What is Cylinder: Definition and 1000 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. G

    Finding surface charge densities and potential (metal cylinder)

    Homework Statement A solid metal cylinder of radius ##R## and length ##L##, carrying a charge ##Q##, is surrounded by a thick coaxial metal shell of inner radius ##a## and outer radius ##b##. The shell carries no net charge. a) Find the surface charge desnities ##\sigma## at ##R##, at ##a##...
  2. PetePetePete

    Stress and Strain Coursework Question

    I am struggling with a question in my coursework, and would appreciate some guidance. The question is: The component shown in Fig 1 is made from a material with the following properties and is subjected to a compressive force of 5kN. Material Properties : Young’s Modulus of Elasticity – 200...
  3. T

    Qualitative: A Uniformly Charged Cylinder

    Homework Statement This is just a qualitative question that is along side my main lecture with Griffiths EM book. Basically we have a very long cylinder with charge density sigma and radius a along the z axis. This is mostly beside the point and is just to setup the question. The question...
  4. B

    What is the height of liquid in a horizontal cylinder with 1/3 volume filled?

    Good day all, someone gave me this problem to try to figure out (for fun) and I'm having a bit of a hard time: A closed cylinder of radius R and length L is filled with liquid. The volume of the liquid is equal to 1/3 the total volume of the cylinder. If the cylinder is layed flat (horizontal...
  5. L

    Solving for Acceleration of Mass on Cylinder w/ Frictionless String

    Homework Statement [/B] A solid cylinder of mass m and radius r lies flat on frictionless horizontal table, with a massless string running halfway around it, as shown in Fig. 8.50. A mass also of mass m is attached to one end of the string, and you pull on the other end with a force T. The...
  6. T

    Get Help Solving a Cylinder in Equilibrium Problem

    Homework Statement Homework EquationsThe Attempt at a Solution Since the cylinder is in equilibrium ,net force and torque on it should be zero. I am not sure whether we are required to calculate force due to the two fluids as it seems to be a simple conceptual problem . I think I am...
  7. J

    When does the plate of glass loosen from a glass cylinder in water?

    Homework Statement A thin glass plate is pressed at the end of a glass cylinder. The glass cylinder with the glass plate at the bottom is dipped in water so that the plate is 25 cm under the water surface (The glass cylinder i open, meaning only the bottom part is closed, due to the glass...
  8. 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?
  9. E

    Total moment of shear stress about the center line of a cylinder

    http://postimg.org/image/onxjqc26l/ I have found the shear stress of the inner cylinder to be 405 Pa like in the solution but I am having trouble visualizing the total moment of this stress about the center line. I was wondering if someone could explain where that d(theta) in the moment...
  10. P

    Parameterising a cylinder and determining the flux.

    Hi, I am wondering how i could parameterise the following rectangular cross section of the hollow cylinder in cylindrical co-ordinates. If this surface is better parameterised via a different co-ordinate system then by all means use that system. After I have completed the parameterisation i...
  11. W

    Electric Fields: Thin wire in conducting cylinder

    Hello PF, I am having a bit of difficulty understanding this question. Homework Statement "A thin wire with linear charge density λ is surrounded by a conducting cylindrical shell." (There is a hollow cylinder with a wire though it) "If the electric field must be zero inside a conductor, is...
  12. I

    Experiment on piston cylinder, issues with Ideal gas law

    Hello everyone, I have an rather large piston-cylinder containing gas that is compressed when the piston extends. Using three sensors I am measuring the pressure, temperature and volume of the gas while I force the piston out using a winch. The system is closed and no gas is released or added...
  13. Y

    Thermodynamics of heating water in a cylinder with piston

    Homework Statement Consider water contained in a cylinder at 25C with a frictionless piston with some weights on it. Initially the pressure inside the piston is 100kPa and then the water is heated such that the water does 290kJ/kg of work on the piston. Find the final temperature of the...
  14. E

