What is Cylinders: Definition and 272 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. J

    Stress Analysis - compound cylinders

    Homework Statement problem attached Homework Equations attached but lame equations i think they are? The Attempt at a Solution attached Hey this is an assignment question that i have wasted countless hours on trying to solve without success. The problem is WBVMMECH025 from the...
  2. G

    Understanding Poisson's Ratio and Restrained Cylinders

    Hey. I have a couple of questions about Poisson's ratio I hope you guys can answer. If I have a cylinder made of, let's say steel. Steel has a Poisson's ratio of roughly 0.33. The cylinder is restrained in the vertical direction so no displacement can occur. If I apply an internal pressure...
  3. M

    Double Integrals Bounded by Cylinders

    Homework Statement Bounded by the cylinders x2 + y2 = r2 and y2 + z2 = r2 We're supposed to stick to double integrals as triple integrals are taught in a later section. The Attempt at a Solution Edit: Alright, I think I go to the right answer. x = sqrt(r2 - y2) z = sqrt(r[SUP2[/SUP] - y2)...
  4. V

    Capacitance of infinite cylinders

    Homework Statement I have two coaxial infinite cylinders and I must find their capacitance, where r_{1} < r_{2} Homework Equations The Attempt at a Solution I got an answer (for finite cylinders) that is inversely proportional to Ln (r_{1}/r_{2}). Assuming this answer is correct (if someone...
  5. N

    What is Gauss's Law for a Concentric Cable?

    Homework Statement The figure below shows a portion of an infinitely long, concentric cable in cross section. The inner conductor has a linear charge density of λ = 6.10 nC/m and the outer conductor has no net charge. http://www.webassign.net/tipler/23-36alt.gif (a) Find the electric field...
  6. Z

    What Happens When Combining Mass and Incline in Cylinders?

    hi my question is fully attached as an image. for cylinders with the same mass i know how to sort them. the smaller the i the faster it will go. but what happens if i have combination of change of i and m. i guess i will need a less intuitive approach. can some one tell me how to do this...
  7. G

    Do heavy and light cylinders roll the same?

    I understand why a heavy item and a light item both fall a given distance in the same time - in a vacuum, etc. What happens in the case of a cylinder rolling down an inclined plane with no slippage? Would a heavy cylinder reach the bottom at the same time as would a light cylinder? What if...
  8. B

    Stress in thick walled cylinders

    Hi guys, I found some experimental data on a website the other day and i have been trying to do some calculations. Im getting suck up on the rearrangement(never been my strong point) and its driving me bonkers! Any help at all would be appricated. need to have er as the subject...
  9. R

    Surface area enclosed by Cylinders

    I want to know how Surface areas enclosed by Cylinders , Cones..etc can be calculated using calculus integration...
  10. D

    [Check for errors]- FREE BODY DIAGRAM for 2 Cylinders.

    Ok as you seen I been trying to get familiar with a few different type of exercises, this is a FBD type exercise. I attached the picture showing the exercise done, I just want you to check if you notice any errors, thanks you. Homework Statement Cylinder A- Mass 75kg and...
  11. K

    Longitudinally locked rotating cylinders

    I need to make two close fitting cylinders that are longitudinally locked in position but need to rotate against each other. I want to make this in as few parts as possible. I was thinking of machining grooves in each cylinder and placing the Teflon ring in the groove of the inner cylinder...
  12. T

    Thick Cylinders: Internal & External Pressures, Hoop & Radial Stresses

    Homework Statement A thick cylinder of 100mm internal radius and 150mm external radius is subjected to an internal pressure of 60MN/m^2 and an external pressure of 30MN/m^2. Determine the hoop and radial stresses at the inside and outside of the cylinder together with the longitudinal stress...
  13. fluidistic

