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. M

    Write the density and its associated uncertainty of a cylinder

    Homework Statement Need to find the volume and density of a cylinder with measurements, height=0.03378m diameter=0.01876m and mass=7.99g +/- 0.01 kg And also its associated uncertainties. Homework Equations V=L*Pi*R^2 =0.00000933716m^3 p=M/V =0.0000008288 The Attempt at a...
  2. M

    Finding the electric field of a uniformly charged cylinder using Gauss' law

    Homework Statement A very long cylinder has charge density L/m and radius a. Find the electric field at a distance r, with r > a. The Attempt at a Solution I construct a gaussian cylinder around it with radius r, and then from Gauss' law the field at any point on it's side surface is E=...
  3. jaumzaum

    How Does Cylinder Dynamics Change When Rolling Down a Steep Inclined Plane?

    If we had a cylinder rolling down a ramp, with scalar friction coefficient us and kinetic friction coefficient uc, and we assume for example that the inclination of the ramp is enough to make the cylinder reach the acceleration needed to exceed the scalar friction of rolling. It means that the...
  4. G

    Stokes Theorem paraboloid intersecting with cylinder

    Homework Statement Use stokes theorem to elaluate to integral \int\int_{s} curlF.dS where F(x,y,z)= x^2 z^2 i + y^2 z^2 j + xyz k and s is the part of the paraboliod z=x^2+ y^2 that lies inside the cylinder x^2 +y^2 =4 and is orientated upwards Homework Equations The Attempt at a...
  5. S

    Clarification regarding rolling cylinder with CG slightly above

    Hi Can anyone please clarify the following? Let there by a rolling cylinder on an inclined plane. Let the solid cylinder(with Center O) on the inclined plane has Center of gravity at a distance 'c' slightly above O. If the cylinder is displaced slightly through an angle θ then [Let N =...
  6. O

    Cylinder oscillating in water.

    ωHomework Statement A cylinder of diameter d floats with l of its length submerged. The total height is L. Assume no damping. At time t = 0 the cylinder is pushed down a distance B and released. What is the frequency of oscillation? Homework Equations f = ω/2\pi Ma =...
  7. M

    Is there a solution for compression of cylinder?

    Hello, for some reason I can't seem to be able to find this. Suppose you have a elastic cylinder, a full cylindrical bar (not hollow), and you want to compress the two end faces (axial compression) together and find the stress in the axial direction...or strain. I can't seem to be able...
  8. H

    Find the angular speed of a cylinder with a spring

    Homework Statement A cylinder of radious r=10cm and mass m=1Kg is attached to a spring of constant k=18N/m. In every moment the cylinder rolls without slipping over the inclined plane with an angle of 30º. The other extreme of the spring is attached to a fixed point O, as shown. If the...
  9. andvaka

    MHB Integration Application: Find the force on each end of the cylinder

    A cylinder shaped container of tar has a diameter of 2m. If it is half full of tar with a density of 920 kg/(m^3) and is on it's side, find the force on each end. Helpful hints: 920 kg per m^3 is the mass density not the weight density. Take g= 9.8 m/ sec^2Please assist. I'm not sure at all how...
  10. W

    How to modal a voltage gradient from a single cylinder

    Hello, I am a bit trumped. I know how to calculate the voltage of a single uniform cylinder: V(r) = (-q/2 Pi ep0) Ln(r/R0) + V0 q: Charge density r: radius from outside of the cylinder. r >= R0 R0: radius of the uniform cylinder V0: applied voltage to the cylinder Here is my...
  11. J

    How to calculate resistivity of coaxial cylinder

    Is it any model on resisivity of two tightly-attached coaxial cylinder? For example, a copper core wire is coated with layer of aluminum. How to calculate the final resistivity along axis?
  12. P

    Mie scattering of infinite cylinder (light parallel to axis)

    I've been reading a few books on scattering of light from particles, in particular mie scattering of cylinders. At first I want to look at infinite cylinders, then finite cylinders once I understand a bit better. The problem is that all of the books I've looked at treat the problem where...
  13. M

