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. D

    I Surface roughness and Magnus force of a cylinder

    I know that the surface roughness plays an role in the Magnus force exerted of a rotating cylinder. But, i cannot find an equation that includes the surface roughness in the equation of the Magnus force. If someone could state the formula (and preferably a source to read up more on it) it would...
  2. oneofmany850

    Magnetic field inside a cylinder with an offset hole

    Homework Statement Metal cylinder of radius a has the z-axis as its symmetry. It has magnetic field at any point P as: $$B[x,y,z] = \frac{1}{2} \mu_0 J_z [-ye_x + xe_y]$$ A cylindrical hole of radius b which is displaced from the cylinder's axis by d in the x direction. The magnetic field...
  3. F

    Volume of a Cylinder: Find via Polar Graphs

    Homework Statement Find the volume of solid bounded below by plane z = 0 , and above by z = 10 , sides by (x^2) + (y-1)^2 = 1 .. Homework EquationsThe Attempt at a Solution I fins the area of the base first , which is pi (1^2) = pi , then i integrate with the length , which is from z = 0 to...
  4. X

    Volume of a Region inside a cylinder and sphere (Symbolic)

    Homework Statement Suppose W is the region inside the cylinder x^2+y^2=a^2 and inside the sphere x^2+y^2+z^2=b^2, where 0<a<b. Set up an iterated integral for the volume of W Homework Equations x^2+y^2+z^2=b^2 x^2+y^2=a^2 0<a<b The Attempt at a Solution I converted to cylindrical coordinates...
  5. dykuma

    Partial Differential equation, Temp in a Cylinder

    Homework Statement Homework Equations The Attempt at a Solution Because we are only looking at a cross section, I tried to reduce 5.3 down to just being a function of R and Theta. However I reasoned that there should be, based on this problem, no dependence on Theta either, so I figured I...
  6. C

    Cylinder carrying volume and surface current, H field

    Homework Statement We have an infinite cylinder that, from radius 0 to a, has a volume current density ##\vec{J(r)}=J_{0}(r/a) \hat{z}## , then from a to 2a, it has a material with uniform linear magnetic permeability ##\mu=(3/2)\mu_0## , and at the surface, it has surface current...
  7. Ketav

    Calculus: Verify Thick Walled Cylinder Equations

    Homework Statement I have a system of two ordinary differential equations as shown below. I have to prove that the Lame's exact solutions for a thick walled cylinder loaded by internal pressure satisfies the equations. The next step is to integrate the equations to obtain an equation for U...
  8. I

    Inertia matrix of a homogeneous cylinder

    Homework Statement [/B] Homework Equations N/A The Attempt at a Solution What I am confused about is where they got the (1/4)mR^2 + (1/12)ml^2 and (1/2)mR^2 from? I am guessing that these came from the integral of y'^2 + z'^2 and x'^2 +y'^2 but I don't understand how this happened exactly...
  9. HyperTechno

    Does using dual spark plugs per cylinder make any difference?

    There is this bike manufactured in India with a 180CC single cylinder petrol engine with Twin Spark plugs. They highly market their "twin spark technology". Well according to my knowledge, I don't think that will make much difference in performance and efficiency. What do you think? Is this just...
  10. FallenApple

    Mechanism For Oscillation of Cylinder

    Homework Statement [/B] Begin with a solid cylinder of mass M and radius R. A hole is bored through this cylinder with radius r < R/2, parallel to the axis of the cylinder and with the surface of the hole touching the cylinder’s axis. This modified cylinder then rolls on a horizontal surface...
  11. M

    I Torsion on cylinder described differentially

    Hi all, In this article, page 7 - 3 there is a drawing of a Cylinder suffering Torsion. In the next page it says: ftp://www.bauwesen.fh-muenchen.de/Bauwesen/Konrad/Baustatik_1/Festigkeitslehre/kap07.pdf γ⋅dx = r⋅dϑ From my observations i come to tan γ=s/x ; tan ϑ=s/r ; therefore x⋅tan γ =...
  12. R

    Off center hole in a current-carrying wire - magnetic field?

