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. V

    Magnetic Field and infinite cylindrical shell

    Homework Statement An infinite cylindrical shell has inner radius 'a' and outer radius 'b'. The shell carries a charge density J(s) = Cs^2 + Ds. Where 'C' and 'D' are constants. Find B everywhere. Homework Equations The Attempt at a Solution My thought was to find the field do...
  2. P

    What is the optimal radius for the inner cylinder of a cylindrical capacitor?

    A capacitor consists of two thin infinite concentric cylinderss with inner and outer radii a and b. If the outer cylinder has radius 10mm and the breakdown electric field of air is 3V per micrometre, what radius should be choosen for the inner cylinder in order to maximum the potential diffence...
  3. T

    Need help, can someone explain cylindrical shell method for volume?

    im stuck and my book doesn't explain much on how to get the volume of a shape by the cylindrical shell method. What i really need is to show how to get the general formula of a volume of a sphere and a cone using cylindrical shells.
  4. T

    Current Inside long cylindrical Conductor

    Hi guys, I was wondering if someone could help explain something to me. I am just starting out learning about Ampere's law. I am looking at this example in the book and I don't get it. They have a cylindrical conductor with Radius R and current I. The current is uniformly distributed over the...
  5. D

    What is the tension in the cylindrical wire?

    A cylindrical wire is placed over a frictionless pulley with one end of a wire connected to a 5.8 kg mass and the other to a 1.5 kg mass. If g=9.8 m/s/s, what is the tension in the wire? I have no idea how to start on this.
  6. J

    Vector question: dot product in cylindrical coordinates

    Hello. To find the work of a force, I have to perform a dot product between the force and a infinitesimal displacement. If they are in cylindrical coordinates, I can't manage to make the dot product. Please, could you help me? Thank you.
  7. B

    Can a Cylindrical Thermistor be Used to Build a Fuel Flow Meter?

    I need Cylindrical Thermistor to build a fuel flow meter. Need suggestions... Thanks
  8. R

    How to Graph r=2cos(theta) in Cylindrical Coordinates?

    I'm having some trouble understanding exactly how to graph this problem using cylindrical coordinates. The coordinates they give me is r=2cos(theta) How do I go about beginning to determine how to graph this with only the radius?
  9. F

    Spherical, Cylindrical Coordinates - quick easy questions

    EDIT: I figured it out. I'm sick, tired, and just confusing myself. I have a test in a few hours, and would like to clear some easy stuff up so I'm not thinking about it during the test. 1) Vector subtraction works in spherical and cylindrical coordinates right? That is to say, \vec {AB} ...
  10. N

    Calculate Volume of Cylindrical Shells

    Use cylindrical shells to calculate the volume of the solid obtained by rotating the region bounded by y=x and y=x^2-2x about the line y=3 I know how do set the problem up and how to do it, I just don't know how to write "y=x^2-2x" in terms of "x". This is how I think the problem should be set...
  11. mbrmbrg

    Volume of Solid Revolving Around X Axis: Cylindrical Shell Method

    Use the method of cylindrical shells to find the volume of the solid generated by revolving aabout the indicated axis the region bounded by the given curves. x=y, x+2y=3, y=0; about the x axis. Latest version of my work: (I don't know how to paste a graph into the post. But I graphed my...
  12. J

    Volume of water flowing out a cylindrical pipe

    Water is flowing down a cylindrical pipe of radius r. (a) Write a formula for the volume, V, of water that emerges from the end of the pipe in one second if the water is flowing at a rate of (i) 3 cm/sec (ii) k cm/sec (b) Graph your answer to part (a)(ii) as a...
  13. S

    How Can I Solve a Volume Problem Using the Cylindrical Shell Method?