    Finding Charge p.u.l. Along Infinitely Long Cylinder

    Homework Statement An infinitely long cylinder of radius a in free space is charged with a volume charge density ρ(r) = ρ0*(a-r)/a (0 ≤ r ≤ a), where ρ0 is a constant and r the radial distance from the cylindrical axis. Find the charge per unit length of the cylinder. Homework Equations...
  15. O

    Potential at all points due to uniformly charged infinite cylinder

    Homework Statement Infinitely long cylinder of radius R with uniform charge ρ. Calculate the electric potential at all points in space. Homework Equations V(a)-V(b)=-∫ba\vec{E}(\vec{r}')°dr'\hat{r} The Attempt at a Solution Generally potential is calculated with a reference...
  16. P

    Gas Expansion in insulated cylinder (piston & Diaphragm)

    I attached an image of two expansion cases I am analyzing. Both cases involve an insulated cylinder that is divided by a separating element (diaphragm for case A and piston for B). The portion on the right is evacuated. The left contains a calorically perfect gas with an initial pressure and...
  17. davidbenari

    Finding the linear density of charge on a cylinder

    Homework Statement A rod with charge linear density λ is located at the long axis of a cylinder with charge linear density 2λ. With this information use Gauss's law to find (a) the charge linear density on the interior and exterior surfaces of the cylinder (b) the electric field outside of the...
  18. Z

    Investigation of a Rotating Cylinder

    Hello all, I have some confusion about rotating. The bad thing is that I don't know where the point is which my confusion starts. As I want to check also my fundamental knowledge about the topic I will ask my questions step by step to see where my problem begins. I hope you don't mind. My...
  19. S

    Cylinder with piston separating two sections containing two gases.

    Homework Statement A closed, insulated cylinder is divided into two equal parts by a piston. One compartment contains Nitrogen at T=300K, P1=5bar, the other Carbon Dioxide at T=300K, P2=20bar. The cylinder contents then reach mechanical and thermal equilibrium. 1. Assuming that the gases...
  20. squelch

    Help with Cylinder Volume Calculation: Part C

    This is from a physics course, but felt more appropriate to post here. I just want some sanity checking on my procedure, since I'm not this far in my calculus course yet but am having to work through it anyway for physics. I have no idea how to approach part c, not even an inkling of where...
  21. N

    Getting two difference results when calculating volume of cylinder?

    This actually isn't a homework problem -- I'm just trying to understand an example in my textbook. The example shows how to calculate the volume of a cylinder (maybe it's actually a shell, I'm not sure) using an integral, but it occurred to me that I should be able to simply "unwrap" the...
  22. O

    Volume bounded by cylinder and planes

    Must double integrate using type I or type II planar region D to find volume bounded by Cylinder y^2+z^2=4 And Planes X=2y X=0 Z=0
  23. A

    Potential difference in uniformly charged cylinder

    Homework Statement Charge is uniformly distributed with charge density ρ inside a very long cylinder of radius R. Find the potential difference between the surface and the axis of the cylinder. Express your answer in terms of the variables ρ, R, and appropriate constants. Homework Equations...
  24. wolf1728

    Cylinder Calculator - Volume Area Radius Height

    Maybe I'm plugging my website but I just finished writing a versatile cylinder calculator. If you know two variables (Volume Area Radius Height), it calculates the other two. http://www.1728.org/diam.htm It was a little tricky deriving the formulas but I'm glad I did. (Yes, I know if you...
  25. D

    Cylinder with piston, stationary state

    Homework Statement We have a horizontal cylinder with an ideal piston, both are made from a heat nonconductive material. There is 10 liters of steam at 3 bars and 200 degrees Celsius in the cylinder. The cylinder is surrounded with atmosfere with pressure of 1 bar and temperature at 20 degrees...
  26. B

    Moment of Inertia of Hollow Cylinder Derivation

    For a uniform, hollow cylinder, why is this derivation wrong? M = mass of whole solid cylinder m = mass of missing cylindrical piece R = radius of whole cylinder r = radius of missing cylindrical piece moment of inertia = moment of inertia of whole cylinder - moment of inertia of...
  27. S

