# Cylinder Definition and 65 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. ### Number of Decks on a Rotating Habitat

My current spaceship design with several ring habitats (6 in my case) works well for worldbuilding purposes, in the sense that the reader should easily be able to tell what types of facilities can be found where on the ship. That’s because the rings distinguish themselves from each other by...
2. ### Is a solid cylinder considered thick or thin?

I have a solid cylinder of diameter 40mm and length 14mm and I have used plane stress approximations in my calculations so far. I know for to assume a thin walled cylinder/tube the wall thickness needs to be less than 1/20 of tube or cylinder diameter. However, what I have found so far is that...
3. ### Ball rolling within a rolling cylinder

Cylinders rolling down inclines are a common demo. But how do you model the movement of a sphere rolling within a rolling cylinder? I teaching a physics class and this question came up and my dynamics math is a little rusty. But I haven't found anything like this in any book or online. There's...
4. ### Calculate the Pressure that Shrink film exerts on a cylinder

First off I am not sure if the equation is even suitable for solving this problem. Secondly, I have no idea how to determine the tension the shrink film can provide. Furthermore, I also think the radius of the film tube has a influence on the pressure, I guess in this problem the tube is...
5. ### Calculate Pressure vessel Collapse Pressure

Homework Statement I have a simple cylindrical pressure vessel with thickness 100m and inner radius 254mm,.the cylnder has flat head closed ends but these are thickness 30mm. I need to calculate the pressure that would cause the vessel to collapse given material properties E=207Gpa, poissons...
6. ### B Solid angle by placing one disk on a cylinder

Hello, I am trying to find an analytical expression to determine the solid angle subtended by a disk source onto the face of the cylinder. I will appreciate if someone can provide me directions. I am aware how to calculate solid angle by a point source to cylinder's face ( omega =...
7. ### Angular speed that breaks a spinning body apart with inertial stress

How to find the angular speed, on which a spinning hollow cylindrical body breaks due to inertial stress(force)? I found 2 sources(http://www.roymech.co.uk/Useful_Tables/Cams_Springs/Flywheels.html (last 2 equations) ...
8. ### I need to maximize my RPMs in a single cylinder flywheel

I am working on a flywheel single-cylinder engine powered by a 40 psi air compressor. My task is to achieve as many RPMs as I can. I have already bored two exhaust ports in the frame as shown in the pictures attached. I've done some 600grit sanding on points of contact, am using lubricant prior...
9. ### Spivak: Conic Sections appendix, problem 1

Homework Statement "Consider a cylinder with a generator perpendicular to the horizontal plane; the only requirement for a point ##(x,y,z)## to lie on this cylinder is that ##(x,y## lies on a circle: ##x^2+y^2=C^2##. Show that the intersection of a plane with this cylinder can be described by...
10. ### Air resistance: cylindrical rotor in stator with air gap

Hello, I am currently doing research on the aerodynamic properties of a rotating cylinder in a cylindrical housing. The cylinder represents a rotor in a electric motor. The air gap between rotor and stator is about 0.5mm. I'm looking for a theoretical analysis and calculation on the...
11. ### Finding the relationship between magnetic momentum and angular momentum

Homework Statement A cylinder with radius ##R## and height ##h## which has a distributed charge on its surface with density ##\sigma## spins over its axis with angular velocity ##\omega##. If the cylinder has a mass density ##\rho##, find the relationship between magnetic momentum and angular...
12. ### Falling solid cylinder with string

Homework Statement Homework Equations m:mass of solid cylinder T: tension in string w:angular velocity The Attempt at a Solution m(g-a)=T mg-ma=T a=v^2/r=w^2r now what?
13. ### Cylinder in 3 D

Homework Statement Let r be a positive constant. [/B] Consider the cylinder x2 + y2 ≤ r2, and let C be the part of the cylinder that satisfies 0 ≤ z ≤ y. (3) Let a be the length of the arc along the base circle of C from the point (r, 0, 0) to the point (r cos θ, r sin θ, 0) (0 ≤ θ ≤ π). Let...
14. ### Logic applied to making isothermal assumption

Homework Statement A thin electrical heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm. The rod (A) has a thermal conductivity of kA = 0.15 W/(m*K), while the tube (B) has a thermal conductivity of kB = 1.5 W/(m*K) and its outer...
15. ### Magnetic field outside a conducting hollow cylinder

Homework Statement A current I flows along the surface of a hollow conducting cylinder. The radius of the cylinder section is r. By using Ampere's law, show that the magnetic field B outside the cylinder is B=\frac{\mu_0}{2 \pi} \frac{I}{r} Homework Equations Ampere's law...
16. A