    Pressure in a piston cylinder assembly when both volume and temperature change

    I have a problem in relation to the pressure in a closed piston and cylinder assembly, I know the compression ratio and want to work out the pressure when the volume is at its lowest, boyles law only seems to works if the temperature remains constant but I know that as the piston moves and the...
  14. A

    Torque required to rotate a hollow cylinder

    First let me start off by saying I was a liberal arts major so I need some help with some formulas I've researched. I'm rotating a hollow cylinder that is 8ft in dia. x 8 ft long. The cylinder weighs 3750 lbs and will be filled with 20,093 lbs of watered sewage sludge. Total weight = 23,843lbs...
  15. A

    Cylinder with uniform magnetization

    A short circular cylinder carries a uniform magnetization M parallel to its axis. I want to know what the divergence of M is. Using divergence in cylindrical coordinates I get that ∇\bulletM = 0. Now I was pretty sure of this result until I read the following in my book: "∇\bulletH =...
  16. C

    Help with protecting cylinder rods

    i'm a machine repairman and the machines i repair are robotic welding machine. one of the problems we are having is weld slag/expulsion getting caught in the area the cylinder rod moves between the mount and the rod. i tell the engineer to make the hole larger to allow the slag to fall out he...
  17. L

    How to calculate the height submerged of cylinder

    A hollow cylinder (but not open ended) is allowed to float on a liquid. Can anyone please help me how to calculate the height (h) it submerge? I want to get a relationship between height and cylinder weight. I can calculate the volume of submerged part. But no idea how to derive a formula with...
  18. D

    Cubical block on a cylinder challenging problem

    Homework Statement A cubical block of side L rests on a fixed cylindrical drum of radius R. Find the largest value of L for which the block is stable. This is problem 6.35 from the Kleppner+Kolenkow Introduction to Mechanics book. I honestly have no clue where to even start on this problem...
  19. N

    Moment of Inertia of a Hollow Cylinder

    Homework Statement A hollow cylinder has mass m, an outside radius R2, and an inside radius R1. Use integration to show that the moment of inertia about its axis is given by I = 1/2*m(R2^2 + R1^2) Homework Equations dm = rho*dV = 2*pi*rho*h*r*dr The Attempt at a Solution This...
  20. DryRun

    Find surface area of cylinder

    Homework Statement Find the surface area of the portion of the cylinder x^2+y^2=4y lying inside the sphere x^2+y^2+z^2=16Homework Equations Double integral for finding surface area. \iint_S d\sigma The Attempt at a Solution At first, i thought it was just the area of the surface of sphere...
  21. S

    Pressure at the bottom of cylinder immersed in two liquids

    Homework Statement A solid cylinder has base area A, height 20 cm and density 0.8 g/cm3, floats in the boundary of oil and water. If the density of oil 0.6 g/cm3, find a. the height of cylinder that immersed in oil and water b. the hydrostatic pressure at the bottom of the cylinder if the...
  22. R

    Lift of a Rotating Cylinder in Inviscid Flow

    Hi I am wondering why a spinning cylinder will produce lift in an inviscid flow. From: http://www.grc.nasa.gov/WWW/k-12/airplane/cyl.html one of the mechanisms for lift generation was the sticking of fluid particles to the wall of the cylinder. I thought that the no slip condition only...
  23. T

    Parameterizing Z-Value in Line Integral for Cylinder (Stokes Thm)

    I am a little confused about how to generally go about applying Stokes's Theorem to cylinders, in order to calculate a line integral. If, for example you have a cylinder whose height is about the z axis, I get perfectly well how to parameterize the x and y components, using polar coordinates...
  24. Z

    Infinite long cylinder for Gauss' law

    Sometimes you want to find the electric field of a loong cylinder carrying for instance a uniform volume charge. Then for easy calculations you approximate the cylinder with an infinitely long one and then put a gaussian surface over the entire thing. Symmetry then dictates that the field point...
  25. S

    Thermodynamics- piston cylinder- 2nd law of thermodyamics

    ( part a only I don't understand how you know from this question that it is a constant pressure process. I thought it is a polytropic process. So it will have a pVγ curve. I was drawing a pV curve. The answer is a straight line parallel to x- axis. My question: How do I know from...
  26. B

    : What is the final temperature of the gas in the cylinder A?