    Please help! How do I do this problem? Using the method of cylindrical shells, find the volume generated by rotating the region the region bounded by the given curves about the specified axis. y=(x-1)^(1/2), y=0, x=5; about y = 3 Please tell me how to set up the integral! Any help is...
  14. S

    Calculate Cylindrical Shell Volume: y=x^2, y=0, x=1, x=2

    find volume: y=x^2, y=0, x=1, x=2 about x=1 I found the height to be x^2 and circumference to be 2pi(1-x) So V= \int_1^2 2\pi(1-x)(x^2)dx This is not giving me the right answer.
  15. P

    Optimisation of a cylindrical container

    Hey I am given the set volume for a cylindrical container and separating pricing for the material used to construct the container, the base and the side wall. The ends of the container cost $0.05 per cm2 and the side walls $0.04 cm2, and the volume is 400 mL. The question asks: What is the best...
  16. S

    Conversion from Cartesian to Cylindrical Coordinates

    Hello. I am interested in learning the mathematical derivation from Cartesian coordinates Navier-Stokes equation to cylindrical coordinates Navier-Stokes equation. These equations have similar forms to the basic heat and mass transfer differential governing equations. I’ve tried looking...
  17. Amith2006

    Field of view of cylindrical mirrors

    Sir, A driving mirror consists of a cylindrical mirror of radius 10 cm and the length over the curved surface is 10 cm. If the of the driver be assumed to be at a great distance from the mirror, what is the field of view of the mirror in radian? I don’t have any idea about cylindrical...
  18. M

    Calculating Mass of Oil in Cylindrical Core

    Hi everybody, didn't really know where to put this thread since it's physics using math, so I'm sorry if it's not in its appropriate place. My problem is: I need to compute the mass of oil in a cylindrical core put into a core holder.it's partially filled of oil. I didn't know how to...
  19. M

    Integral and cylindrical shell

    Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y = x^2 y = 4 x = 0 0 <= x <= 2 So I drew these: http://img131.imageshack.us/img131/9225/math28qi.th.jpg...
  20. M

    Fine tuning a cylindrical Capacitor

    I would like to know about fine tuning of an airplane Fuel Gauging probe. It is basically a cylindrical capacitor made of an inner composite tube of about 0.5 inch diameter and an outer composite tube of about 1 inch diameter. The length of the tubes varies from about 3 inches to 8 inches. The...
  21. F

    Cylindrical Coordinates -Div/Curl/Grad

    We just started a section dealing with div/curl/grad in different orthogonal systems... before I get started doing problems involving these operations I wanted to make sure I am dealing with these operation correctly. Our first homework problem is as follows: In cylindrical coordinates compute...
  22. I

    Rectangular to cylindrical conversion

    Hi =) I was given this problem on a test: a vector A = 2yi - Zj +3xk, was given in rectangular (cartesian) coordinates and I had to convert it to cylindrical coords. What I did to solve it was this: 1) A = 2rsin(theta)i - zj + 3rcos(theta)k 2) partial derivatives a) d/dr =...
  23. M

    Magnetic flux outside cylindrical conductor

    Hey everyone, I have failed to show that the magnetic flux outside a cylindrical conductor is zero. The problem goes like this: a coaxial cable consists of a solid inner cylindrical conductor of radius a and an outer cylindrical conductor of inner and outer radius b and c. Distributed...
  24. B

    Cone Edges in Cylindrical Coordinates

    Hi , I don't know how to get the edge of the cone in cylindrical coordinates. For example, we have a cone starting at the origin, of heigth 2 and the top is a circle of radius 1 (center at the origin). the edge of the cone is z=2r. but I don't know how they find it. Please can someone...
  25. I

    Parabolic cylindrical coordinates

    Can someone, please, show me an example of when you are better of with parabolic cylindrical coordinates than with cartesian coordinates when computing a triple integral over a solid?
  26. T

    Optimization cylindrical can Problem

    Prove that any cylindrical can of volume K cubic units that is to be made using a minimum of material must have the height equal to the diameter.
  27. M