    Optimizing Water Injection for Lean-Burn Combustion in a Single Cylinder Engine

    Hi, all. I'll be experimenting with water mist injection (amongst other things) on a small single cylinder engine. Because the electrical generation capability of the engine's alternator is limited, I have to find some other way of pressurizing the water for injection (not enough juice for an...
  28. D

    Polar Coordinates, intersection of a cylinder with a spher

    Homework Statement Find the Volume of the solid that the cylinder ##r = acos\theta## cuts out of the sphere of radius a centered at the origin.Homework Equations The Attempt at a Solution I have defined the polar region as follows, $$D = \{ (r,\theta) | -\pi/2 ≤ \theta ≤ \pi/2 , 0 ≤ r...
  29. P

    Thermodynamics of a floating cylinder

    I am wondering if my reasoning is correct for determining the energy due to the buoyancy of a deformed water surface. Essentially, one has a floating cylinder that depresses the surface of a liquid in an infinite tank as seen in the figure. I want to compare the energy of a flat surface with...
  30. R

    Understanding Volume of Oblique Cylinders through Integration

    Hi :) I'm doing my A-Levels and have a maths investigation project for which I decided to model the working of a shishi-odoshi. (http://en.wikipedia.org/wiki/Shishi-odoshi) The shape of the water in the shishi-odoshi is a cylindrical segment and I want to use integration to find the...
  31. C

    Creating a temperature differential on SF6 to evacuate a cylinder

    I have a 50KG cylinder with 1-2LB of SF6 at 15PSI. I want to transfer it into another cylinder by temperature differential. Keeping it simple. I try to model it with two cylinders that has a valve on each cylinder. Connecting the cylinder with a 1/4" hose. Both valves are closed. The...
  32. D

    Is the Answer Correct? Dipping a Cylinder w/ Small Hole in Liquid

    An empty cylindrical vessel with a small circular hole of radius r at the bottom is dipped vertically in a liquid of density d keeping the bottom downward. At what maximum depth can it be dipped before the liquid enters into it? The surface tension of the liquid is S. The answer given in the...
  33. 1

    Cylinder with heat generation, Separation of variables

    I'm having some difficulty setting up a problem. I'm trying to model the temperature of a thermistor connected to a constant current source. The thermistor's resistance varies with temperature, so with a fixed current, I would expect to see the thermistor's temperature to oscillate with time...
  34. J

    Ellipsoid intersected by cylinder

    Homework Statement Find volume of the ellipsoid ##x^2 +2(y^2+z^2) \le 10## intersected by the cylinder ##y^2 + z^2 \le 1 ## The Attempt at a Solutionseems like changing to cylindrical coordinates would be best so I have \left\{ \begin{array}{cc} r^2cos\theta + 2r^2sin^2\theta +2z^2 \le 10...
  35. A

    Improving IC Engine Efficiency: Reducing Heat Loss Through Cylinder Walls

    hi.I would like to know something about the IC engine.I just read an article.It said that 30% efficiency is gone through conduction of heat by the cylinder wall.If it is reason for one of the efficiency loss why can't we build an cylinder coated with a material that is non conduction.So only...
  36. STEMucator

    Density of cylinder, error propagation

    Homework Statement The density of a cylinder is calculated from the following data: ##m= (2.8±0.8)g## ##d = (2.2±0.1)cm## ##h = (4.0±1.0) cm## What is the error on the density, before rounding, in ##\frac{g}{cm^3}##? Homework Equations ##V = \pi r^2 h = \frac{1}{4} \pi d^2...
  37. A

    Actuators -- moving piston-fixed cylinder

    what is the advantage of moving piston-fixed cylinder arrangement over visa-versa ??
  38. andyrk

    Time for falling down the incline (Rotating Solid Cylinder)

    Homework Statement A solid cylinder of radius R is spun and then placed on an incline having coefficient of friction μ=tanθ (θ is the angle of the incline). The solid cylinder continues to spin without falling for time: (A)Rωo/3gsinθ (B)Rωo/2gsinθ (C)Rωo/gsinθ (D)2Rωo/gsinθ The Attempt at a...
  39. B

