dx^{\nu}}{ds} -p g^{\mu\nu} since in cylindrical coordinates x^0 =t \qquad x^1 =\rho \qquad x^2 = \phi \qquad x^3 =z using weyl metric...
  3. K

    Transient heat transfer 2-D cylindrical

    Hi All I'm embarking on a model of a large physical system. I have a reasonable concept of the model but need advice on which simulators or programming languages to use. I've developed a (simple) explicit finite difference algorithm in excel for 'a few metres' and 'a few timesteps'. I have...
  4. H

    Calculating the Hydrostatic Force on the wall of a Cylindrical Tank

    How would I go about calculating the hydrostatic force on the walls of an upright Cylindrical Tank. To keep it simple, it is completely full of water, is 1m tall, has a diameter of 1m. Many thanks for anyone that can help.
  5. K

    What is the Critical Radius in Fluid Dynamics?

    Homework Statement http://img571.imageshack.us/i/reaction.png/ Homework Equations Velocity = (R^2-r^2) * dP/(4nL) VMax = R^2 * dP/(4nL) Average velocity = R^2 * (dP/(L*8n)) dP= change in pressure n = viscosity The Attempt at a Solution Average velocity = R^2 * (dP/(L*8n))...
  6. K

    Small hole at bottom of cylindrical tank draining water?

    Homework Statement the tank has a radius of 2m, containing an initial water level of 3m. A hole at the very bottom (underneath) of the tank has radius .005m. How long will it take to empty the tank? Homework Equations Bernoulli's principle. A=radius at top of tank a=radius of...
  7. L

    Finding the bounds of a triple integral in cylindrical coordinates?

    Homework Statement I took a picture of the problem so it would be easier to understand. All I need to know is what the bounds are. Homework Equations In cylindrical: x=rcos(theta) y=rsin(theta) z=z The Attempt at a Solution I don't know why we should change this to...
  8. B

    Thick cylindrical ring find inertia help

    Homework Statement A thick cylindrical ring of inner radius 29.0cm and thickness 2.8cm has a mass of 10.0kg. What is the moment of inertia of this cylinder about its central axis? Homework Equations I = (.5)(m)(ri^2+ro^2) The Attempt at a Solution I tried to use hollow cylinder...
  9. S

    Fluids - Conical vs Cylindrical Water Clock

    I am researching water clocks through history. At some point, it was realized that for the container the water drips from, a conical container with the hole at its point was superior to a cylindrical container with the hole in its side. Could someone explain to me why conical containers are...
  10. P

    Cylindrical Thermal Expansion Problem

    Homework Statement A cylinder is made up of three layers. The outermost (3) is concrete, the middle (2) is air, and the innermost (1) is aluminum. Three diameters are given, which measure from the outer ends of the given layer. d1 = 11.845cm d2 = 11.900cm d3 = 12.000cm \alphaAl = 2.3*10^-5...
  11. Telemachus

    Volume for a cone in cylindrical coordinates.

    Homework Statement Hi there. I haven't used iterated integrals for a while, and I'm studying some mechanics, the inertia tensor, etc. so I need to use some calculus. And I'm having some trouble with it. I was trying to find the volume of a cone, and then I've found lots of trouble with such a...
  12. C

    Resolving a unit vector from Cylindrical coordinates into Cartesian coordinates

    Homework Statement Question 3 (a)A long metal cylinder of radius a has the z-axis as its axis of symmetry.The cylinder carries a steady current of uniform current density J = Jzez. Derive an expression for the magnetic field at distance r from the axis,where r<a. By resolving the...
  13. G

    Electrostatic Potential of cylindrical surface

    Homework Statement The figure shows a section of a cylindrical surface, height h and radius R. The curved surface extends from the z-axis to the y-axis only and has a charge density given by σ(z)= σ0z where σ0is some constant. ind the electrostatic potental at a. (a is at the origin) I'm...
  14. M