    URGENT: What is the final temperature of the gas in the cylinder A? Homework Statement Two cylinders each contain 0.30 mol of a diatomic gas at 250 K and a pressure of 3.0 atm. Cylinder A expands isothermally and cylinder B expands adiabatically until the pressure of each is 1.0 atm...
  27. I

    Designing Shielding Box for High Voltage Cylinder

    i have to design one shielding box. in that there is cylinder having high voltage +60kev. and box having metal plate. so i have to calculate the electric field on that cylinder and then decide , what should be the distance in between plate and cylinder. i have attach the geometry on the file...
  28. S

    Thermodynamics; Finding Work of a Piston cylinder Device

    Homework Statement An insulated piston-cylinder device contains 5 kg of water at 100oC with a quarter of the mass is vapor. The water is compressed reversibly to 900 kPa. Find the work done during this process. Let the ambient temperature to be 27oC. Homework Equations I can use the...
  29. DryRun

    Find eqn of cylinder of height

    Homework Statement How to find the equation of cylinder: x^2+y^2=4 from z=0 to z=2? Homework Equations (x-a)^2+(y-b)^2=r^2 The Attempt at a Solution I can't figure out how to implement the z-coordinate into the general equation of cylinder. In the latter, the height is taken as infinite in...
  30. R

    How Do Faraday's Laws Relate to Magnetic Energy Dissipation in a Cylinder?

    Homework Statement A thin cylinder of radius r, thickness s, and length L, is made of metal with a resistivity of ρ. The cylinder is resting in a uniform magnetic field B0, with the field being in the same direction as the axis of the cylinder. The cylinder is then removed from the field. Find...
  31. L

    Normal Vector for a cylinder

    Homework Statement An infinite cylinder with radius 1 is aligned with axis Y, A point light source with intensity 1 is located at (2,2,10) An observer is located at (3,1,4). He is looking in the direction of the origin of the coordinate system. What are the coordinates of the point on the...
  32. T

    Electric Potential of a Cylinder using Poisson's Equation

    Homework Statement Consider a homogeneously charged, infinitely long, straight wire of finite radius R. Determine the potential \phi(r) of the wire for r ≤ R and for r ≥ R. You must use the Poisson-Equation! Homework Equations Δφ(r) = -ρ(r)/ε ⇔ \frac{1}{r}\frac{∂}{∂r}(r\frac{∂φ}{∂r}) +...
  33. T

    Related rates maxium voulme of cylinder

    If 1200∏ cm^2 of material is available to make a cylindrical can with a circular base an open top, find the largest possible volume of the can. the formulas i used: v=∏* r^2 * h surface area = 2∏r^2 + 2rh my attempt: 1200=r^2h∏ h=1200/r^2∏ SA=2∏r^2+2∏r(1200/∏r^2) =2∏r^2+...
  34. C

    :Problem with a cylinder tank and a nozzle

    urgent :Problem with a cylinder tank and a nozzle Hey guys, I have been given a problem and I really want your help cause I have some doubts:[/B] A cylindrical tank 1.52 m in diameter and 7.62 m high contains cottonseed oil having a density of 917 kg/m3. The tank is open to the atmosphere...
  35. C

    Calculating the driving force in a double-acting cylinder using air

    Hello! I'm completely lost trying to derive an equation that'll give me the driving force in a DAC, and I really need some help from you guys. The purpose of knowing this is to optimize the amount of air that is needed (24 litres are available, pressure up to 8 bar) to drive a...
  36. W

    What is the time tR for a cylinder to transition to pure rolling motion?

    Homework Statement A solid homogeneous cylinder of mass M and radius R is moving on a surface with a coefficient of kinetic friction μk. At t=0 the motion f the cylinder is purely translational with a velocity v0 that is parallel to the surface and perpendicular to the central axis of the...
  37. P

    Solving the Hollow Cylinder Equation

    Homework Statement Hi everyone! I did an experiment recently and I've come really far but I have some difficulties with the final equation. In this experiment you have to explain hollow cylinders rolling down an incline without using advanced physics like moment of inertia or something like...
  38. W

    Pushing a cylinder along a surface with friction.