    Area of a cylinder inside a sphere (surface integral)

    Homework Statement Find the area of the cylinder x^2 + y^2 -y = 0 inside the sphere x^2 + y^2 +z^2 =1 Homework Equations dA = sec \gamma dydz where sec \gamma = \frac{|\nabla \phi|}{|\partial \phi/ \partial x|} The Attempt at a Solution The method shown in this section is to...
  40. J

    Cylinder attached to a block on an inclined plane, rotational dynamics

    Homework Statement A cylinder of mass M and radius R, with moment of inertia: I_c = \frac{1}{2}MR^2 rolls down without slipping through an inclined plane with an angle of θ, while pulling a block of mass Mb with an attached frame (of insignificant mass) which is connected to the axis of...
  41. J

    Moment of inertia of a suspended cylinder

    Homework Statement A uniform cylinder 20 cm long, suspended by a steel wire attached to its mid-point so that its long axis is horizontal, is found to oscillate with a period of 2 seconds when the wire is twisted and released. When a small disc, of mass 10 g, is attached to each end the...
  42. F

    E-field in a cylinder with a hole parallel to its axis

    Homework Statement A long insulating cylinder of radius R1 has a cylindrical hole parallel to the axis of the cylinder. The radius of the hole is R2, and the distance from the centre of the cylinder to the centre of the hole is a. There is a uniform fixed charge per unit volume ρ throughout...
  43. R

    Moment Coefficient for a 3D Rotating Cylinder

    Hi, I'm looking for the Moment Coefficient (Cm) for a 3D Rotating Cylinder, this means, I there is a free stream of fluid and there is inmerse a cylinder rotating about its own axis , and also rotating about an axis parallel to the free stream. I found in the book of Peter Childs, called...
  44. W

    Has this engine cylinder/ block design be done before,would it work?

    I believe artillery guns and barrels that are highly pressurised often use shrink fitting (heating up a tube causing it to expand allowing it to be fitted over a smaller tube which it will apply an inward pressure on when it cools) to oppose the pressure from inside the barrel. Could this...
  45. PeteyCoco

    Green's Function of a homogeneous cylinder

    I've been reading this article for a prof this summer: http://arxiv.org/pdf/1302.0245v1.pdf I'm having some trouble following the math in Appendix B: Green's Function Of A Homogeneous Cylinder (page 9). Can someone explain to me why there is a factor of \frac{1}{\rho\rho'} in front of the Green...
  46. 8

    Orientation of cylinder around massive body

    http://i.imgur.com/ZH9huJt.png Lets suppose this perfectly rigid cylinder has a uniform mass and has a length on the order of the distance between the Earth and Mars or some similar situation. This cylinder is orbiting around the Sun in a 2-body universe. What would this cylinder look like on...
  47. A

    Deriving motion of a displaced piston on a gas cylinder

    First, I'm a second year high school physics student so my thinking may be half-baked. I was wondering what motion a piston would exhibit if it was the frictionless lid of an ideal gas cylinder with a constant amount of air, and if it was pushed or pulled a little bit. There would be a...
  48. E

    Tolerance for pneumatic cylinder and piston

    What is the tolerance for pneumatic cylinder and piston operating about 2 psi, at room temperature, so that the piston can move freely without leakage? The piston diameter is 20 mm.
  49. U

    Boundary Conditions - Cylinder in dielectric

    Homework Statement Part (a): List the boundary conditions Part (b): Show the relation for potential is: Part (c): Find Potential everywhere. Part (d): With a surface charge, where does the Electric field disappear? Homework Equations The Attempt at a Solution Part (a) Boundary conditions...
  50. Matt atkinson

    Flow on the surface of a cylinder

    Homework Statement An infinite cylinder is moving at constant velocity \vec{U} in a stationary background flow. On the surface of the sphere no fluid penetrates, so that \vec{U} \cdot \vec{n} = \vec{u} \cdot \vec{n} . Where \vec{n} is the vector normal to the surface of the cylinder. At...
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