    Homework Statement A long copper rod 8 cm in diameter has an off-center cylindrical hole 4 cm in diameter down its full length. This conductor carries a current of 900 amps flowing in the direction “into the paper.” What is the direction, and strength in tesla, of the magnetic field at the...
  13. C

    Solid bounded by the cylinder (y^2) + (z^2) = 1 , cut by pla

    Homework Statement By using cylindrical coordinate , evaluate ∫ ∫ ∫ zDv , where G is the solid bounded by the cylinder (y^2) + (z^2) = 1 , cut by plane of y = x , x = 0 and z = 0 I can understand that the solid formed , was cut by x = 0 , thus the base of the solid formed has circle of (y^2) +...
  14. Xetricon

    Solve Torque on Cylinder Homework Problem

    Homework Statement A cylinder having a mass of 5.0 kg can rotate about its central axis through point O. Forces are applied as shown in the figure: F1 = 5.0 N, F2 = 6.0 N, F3 = 2.5 N, and F4 = 5.5 N. Also, R1 = 6.5 cm and R2 = 12.0 cm. Find the magnitude and direction of the angular...
  15. M

    In a cylinder, why do we use just the ground area to get p?

    Hi, given an Hydraulic Cylinder with the Formula: F=p*A Why do we use APiston to calculate the Force in Work-Direction? Doesnt it suppose the "Potential Energy" of the compressed air just presses in that Area? Im pretty confused, sorry about the unconcrete question.
  16. M

    Minimizing weight of a cylinder using Lagrange multipliers

    Homework Statement Julia plans to make a cylindrical vase in which the bottom of the vase is 0.3 cm thick and the curved, lateral part of the vase is to be 0.2 cm thick. If the vase needs to have a volume of 1 liter, what should its dimensions be to minimize its weight? Homework Equations...
  17. Z

    Energy per unit length of a cylindrical shell of charge

    Homework Statement "An infnitely long hollow cylinder of radius ##a## has surface charge density ##σ_a##. It is surrounded by a coaxial hollow cylinder of radius ##b## with charge density ##σ_b##. The charge densities are such that the total confguration is electrically neutral. Using whatever...
  18. Blockade

    Finding the voltage at a radius of a cylinder

    Homework Statement Homework Equations Vab = ∫ E*dr The Attempt at a Solution [/B] For part (b) I am not sure if I should set the upper and lower bound of the integral from "R" to "2R" or "2R" to "3R". If done so, this would give me V2R = Vab * ln|3R/2R| / ln |3| instead of what is on the...
  19. T

    Weird thinking of electric field inside a hollow cylinder.

    While I was studying with electric field about cylinder, I learned that for a very long cylinder, the electric field in the hollow of cylinder will be zero. http://physics.stackexchange.com/questions/156789/electric-field-of-hollow-cylinder However, I couldn't accept this intuitively, and...
  20. D

    Temperature in the regulator valve of a cylinder

    Homework Statement There is a cylinder of oxygen connected to a valve (A) and then to connected to a regulatory valve. The volume of both valves and the pipes between them is Vr and can be disconsidered in regard to the cylinder's volume. The oxygen can be considered a perfect gas with...
  21. T

    Electric field inside and outside a charged cylinder

    Homework Statement WITHOUT using Gauss's law calculate the electric field at all points outside and inside an infinite cylinder with circular cross section of radius b and charge density ρ Hint: Use cylindrical coordinates and place the target charge on the x axis..Homework Equations E =...
  22. D

    Volume of cylinder bounded by two dependent planes, ideas?

    Homework Statement [/B] Calculate the volume bounded by the plane/cylinder x^2+y^2=1 and the planes x+z=1 and y-z=-1. Homework Equations / The attempt at a solution[/B] It is pretty basic triple integral in cylindrical coordinates. For some reason, I can't get the right answer. I'm using...
  23. T

    Removing a crane cylinder, force calculation

    Hi I'm working on a project out in the North Sea on an oil rig, we need to remove a hydraulic cylinder from a crane, I have attached a drawing the red cylinder B needs to be removed. To do this we will move the crane boom to the position shown by the orange lines and rest the end down on the...
  24. R

    Experimentalists : sample of gas from cylinder

    Hi, are there any experimentalists here? I have gas in a cylinder. I have just been taking samples of gas from a tube connected to the outlet, but air is getting in the syringe. So I went over to chemistry and got a round bottom flask with 3 inlets / outlets and a septum, so its like this: I...
  25. G