    Solving Electric Field & Potential for Charged Cylinders

    Homework Statement 2 long cylinders with radius a and b (a<b) have a charge density by unit of length worth - \lambda and \lambda respectively. Use Gauss's law to find the electric field in every point of the space. Find the potential in all points of the space, assuming that the potential...
  14. P

    Lab question regarding cylinders

    hi im trying to do a lab on rotational inertia of a hollow cylinder i plan to roll a hollow cylinder down an incline and see how the inner radius, outer radius, and mass affects the final translational velocity but i am not sure what i can use for the cylinder to sufficiently control and...
  15. D

    IEC 60529 Definition of "Finger Safe" for Cylinders

    "Finger Safe" I'm searching for a precise definition of "Finger Safe" according to IEC 60529 which defines IP2X as "finger safe" for diameters > 12.5mm. Does thes mean a cylinder of > 12.5mm dia. an not touch the contact? Or is there a radius on the end of the cylinder? How long is the...
  16. D

    Resonant Frequencies of Coaxial Cylinders

    Does anyone know of a formula for determining the various resonant frequencies of 2 coaxial cylinders with radius a and b and height h? Thanks.
  17. P

    Rolling Cylinders: Find Final Velocity & Height

    Homework Statement A thin cylindrical shell and a solid cylinder have the same mass and radius. The two are released side by side and roll down, without slipping, from the top of an inclined plane that is 1 m above the ground. The acceleration of gravity is 9.8 m/s2. Find the final linear...
  18. B

    How to plot 3D cylinder shapes in Mathematica?

    hey How can i do that? Can anyone of you help me?greets button MATHEMATICA
  19. C

    Volume of the intersection of two cylinders by polar co-ordinates

    Volume of the intersection of two cylinders by cylinderical co-ordinates Homework Statement find Volume of the intersection of two cylinders by cylindrical co-ordinates The Attempt at a Solution IN the attached file I found it's 8(a^3)/3 It should be 16 not 8
  20. D

    Volume of 3 intersecting Cylinders

    Homework Statement I am trying to find the volume of three intersecting cylinders that intersect at right angles given that the radius is 5. I have found many sites that state just the answer, but I am after the proof for it showing all of the working. I know how to prove the rule for 2...
  21. C

    Length of Wire Around Circle of Cylinders.

    Alright guys, wouldn't have wanted this to be my first post, but here it goes; I'm trying to find out the length of a loop which is enclosing 'n' number of cylinders. I've found the length of the loop touching the cylinders, and now need to find the rest of the length of the loop (which is...
  22. S

    Gauss's Law 2 concentric cylinders in electrostatic equilibrium

    Homework Statement Consider the cross sections of two, very long, concentric, metallic, hollow cylinders placed in a vacuum. The small cylinder has inner radius A and outer radius B while the larger cylinder has inner radius 2A and outer radius 2B. Initially the small and big hollow...
  23. T

    Fluids at rest: two connected cylinders

    Homework Statement [This probably seems really easy to the physics whizzes out there but...*blushes*] Two identical cylindrical vessels with their bases at the same level each contain a liquid of density 1.30x103 kg/m3. The area of each base is 4.00cm2, but in one vessel the liquid height is...
  24. fluidistic

    Cylinders (or pulley) cord-motion

    Homework Statement Hi PF, See figure for a clear view of the situation. (There's a cylinder attached to a ceiling so that it cannot move. There's a cord on it and the cord goes down until another cylinder is attached to it. So that the only cylinder that can move is the one at the bottom...
  25. R

    Three Cylinders (rotational kinematics)

    Three identical, solid, uniform density cylinders, each of mass 16 kg and radius 1 m, are mounted on frictionless axles that are attached to brackets of negligible mass. A string connects the brackets of cylinders #1 and #3 and passes without slipping over cylinder #2, whose bracket is attached...
  26. B

    Concentric cylinders E field

    Hello: Can someone help? I have 2 concentric cylinders which are both conductors. The inner conductor has linear charge density of 6 n C/m. The outer conductor has no net charge. The inner conductor has R of 0.015m, the distance between the inner conductor and the inner wall of the...
  27. L