    Calculating Electric Field E^pho in Cylindrical Coordinates

    How would I go about working out the Electric Field E(X) in cylindrical coordinates? The question is, Suppose pho = pho(r) find E^pho. Suggestion to use Greens & Gauss theorem
  15. fluidistic

    Differential x, cylindrical coordinates

    1. Homework Statement +attempt at solution+equations In Cartesian coordinates, x translate into x=r \cos \theta into cylindrical coordinates, y=r \sin \theta and z=z . However dx=\cos \theta dr - r \sin \theta d\theta. This is what I don't understand. Since x is a function of both...
  16. F

    Working out formula for cylindrical capacitor

    Homework Statement Find the potential of a cylindrical capacitor Radius of both cylinder plates, x and y where x<y Height of the cylinder: h Charge on the plates: qHomework Equations E = \frac{q}{A\epsilon_0} = \frac{q}{2\pi r h \epsilon_0} \Delta V = \frac{\Delta U}{q} = - \int_a^b E drThe...
  17. C

    Electric Field Strength Inside a Cylindrical Non-conductor

    Homework Statement Hey everyone, I'm just studying some physics, and came across this question where I don't know why I'm wrong =( It's from Physics (5th Ed.) by Halliday, Resnick and Krane - Chapter 27, Exercise 22 Positive charge is distributed uniformly throughout a long, nonconducting...
  18. J

    Washer vs cylindrical shell method for computing volumes

    Hello, Homework Statement My problem regards the disk|washer, and cylindrical shell methods for finding volumes in single variable calc. My problem is basically am I understanding these two methods and their relationships properly. Fundamentally, these methods are indentical, as we can...
  19. M

    Div, grad and curl in cylindrical polar coordinates

    Homework Statement Hi, i am trying to find the div, grad and curl in cylindrical polar coordinates for the scalar field \ phi = U(R+a^2/R)cos(theta) + k*theta for cylindrical polar coordinates (R,theta,z) I have attempted all three and would really appreciate it if someone could tell me...
  20. R

    Calculating Volume Levels of a Cylindrical Tank

    Homework Statement I need to create a function that will supply me with a vector that lists the heights at which markers should be placed on a tank to display the volume at that level. The tank is a cylinder on its side with 2 boxes on either end to make it free standing (image attached)...
  21. M

    Cylindrical electromagnetic cavity.

    Homework Statement A cylindrical electromagnetic cavity 4.8cm in diameter and 7.3 cm long is oscillating. a) Assume that, for points on the axis of the cavity Em=13kV/m. The frequency of oscillation is 2.4 GHz. For such axial points, what is the maximun rate (dE/dt)m, at which E...
  22. Saladsamurai

    Mathematica Mathematica: Div in Cylindrical and Shadowing

    Mathematica: Div in Cylindrical and "Shadowing" I have a vector given in cylindrical coordinates. I know that the divergence of the vector should be zero. However, I am not sure why Mathematica is not returning zero. Also, the Div operator is showing up red (Div) and it is saying something...
  23. B

    Triple Integral Limits Help. Cylindrical Coordinates

    Homework Statement Find the volume of the solid bounded by the paraboloids z=x^2+y^2 and z=36-x^2-y^2. Answer is: 324\pi \\ Homework Equations r^2=x^2+y^2 x=rcos0 y=rcos0 The Attempt at a Solution 36-x^2+y^2=x^2+y^2\\ 36=2x^2+2y^2 18=x^2+y^2 r^2=18 V=\int_{0}^{2\pi} \int_0^{3\sqrt{2}}...
  24. P

    What is the electric field at a point 4 cm from the axis of a cylindrical shell?