    Propagation of Uncertainty - Hollow Cylinder

    Hi, I'm having quite a bit of trouble finding the propagation of uncertainty (using partial derivatives) of the volume of a hollow cylinder. The examples in my tutorial only demonstrates how to find the propagation of uncertainty on simple operations such as x + y, x/y, etc... 1. Homework...
  26. R

    Calculate the lateral strength / buckle point of a cylinder

    Hello. Here is my problem: I want to mount 2 solar panels on a horizontal 10 foot bar. (panels are 5' and 20-40/lbs each - so 80lbs) is there a formula i can use on each material option to figure out what material to use for the 10 foot bar (what won't break under the weight of the panels or...
  27. astrocytosis

    Gas inside an expandable cylinder raises lid on spring

    Homework Statement An expandable cylinder has its top connected to a spring of constant 2000 N/m. The cylinder is filled with 5L of gas with the spring relaxed at a pressure of 1 atmosphere and a temperature of 20C. If the lid has a cross-sectional area of 0.01m2 and negligible mass, how high...
  28. D

    Atmospheric Pressure on Shaft of piston cylinder assembly

    Homework Statement In a vertical piston cylinder assembly, a vertical shaft whose cross sectional area is 0.8 cm^2 is attached to the top of the piston. Determine the magnitude F, of the force acting on the shaft, in N, required if the gas pressure inside the cylinder is 3 bar. The masses of...
  29. A

    Vapor Pressure In Closed Cylinder

    Hi There, I am trying to understand if I have a vacuum in the below scenario or simply just really low pressure. A pump supplies a pipe with a constant supply of water at one end (Point A) the water discharges several kilometers away at some lower elevation (Point B). At "Point A" a valve...
  30. N

    MHB How to Maximize the Volume of a Cylinder with a Given Perimeter?

    it is given that the perimeter of the rectangle is (80 + 120 + 80 + 120) = 400 cm From this you need to make a cylinder with maximin volume: 400 = 2r + 2h 2h = 400 - 2r h = 200 - r . We wish to MAXIMIZE the total VOLUME of the resulting CYLINDER V = πr^2 h However, before we differentiate the...
  31. P

    How to Charge a 4P 1S cylinder Lipo Pack

    Hello, I have recently bought 4 cylindrical lithium ion batteries from hobby king to make a battery pack. To do this, I put all 4 of them in Parallel, so that the voltage would stay the same, but the capacity would increase. It says on Hobby king that they can charge at 5C, and since they are...
  32. physea

    I Comparison of solid and hollow cylinder

    Hello! We have a solid cylinder and then we take that and drill its core so that it becomes hollow. In which case the cylinder will be stronger? Thanks!
  33. M

    MHB Calculating Volume of a Solid by Subtracting Volumes of Basic Shapes

    Please solve this problem :)
  34. R

    I Calculating FvD for Hydraulic Cylinder with Air Bubble

    I want to calculate the force-displacement curve for a damper that would have hydraulic oil with an air bubble in it, so very similar to an air spring with a limited amount of volume. I came up with the following solution: F(x)=Po*A((Vo/Vo-A*x)-1) where F would be the external force applied...
  35. R

    2 Cylinder elastic rotational collision

    Homework Statement [/B] A cylinder with mass 3kg slides on ice with its base surface at 5m/s and collides with an identical but stationary cylinder. The collision is elastic. After the collision, the center-masses of the cylinders move at angles 45 and 30 degrees from the starting direction...
  36. F

    Infinite cylinder covered by a single chart

    Homework Statement This is a problem from Spacetime and Geometry by Carroll, Just because a manifold is topologically nontrivial doesn't necessarily mean it can't be covered with a single chart. In contrast to the circle ##S^1##, show that the infinite cylinder ##RxS^1## can be covered with...
  37. R

    Maximum speed of a cylinder dropped on a spring

    Homework Statement Cylinder A (mass = 5kg) is released from rest at a height h =100mm above a spring of stiffness k = 1.8 kN/m. Determine, (i) the maximum compression of the spring, (ii) the spring deflection when the cylinder’s velocity is a maximum, and, (iii) the maximum velocity of the...
  38. Hamal_Arietis

    What is the Velocity of a Cylinder on an Inclined Plane with a Magnetic Field?