    If I push a cylinder along a surface with friction then am I right in saying that it would almost instantly start a pure rolling motion with a combination of translational and rotational kinetic energy? Or would it start initially with pure translational motion and gradually accelerate...
  39. P

    Magnetic Field in cylinder

    Homework Statement A conducting cylinder of radius r0 carries a current I uniformly throughout its volume. Find an expression for the magnetic field H at a distance r from the axis of the cylinder (a) for r < r0 , and (b) for r > r0 . Homework Equations Biot-Savart Law Amperes Law...
  40. D

    Parametrizing Intersection of Cylinder and Plane

    Homework Statement Let C be a cylinder of radius 1. It is cut by the x-y plane from below, and by the plane z-x=1 above. Parametrize all the surfaces of the cylinder. Find a unit normal (pointing outward) for each surface. Homework Equations Equation for a cylinder: x^2+y^2=1 Equation of the...
  41. M

    Find the volume of the region bounded by parabolic cylinder and planes

    Homework Statement Find the volume of the solid bounded by the parabolic cylinder y = x^2 and the planes z = 3-y and z = 0Homework Equations The Attempt at a Solution Obviously, a triple integral must be used in the situation. Our professor never explained how to find the limits of...
  42. A

    Inviscid flow around cylinder in presence of wall

    Hi there, Is there someone who would know how to solve the following potential flow theory problem: How to find the flow field and resulting force on a cylinder moving at a constant velocity through a stagnant fluid in the presence of a wall. The motion of the cylinder is parallel to the...
  43. H

    Automotive HELP: High Performance Free Flow Exhaust For Single Cylinder (153cc) Engine

    Before I Start here is a disclaimer - I am not a professional CAD or Mechanical Engineer to know much about this. Also, All information I have is from the internet and have NO practical knowledge. Here we go then. I am currently working on building a High Performance Free Flow Exhaust...
  44. I

    Frozen-in magnetization in a long cylinder

    "frozen-in" magnetization in a long cylinder hi I am doing this problem from Griffiths EM book on page 272 (3ed.) An infinitely long cylinder of radius R, carries a frozen-in magnetization parallel to the axis \mathbf{M}=ks\;\hat{z} , where k is a constant and s is the distance from the...
  45. P

    Moment of Inertia of a cylinder with varying density

    A cylinder with radius R and mass M has density that increases linearly with distance r from the cylinder axis, ρ = αr, where α is a positive constant. Calculate the moment of inertia of the cylinder about a longitudinal axis through its center in terms of M and R. I have I = ∫r^2dm and ρ...
  46. K

    Forces acting on a falling cylinder?

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  47. K

    What Forces Act on a Descending Cylinder Attached to a Tape?

    Homework Statement A cloth tape is wound around the outside of a uniform solid cylinder (mass M, radius R) and fastened to the ceiling as shown in the diagram below. They cylinder is held with the tape vertical and then released from rest. as the cylinder descends, it unwinds from the tape...
  48. P

    Capacitance and Other Traits of a Coaxial Cylinder

    This is for an electromagnetic theory class. Homework Statement Prompt can be seen here Homework Equations J = I/A, J = σE, V = Ed, C = εA/d The Attempt at a Solution I'm having trouble mostly with parts i and ii, as the rest are fairly simple to acquire after figuring out those two...
  49. G

    Finding the domain of integration in spherical coordinate of a shifted cylinder

    So I've done some problems where a sphere intersects with a cylinder and I needed to find the volume of the intersected region using triple integrals. For example, if I needed to find the domain of integration for the intersection of the sphere $$x^2+y^2+z^2=a^2$$ and the cylinder...
  50. E

    Cylinder Rolling Down an Inclined Plane

    Homework Statement A 3.0kg solid cylinder (radius=.15m, length=.7m) is released from rest at a top of a ramp and allowed to roll without slipping. The ramp is .9m high and 5m long. Find the rotational and translational kinetic energy. Homework Equations krot=1/2Iw^2 Ktrans=1/2mv^2...
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