    Homework Statement A cylindrical shell of radius 9.9 cm and length 286 cm has its charge density uniformly distributed on its surface. The electric field intensity at a point 23 cm radially outward from its axis (measured from the midpoint of the shell ) is 44800 N/C. Given: ke = 8.99 × 10^9...
  25. S

    Dynamics - Cylindrical Coordinates

    Homework Statement A cam has a shape that is described by the function r = r_0(2 - cos \theta), where r_0 = 2.25 ft. A slotted bar is attached to the origin and rotates in the horizontal plane with a constant angular velocity (\dot{\theta} dot) of 0.85 radians/s. The bar moves a roller...
  26. C

    Cylindrical and Cartesian Coord. dot product

    Homework Statement I'm given 2 unit vectors a_x and a_theta. I need to find the dot product between the two. Homework Equations Conversion from Cylindrical to Cartesian x = r * sin(theta) y = r * cos(theta) z = z Conversion from Cartesian to Cylindrical r = sqrt(x^2 +...
  27. H

    Potential of Concentric Cylindrical Insulator

    Homework Statement An infinitely long solid insulating cylinder of radius a = 3.2 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 22 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner...
  28. T

    Area by washers and/or cylindrical shells: other than x,y

    What if you want to rotate around something other than the x/y axis? For example: Homework Statement y=x, y=0, x=1, rotated around the line x=-1 Homework Equations or The Attempt at a Solution V= ⌠(between 0 and 1)π[1+x]^2 dx = π(1/3(x)^3+x^2+2x),x=0, x=1...
  29. H

    Line Charge and Charged Cylindrical Shell

    Homework Statement An infinite line of charge with linear density λ = 8.8 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.9 cm and outer radius b = 4.1 cm. The insulating shell is uniformly charged with a volume density of ρ = -659 μC/m3. What is Ex(R), the...
  30. H

    Line Charge+ insulating Cylindrical Shell

    Homework Statement An infinite line of charge with linear density λ = 8.8 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.9 cm and outer radius b = 4.1 cm. The insulating shell is uniformly charged with a volume density of ρ = -659 μC/m3. What is λ2, the...
  31. B

    Cylindrical shells to find volume.

    Homework Statement Funky, all the surrounding exercises are quite easy, so I assume this is too... my brain's just not catching it... Use cylindrical shells to find the volume of the shape formed by rotating the following around the y-axis. The (x,y) graph before rotation: use the area...
  32. H

    Vectors in Cartesian Cylindrical Spherical

    I do not understand when we are given a vector at point P(x,y,z) or in different forms cylindrical and spherical. What does it mean at point?? I mean aren't vectors supposed to start at origin, even if they don't how will that make a difference in their magnitude or angle between them. For...
  33. S

    Pressure in a Cylindrical Tank

    Homework Statement On the afternoon of January 15, 1919, an unusually warm day in Boston, a 26.0 m high, 27.4 m diameter cylindrical metal tank used for storing molasses ruptured. Molasses flooded the streets in a 9 meter deep stream, killing pedestrians and horses and knocking down buildings...
  34. B

    How do you express the center of a circle in cylindrical coordinates?

    This is something I have zero familiarity with. Anyways, I was given the equation: r=2asin(theta)+2bcos(theta) and had to prove that it was a circle, and then state its center in cartesian and cylindrical coordinates. After making the appropriate substitutions and completing the square...
  35. O

    Strength of materials(longitudal stress in thin cylindrical shells

    In Rc Stephen's book Strength op materials, the longitudinal stress in a cylinder(see) attachment caputure.jpeg. My question is how is the area(pi X d X t ) is derived as my calculations show that this area should equate to (pi x d x t + t x t)
  36. S

    Fluid Mechanics equations in Cartesian and Cylindrical coordinates?

    Homework Statement Not really a homework question, but more of a concept question which I'm unfamiliar with. So as we know, equations can be in any coordinate, but how do you convert them from one to another? For example, a few equations from fluid mechanics. the first equation is the vector...
  37. atomqwerty

    Cylindrical and spherical coordinates

    Homework Statement Write the vector D_{p}=2\partial/ \partial x-5\partial/ \partial y+3\partial/ \partial z \in T_{p}\Re^{3} in cylindrical and spherical coordinates Homework Equations NA The Attempt at a Solution x=r cost y=r sint z=z ...
  38. S

    Surface integral in cylindrical coordinates

    Hello everybody! Although this may sound like a homework problem, I can assure you that it isn't. To prove it, I will give you the answer: 40pi. So.. I'm self-studying some electrodynamics. I'm using the third edition of Griffiths, and I have a quick question. For those who own the book and...
  39. G