    Magnetic Field at Radial Distance of 1.15 cm from Cylindrical Conductor

    Figure 29-62 shows a cross section across a diameter of a long cylindrical conductor of radius a = 2.00 cm carrying uniform current 154 A. What is the magnitude of the current's magnetic field at the following radial distances? http://www.webassign.net/hrw/hrw7_29-62.gif I figured out parts...
  28. quasar987

    Proving Laplacian in Cylindrical Coordinates

    I'm supposed to prove the laplacian in cylindrical coord. is what it is. I tried tackling the problem in two ways and none work! I have no idea what's the matter. The first way is to calculate d²f/dr² , d²f/dO² and d²f/dz² and isolate d²f/dx² , d²f/dy² and d²f/dz². In cylindrical coord...
  29. T

    Rotation of cylindrical habitat in space?

    I have this question on this article by G.K. O'Neill,1974. who proposed having a cylindrical habitat in space. Then the article posed a question asking me to ponder on the speed of the rotation of the cylinder such that it wld imitate Earth's gravitational field at the walls of the cylinder...
  30. T

    Rotation of cylindrical habitat in space

    I have this question on this article by G.K. O'Neill,1974. who proposed having a cylindrical habitat in space. Then the article posed a question asking me to ponder on the speed of the rotation of the cylinder such that it wld imitate Earth's gravitational field at the walls of the cylinder...
  31. A

    Solving an Exercise Involving a Cylindrical Tube of Air

    Hi to you all.i have an exercise i cannot solve.i think something is missing. Cylindrical tube V=10L opened at the top has air with a temperature of T1=27 oC.We provide heat to the tube until the temperature reaches the value of T2=327 oC.A)we have to find the amount of air that leaves from...
  32. W

    Cylindrical and Spherical Coordinate systems

    I have a question about the equation mechanics of cylindrical and spherical coordinate systems This is basically about the velocity and acceleration equations of both Let me just give an example from cylindrical \vec v = \dot r\hat e_r + r\dot\theta\hat e_\theta + \dot z\hat k and...
  33. D

    Heat Transfer Problem in Cylindrical

    I don't understand this problem. I think it is difficult for me. Please anyone suggestion this problem to me. Thanf you Let us cosider steady state heat transfer problem in which laplaceT(r)=0 What is the temparature at the center of a thin disc of radius a whose average boundary...
  34. M

    Finding mag E of 2 thin-walled concentric cylindrical shells

    Two long, charged, thin-walled, concentric cylindrical shells have radii of 3.0 and 6.0cm. The charge per unit length is 5.0x10^-6 C/m on the inner shell and -7.0x10^-6 C/m on the outer shell. What are the magnitude E and direction radially inward or outward? I figured I could use the...
  35. B

    Calculate Volume with Cylindrical Shells: y=x^2-3 & y=2x

    Hi I'm stuck on an integration problem where I need to use the method of cylindrical shells to calculate a volume. Q. Using the method of cylindrical shells, find the volume generated when the area bounded by the curve y = x^2 - 3 and the line y = 2x is revolved about the line x = 7. The...
  36. M

    Capacitance Variations in Cylindrical Capacitors

    The capacitance measurements of “Fuel Gauging Tubes” (FGT) that are composed of carbon composite inner and outer tubes shows unacceptable level of variations and I need to reduce the variation of capacitance. I would like to know what are the contributing factors to capacitance variations...
  37. R

    Solving a Cylindrical Brick Chimney Toppling Problem

    I'm having trouble with solving this problem: Suppose we have a cylindrical brick chimney with height L. It starts to topple over, rotating rigidly about its base until it breaks. Show that it is most likely to break a distance L/3 from the base because the torque is too great. So I'm...
  38. R

    Cylindrical interior (first ark) starship to Alpha Centauri - by A. Ahad

    This gigantic thing here called the Centauri Princess, can it be built in the next few hundred years? http://www.astroscience.org/abdul-ahad/firstarktoalphacentauri.htm That would be the greatest engineering achievement in all human history...
  39. K

    Why Does the Cylindrical Shells Method Give a Different Volume for a Torus?