    Angular momentum with cylinders rolling

    Homework Statement A think cylindrical shell and a solid cylinder have the same mass and radius. The two are released side by side and roll down, w/o slipping, from the top of an inclined plane that is 4.9m above the ground. When the first object reaches the bottom, what is the height above...
  28. C

    Cylinders and Quadric Surfaces

    Homework Statement Consider the equation below. x^2 = 3y^2 + 5z^2 Reduce the equation to one of the standard forms. I believe its surface is a cone, but I'm not sure how to get it into the form z^2/c^2 = x^2/a^2 + y^2/b^2 thanks!
  29. M

    Solving Tricky Math Problems: Cylinders, Curves and Scooters

    I'm really having trouble with these three problems. I'd post my attempts but most of it is in graph from. 3. David subjects a cylindrical can to a certain transformation. During this transformation the radius and height vary continuously with time. The radius is increasing at 4 in/min...
  30. J

    Surface of a sphere intersecting two cylinders

    Homework Statement Find the surface area of the surface x^2 + y^2 + z^2 = a^2 , that is outside the two cylinders x^2+y^2=\pm ax. (a>0) Homework Equations ds= \sqrt{1+(Z_x')^2+(Z_y')^2}dxdy The Attempt at a Solution The intersections are clearly four ellipses. I will try to...
  31. E

    Circle of Cylinders: Finding Length & Area

    I have an EPW that I don't quite know how to get started. Below is the EPW question and then after that is what I am stuck with. There are n identical cylinders glued upright to a board. Each cylinder has a radius of r and that centers of their bases lie on a large cirlce of radius R They...
  32. E

    Circle of Cylinders: Find Length, Area & Formulae

    I have an EPW that I don't quite know how to get started. Below is the EPW question and then after that is what I am stuck with. There are n identical cylinders glued upright to a board. Each cylinder has a radius of r and that centers of their bases lie on a large cirlce of radius R They...
  33. P

    Resonant frequincy of capped cylinders

    I'm looking for a formula to calculate the resonant frequency of a capped cylinder. I have found a link to a formula but was surprised to see that cylinder radius is not taken into account when making the calculation. It was my understanding that the larger the radius of a cylinder the lower...
  34. R

    Mathematica Graphing cylinders in Mathematica

    Below is some code that creates a semi-transparent cylinder. firstcylinder = ParametricPlot3D[{Cos[t], u, Sin[t]}, {t, 0, 2 Pi}, {u, -2, 2} , PlotStyle -> {Red, Opacity -> .3}, Mesh -> None]; Show[firstcylinder] Draw a second cylinder that is perpendicular to the given cylinder. Draw a...
  35. D

    Find the velocity of a block + 2 cylinders acted on by a force for 2meteres

    Homework Statement A 50 kg block is transported a short distance by using two cylindrical rollers, each having a mass of 17.5 kg. If a horizontal force P=125N is applied to the block, determine the block's speed after it has been displaced 2m to the left. Originally the block is at rest. No...
  36. A

    Residual stresses in thick walled cylinders (autofrettage)]

    Homework Statement 1. from a design engineers point of view identify consisely the relative meris of the emperical TRESCA and VON MISES approaches as applied to open ended thick walled cylinders. Hence specify with reasons what you believe to be the most appropriate approach...
  37. S

    Calculating the Intersection of Two Cylinders at Right Angle

    Homework Statement Consider two quarters of a cylinder of radius R. What is the volume of a the intersection of a two quarters of two cylinders if the quarters meet at a right angle? Two sides of the bounded region will be rectangular according to this arrangement. (see the diagram when it...
  38. A

    Calculating Surfaces of Intersecting Cylinders

    1. Homework Statement Find the surface area of the region common to the intersecting cylinders x^2 + y^2 = 1 and x^2 + z^2 = 1. 2. Homework Equations 3. The Attempt at a Solution I know that the answer is 16 but why? How can we parametrize this surfaces? The...
  39. S