    Calculate a Triple Integral using the cylindrical coordinate system

    I don't understand what's wrong with it:
  40. R

    Volume by Slicing: A cylindrical wedge, help needed please

    Homework Statement Find the volume of curved wedge that is cut from a cylinder of radius 3m by two planes. One plane perpendicular to the axis of the cylinder, the other plane crosses the first plane at a 45 degree angle at the centre of the cylinder. (Hint: let the line of intersection of the...
  41. B

    Electromagnetism: cylindrical or rectangular coordinates.

    Hi. Sorry my spelling, because I am not English. Homework Statement In a sphere truncated sector with an angle of 60 degrees, there is a uniform charge distribution, \rho. Calculate the electric field in (0,0,0). The sector starts in z=a and ends in z = b. The sphere center is in (0,0,0)...
  42. J

    Change of Variables to find the volume of a part of a sphere in CYLINDRICAL coords

    Make the indicated change of variables (do not evaluate) (Not sure how to write an iterated integral with bounds so I will try and explain by just writing the bounds) (I also tried using the symbols provided, but everything I tried just put a theta in here so I gave up) \int\int\intxyz...
  43. C

    Use cylindrical coordinates to find volume

    Homework Statement Use cylindrical coordinates to find volume... Homework EquationsInside: x2+y2+z2=16 Outside: z=sqrt(x2+y2) The Attempt at a Solution Cylindrical coordinates have always been a problem for me, so I initially tried to put them into spherical and then convert them over, but...
  44. S

    Spherical and cylindrical coordinates, not a problem

    Homework Statement do we only use spherical and cylindrical coordinates for triple integrals? or for double too? thanks for your replies in advance
  45. M

    Radial component of a velocity vector - cylindrical coordinates

    Hi there, I'm trying to determine the radial component of a velocity vector in a disk. The vector doesn't (necessarily) start from the centre of the disk and can be pointed in any direction. I've attached a .pdf with the schematics - it seems like a simple problem but it has me stumped...
  46. G

    Ampere's Law with an open cylindrical shell

    Homework Statement A long, hollow conducting pipe of radius R and length L carries a uniform current I flowing around the pipe. Find expressions for the magnetic field (a) inside and (b) outside the pipe. Hint: What configuration does this pipe resemble? Homework Equations Ampere's Law...
  47. B

    Calculate optical path in SELFOC cylindrical fiber optic

    Hi. This is my first message in this forum. I'm not English, so sorry my spelling. Homework Statement Calculate the optical path done by a meridional ray, supposing it covers a horizontal distance, d, in z-axis direction. \gamma_0 is the launch angle (with z-axis).Homework Equations Optical...
  48. T

    Flux through cylindrical wedge

    Homework Statement Given \textbf{F} = x\textbf{i} + y\textbf{j} + z\textbf{k}, what is the flux of \textbf{F} through the cylinder x^2 + y^2 =1 bounded by the planes z=0, x+y+z=2. The Attempt at a Solution By Gauss' Theorem, \int\int_{S}\textbf{F}\cdot d\textbf{S} =...
  49. C

    Finding the Potential Between Two Coaxial Cylinders Using Laplace's Equation

    Homework Statement Two coaxial cylinders, radii {a,b} where b>a. Find the potential between the two cylinder surfaces. Boundary conditions: V(a,\phi) = 2 \cos \phi V(b,\phi) = 12 \sin \phiHomework Equations Solution by separation of variables: V(r,\phi) = a_0 + b_0 \ln s + \sum_k \left[...
  50. T

    Integration and cylindrical and spherical coordinates

    Homework Statement I have three problems and I could really use some help. 1. Integrate the function f(x,y,z) = y over the part of the elliptic cylinder x^2/4 +y^2/9 = 1 that is contained in the sphere of radius 4 centered at the origin and such that x≥0, y≥ 0, z≥0. 2. Find the total...
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