    I know one can figure the volume of a torus by the difference of two volumes, but I'm trying out the method of cylinderical shells. As far as i understand, you can often create a primitive with a calcuable volume and approximate the volume of the shape you wish by scaling the primitive along the...
  40. S

    Gradient in cylindrical coordinates

    How can you derive the gradient of a vector R^3 to R in cylindrical coordinates?
  41. T

    Help Solving a Problem with Cylindrical Wires: Magnetic Force Calculation

    Could anyone please help me with the following problem? A compact package contains n = 100 long straight wires, shaped like a cylinder with a radius of R = 0.500 cm. If each wire conducts i = 2.00 A, calculate the intensity and direction of the magnetic force per unit of length acting on a...
  42. S

    Question on Divergence in Cylindrical Coords

    Hey, I have a question on a derivation The following is in my textbook (V = vector): \nabla \cdot V = \frac {1}{r} \frac {\partial{(rV_{r}})}{\partial{r}} + \frac {1}{r} \frac {\partial{V_{\theta}}}{\partial{\theta}} + \frac {\partial{V_{z}}}{\partial{z}} where: \nabla = \hat {r}...
  43. H

    Use the cylindrical coordinates to find the volume

    I'm having trouble figuring out this volume. Use the cylindrical coordinates to find the volume of the solid S bounded by z=x^2 + y^2 and z=12 - 2x^2 - 2y^2 I've included a pic of what I think the regions and the solid look like...
  44. D

    Fluid dynamics - dissipation using cylindrical coordinates

    I have this flow field in cylindrical coordinates of which I would like to calculate the dissipation as a function of these coordinates. Now in my fluid dynamics notes I found the following expression(s) for the dissipation: 2 \mu (e_{ij} -\frac{1}{3} \Delta \delta _{ij} )^2 = 2 \mu (...
  45. N

    Cylindrical polar co-ordinates

    My notes have an example of verifying the divergence theorem using cylindrical polars. There's a vector field, A(r) = x(x-hat) + y(y-hat) + z^2(z-hat) and my notes say: "Note that rho-hat = cos phi(x-hat) + sin phi(y-hat) and phi-hat = -sin phi(x-hat) + cos phi(y-hat) and so A(r) =...
  46. V

    Setting up a triple integral in cylindrical coordinates?

    The problem says to find the volume of material cut from the solid sphere, r^2 + z^2 \le 9 by the cylinder, r = 3\sin\theta I don't know how to graph the first equation, but I can do the second in polar coordinates. How do I go about converting to use cylindrical coordinates?
  47. A

    Calculating Total Current in Cylindrical Wire at 60 Hz

    I have a thick cylindrical wire that I make it 10 smaller pieces and the area remains constant. How do I find the toatal current at 60 Hz? given sigma, miou, and radious I also need to find the total current for a given maximum current density that was given for the thick wire for AC. How to...
  48. A

    What is the Electric Field of a Cylindrical Capacitor?

    For some reason, I am having a lot of difficulty finding the electric field between two co-axial cylinders. In fact, I pretty much know that it should be: \frac{Q}{2\pi \epsilon _0 Lr} Where Q and -Q are the charges on the two cylinders, L is the length of the cylinders, and r is the...
  49. V

    Understanding the Chain Rule in Cylindrical Coordinates

    I find this passage \frac{\partial}{\partial x} = \cos(\phi)\frac{\partial}{\partial \rho } - \frac{\sin(\phi)}{\rho}\frac{\partial}{\partial \phi} difficult to understand. My teacher wrote this as an explanation: \frac{\partial V}{\partial x} = \frac{\partial\rho}{\partial...
  50. H

    Cylindrical and spherical coordinates

    How do I get the bounds for a function w/out drawing a graph?? Like, Volume of the solid bounded above by the sphere r^2+z^2=5 and below by the paraboloid r^2=4z. How would I get the bounds for these in cylindrical coordinate (r dz dr dtheta)? ***Mass of the solid inside the sphere p=b and...
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