    Static problem with three cylinders

    Homework Statement Static problem Three identical cylinders of mass m are arranged in a triangle as shown: http://img440.imageshack.us/img440/2040/cylindersjo4.jpg The friction coefficient between cylinders is "u1" and between cylinders and ground "u2". What condition must satisfy...
  40. L

    Contact between skewed cylinders

    Hi, when two cylinders in contact, but not parallet to each other (skewed), are rotating, there is a development of forces between them which tends to push one cylinder along its rotation axis and the another one to the opposite side. In other words, there will be translation movement between...
  41. L

    Exploring the Effects of Skewed Cylinders in Rotary Kilns

    Hi, when two cylinders in contact, but not parallet to each other (skewed), are rotating, there is a development of forces between them which tends to push one cylinder along its rotation axis and the another one to the opposite side. In other words, there will be translation movement between...
  42. S

    Friction between two rotating cylinders

    I have two hollow cylinders of different sizes. The smaller cylinder is inside the larger cylinder but NOT concentrically. The OD of the smaller cylinder contacts the ID of the larger cylinder at the 6 o'clock position. Both cylinders rotate but in opposite directions. An actuator pushes the...
  43. Y

    Volume of Triangle Rotated Around Its Base: Shells & Cylinders

    I'm having trouble on this problem - Find the volume of the object created by rotating an equilateral triangle around its base. Solve using both shells and cylinders. Any help would be appreciated :)
  44. F

    What Determines the Order of Arrival of Cylindrical Masses on an Incline?

    Homework Statement The five masses below all have the same radius and a cylindrically symmetric mass distribution. They start to roll down an inclined plane, starting from rest, at the same time and from the same height. Give theri order of arrival at the bottom (i.e., ABCDE, DCBAE) A...
  45. M

    Volume and Pressure Cylinders

    Homework Statement Problem comes straight from a 2001 AP Physics B test http://img151.imageshack.us/img151/6159/physicscylinderszq4.png Homework Equations PV = nRT KE = 3/2KT deltaU = Q+W The Attempt at a Solution Okay, for the first two (a and b) I arrived at an answer...
  46. B

    Calculating Forces on Cylinders on Inclines

    Homework Statement This is a sample exam problem. We have an exam coming up, and I think I better know how to do this problem(the right and quick way). I'm just copying and pasting the problem. 2. Two identical metal cylinders are stacked as shown in Figure 2. The weight of each...
  47. B

    What is the force exerted on cylinder A in a V-shaped trough?

    Homework Statement Ok, my problem has 3 smooth homogeneous cylinders(A,B,C), which are stacked in a V shaped trough.(the cylinders...look more like circles) are also all touching each other and each is touching a surface of the trough. The trough angles are Left = 30 deg and right = 45 deg...
  48. S

    Friction of spheres & cylinders

    Hi, I am doing a project involving spherical wheels. I need some help with regards to the role played by friction on motion of spheres and cylinders (normal car wheels) on roads. Will friction act forward or backwards ?? Which type of wheel would be more advantageous ? Would appreciate any...
  49. R

    Pressure of stagnant fluid volume in rotating cylinders

    I have a high speed rotating shaft (~30,000 rpm). Outside the shaft I have a relatively stagnant volume of fluid surrounded by a non-rotating cylinder (housing). I am looking to find a 'simple' laminar flow model to describe the pressure of the fluid fat any point radially from the OD of the...
  50. B

    How do I find the volume between intersecting cylinders using triple integrals?

    Hi, I'm having trouble with the following question. Q. Use triple integrals and cartesian coordinates to find the volume common to the intersecting cylinders x^2 + y^2 = a^2 and x^2 + z^2 = a^2. This question pops up in basically every introductory calculus text. I've seen it before but I...
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