### Pascal's Law Problems

Homework Statement The large cylinder in a hydraulic press has 3 times the surface area of the small cylinder. What force should be applied to the small cylinder to create a lifting force of 7200 Newtons In a hydraulic-brake system, a force of 25 N can be applied to a surface area of 5 cm^2...
17. M

### Proving the equation for the height of a cylinder

Homework Statement Consider a sphere of radius A from which a central cylinder of radius a (where 0 < a < A ) has been removed. Write down a double or a triple integral (your choice) for the volume of this band, evaluate the integral, and show that the volume depends only upon the height of the...
18. ### Phases of hydrocarbons in a compressed gas cylinder

I'm currently in the process of selecting gas mixtures to calibrate a gas chromatograph. One of the gas mixtures I'm interested in has the following composition by percent volume: methane (CH4): 95% carbon dioxide (CO2): 1% butane (C4H10): 1% acetylene (C2H2): 1% nitrogen (N2): 2% The gas...
19. B

### Choosing Axis of Rotation in Cylinder Oscillation Problem

Homework Statement Here is a problem we worked in class. I already know the answer, just had a question on the method. Two cylinders are connected with by a small rod (with presumably negligent mass) through their centers. The cylinders can roll freely. A spring is attached to the small rod...
20. O

### Period of Oscillation of a Cylinder Attached to Two Springs

Homework Statement A solid cylinder of mass, M, is connected to two springs of total stiffness, k. The springs are connected tangentially (on top) to the cylinder. The other ends of the springs are attached to walls. What is the period of oscillation of the cylinder assuming that it does not...
21. R

### Drive Shaft stress

Long drive shaft of 5 inches fits into the end fitting and is rigidly attached by the bolts. Input torque is equal to output torque as we are ignoring losses from bearing. Let's assume that the load on the shaft is equal to 3*weight. (3 g's) (looking for more conceptual understanding rather...
22. ### Cylinder & Mineral: Thermal Dilation

Homework Statement A hollow aluminum cylinder with a depth of 20.0 cm has an internal capacity of 2.000 L at 20.0 C. It's full with mineral turpentine, at 20.0 C. The two of them are heated slowly, until the temperature reaches 80.0 C. a) How much of the mineral is spilled outside the...
23. ### I Intersection between line and cylinder

I have an expression for a "line- to sphere intersection" that works: a = 1 + Ax^2 + Ay^2 b = 2*(-zs + Ax*(Bx-xs) + Ay*(By-ys)) c = zs^2 + (Bx-xs)^2 + (By - ys)^2 - R^2 This is part of a code in Matlab, and works fine. It is derived from substituting (x=Ax*z+Bx, y=Ay*z+By) into...
24. ### External pressure on cylinder

Hello, This is a real simple question but I am having a hard time to answer it. We have cylinder with outer Radius Ro, Inner Radius Ri. Internal pressure = 0. External pressure = to be find. Material is Nylon. I would like to know: External pressure Po at which the tube/cylinder will go under...
25. ### Torque needed to rotate a cylinder

Hello, I'm designing a machine as a final assignment for my internship. It's a machine that wraps SS tubing around a cylinder, making coils. While trying to figure out how much torque I'd need to rotate the cylinder I found that I'm really in the dark on the subject (the teacher I had didn't...
26. ### Potential of dielectric cylinder with constant polarization

Homework Statement The dielectric cylinder is radius R and thickness d. Origin is at the center of the cylinder, which is oriented along the z-axis. It has polarization P=pz∧I need to calculate the potential V(0,0,h) at h>d/2. Homework Equations σb=P⋅n∧...
27. ### Finding frequency of a specific mechanical oscillator -- horizontal rod on pivot

Homework Statement There is a cyllinder with radius 0.5 m fixed on the wall. We put a 6 metres long thin rod with mass 0.3 kg on it, which does not slip. I would like to calculate the oscillating time. It is a part of a clock, so the oscillating time is probably 1 or 2 seconds, but I got...
28. ### Gravitational force on an astronaut from a nearby massive torus

Homework Statement There are a big object and an astronaut in space. How do we calculate the gravitational force between them. I enclose a photo. I have given the mass of an astronaut, the dimensions of this giant ring and density of the ring. There is also a mistake in the photo. The astronaut...
29. ### Determining the capacitance of the two conductors

Homework Statement For a given system, a conducting cylinder with radius ##r=a## with a linear charge density ##Q'## and a conducting surface at a distance ##z=h## from the cylinder, calculate the linear capacitance of the cylinder.Take that ##h>>a## ##C'=\frac{Q'}{U}## Homework Equations 3...
30. ### 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...
31. ### 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...
32. ### 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...
33. ### 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...
34. ### 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...
35. ### What does divergence of electric field = 0 mean?