    Homework Statement At the height h, from the top of inclined plane forming an angle α with the horizontal, a disk slips down which has radius R, thickness d, mass m and resistivity ρ. On inclined plane, an area S is very small square that has a magnetic field B. The magnetic field B is...
  39. S

    A solid cylinder of uniform density of 0.85 g/cm3 floats in

    Homework Statement A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring. https://s1.lite.msu.edu/res/msu/kashy/physicsLib02/32_Fluids1_Pascal_Arch/graphics/archimedes.gif Its circular surfaces are horizontal. What effect will the...
  40. Andy Resnick

    A Q: Stokes paradox (flow around a cylinder)

    Can anyone recommend a good (peer reviewed) reference that discusses low Reynolds number flow around a cylinder? I'm specifically looking for derivations of the drag coefficient. The usual 'gold standard' references...
  41. P

    I Cylinder Compression: Pressure & Temperature Change

    Hello, according to thermodynamics the compression of a cylinder can both increase pressure and increase temperature. Unfortunately there is no law that gives us boh presure and temperture change given the change of volume, previous temperature and previous pressure? Usually we do either assume...
  42. B

    Cylinder rolling thanks to external torque.

    Homework Statement A cylinder of mass m and radius R is set on a plane, with large enough friction coefficient to ensure at any moment rolling without slipping. A constant torque is applied along the axis passing through the center of mass (G) of the cylinder and perpendicular to the basis of...
  43. V

    Cylinder hitting inclined plane

    Homework Statement Homework EquationsThe Attempt at a Solution To bring the cylinder to a stop both linear impulse and angular impulse would be required . Linear impulse would be provided by the normal force from the plane whereas the angular impulse has to be provided by the frictional...
  44. F

    Flux integral over a parabolic cylinder

    Homework Statement Evaluate ##\int\int_S \textbf{F}\cdot\textbf{n} dS ## where ##\textbf{F}=(z^2-x)\textbf{i}-xy\textbf{j}+3z\textbf{k}## and S is the surface region bounded by ##z = 4-y^2, x=0, x=3## and the x-y plane with ##\textbf{n}## directed outward to S. The attempt at a solution I've...
  45. Kirito123

    Finding height and volume of a cylinder

    Homework Statement Homework Equations Volume for cylinder = Pi (r)2 h Optimise : 1. make the best or most effective use of (a situation, opportunity, or resource). 2. rearrange or rewrite (data, software, etc.) to improve efficiency of retrieval or processing. The Attempt...
  46. S

    Terminal Velocity of a Cylinder Freefalling Through a Fluid

    Hello :) I am an engineer and I am trying to analyse a system which basically contains a cylindrical body free-falling through a body of static water beginning with zero velocity. I am ultimately trying to find what the velocity of the object would be at a depth of 20m. In order to do this I...
  47. Nemo's

    Calculate Pressure in piston cylinder after heating

    Homework Statement Water is contained in a cylinder fitted with a frictionless piston (figure shows that atmospheric pressure acts on piston from above). The mass of the water is 0.45 kg, and the piston area is 0.186 m2. Initially, the water conditions are 110oC and 90% dryness fraction, and...
  48. M

    Heat Transfer Coefficients: Free and Forced Convection

    Hi all. I'm currently working on a problem where I have to determine individual and overall heat transfer coefficients for a vertical cylinder with water flowing on the inside and steam on the outside (parallel flow), studying the cases of free and forced convection. I only have four...
  49. artoribio

    Question about E-Fields and Potential of a Coaxial Cylinder

    Homework Statement I have posted the given question and conditions in the attached image Homework Equations (Q_enclosed/ epsilon_0) = closed integral (E-field) dA Q_encolsed = p*A V(r)= -Int_(from origin to r) (E-field(r'))*dl' The Attempt at a Solution [/B] a) E=0------>For r<a...
  50. K

    Mass falling and pulling a cylinder without sliding

    Homework Statement A cylinder of mass M and radius r is at distance l0 from the edge. mass m is hanging from a rope. no friction at the weightless pulley. the cylinder starts rotating without sliding. What's the acceleration of the COM of the cylinder. What's the velocity of the COM of the...
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