Homework Statement I just want to focus on the divergence outside the cylinder (r >R) Homework Equations The Attempt at a Solution For r > R, I said ∇ * E = p/ε But that's wrong. The answer is ∇ * E = 0 I'm confused because there is definitely an electric field outside the cylinder (r...
36. ### A Project img on X-Y surface to a cylinder placed in center....

Hi , I came across a problem ,I've search a lot but couldn't exactly find the solution. here is my problem: suppose there is an image ( I call it IMG_A),place IMG_A in the X-Y plane , put a mirror cylinder at the center of IMG_A. what we see in the cylinder mirror is a deform image (I call it...
37. ### Falling chain on a cylinder

Hi! I am struggling with this problem the last two days and I cannot decide which solution is correct. Homework Statement A cylinder of radius R is fixed horizontally on the floor. A uniform chain of mass M and length L (L<πR/2) is placed on the cylinder in such a way that one end of the...
38. ### Volume of a cylinder and radius

Ok so i know the equation for the volume of a cylinder and the equation for calculating the radius. But when calculating the radius does the volume need to be converted into cubic inches or can it stay as imperial fluid ounces. Thanks
39. ### Rolling without slipping over a plank

Homework Statement This is just a general case I'm having trouble trying to imagine: https://lh3.googleusercontent.com/-mTyOwzfLy0E/VluaNlxEddI/AAAAAAAAAEk/2Creguw3xzY/w530-h174-p-rw/Screenshot%2Bfrom%2B2015-11-29%2B21%253A34%253A50.png Suppose there is a cylinder, kind of like a yo-yo, that...
40. ### Using a hot gas to drive a piston: entropy reduction?

Suppose we have an insulated cylindrical container with a piston inserted from one end. Suppose the volume confined by the piston is full of a hot gas. Now let the gas drive the piston so that the volume is increased. Did the entropy of the system decrease because some of the energy of the...
41. ### Cylinder filled with water deflection study

I am having some problems understanding how to apply a distributed load to a cylinder due to it being filled with water. Attached is an image of the cylinder (placed horizontally). The cylinder is symmetric about the y axis. Water is to be filled from the left through the 1" hole. The cylinder...

I have a horizontally supported cylindrical tube that is fixed at both ends. I modeled half of it to run the simulation on in Abaqus. The only load that it has is its weight. What I get confused at with cylindrical geometry is applying the load. How should I apply the gravitational load and at...
43. ### 3D object represent with primitive shapes

Hi, Given a 3D object in R3 space can we represent it using three basic primitive shapes like Sphere, Cone and Cylinder? Would this claim be valid?
44. ### Nitrogen in a cylinder - temperature, work and volume

This problem was translated from Swedish, sorry for any grammatical errors. The problem A cylinder with nitrogen gas inside is closed by a tight piston (that can slide without friction against the walls of the cylinder). The piston weighs ##s=12.5 kg## and holds the ##m=28## grams of nitrogen...
45. ### Cylinder with point mass angular momentum

Homework Statement A uniform cylinder of mass M and radius R can be rotated about a perpendicular axle through its centre. A particle of mass m is attached to the cylinder's rim. The system is rotated with angular velocity w about the axle, which is held in a fixed direction during the motion...
46. ### Cylinder Pressure of Combustion Engine

hi, i want to ask about 4 time combustion engine torque. in my example we simulate a single cylinder gasoline 4 time engine which works 1000-4000 rpms and always have same fuel and air mixture in cylinder and so same burn pressure in each power time. these are the rules of question now i want...
47. ### Straight engine vs flat engine on a 1 cyl. motorcycle

Hello everybody I just got an old underbone bike, which I'm planning to build and finish before the end of this year. I found the engine to be quite pathetic (a 4 stroke, carburetted, 100 cc flat engine) so I'm going to do an engine swap with a more powerful but similar engine configuration...
48. ### Force of a bar to stop a rotating cylinder

Hi, I'm having conceptual problems for solving this one. 1. Homework Statement I drew a picture of this problem, which should show up below. Lengths x,a and b were given in the original picture. A rotating closed cylinder is braked with a bar. Its brake shoe is pressed in respect of point B...
49. ### Heat of friction in cylinder-piston

I believe I'm missing something, probably a very stupid question incoming: I am considering process with ideal gas expanding without piston-friction in constant temperature environment. Amount of heat taken from the reservoir is of the same amount as the work done by the expansion of the gas...
50. ### Continuity and Bernoulli's equation in air

Hi, I'm trying to understand vortex shedding and how the Karman vortex street occurs when air flows around a cylindrical object, so far it's going OK but then I came across this part of the explanation which leaves me confused: "Looking at the figure above, the formation of the separation...