# What is Hollow cylinder: Definition and 62 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. ### I Warm-up time for a hollow cylinder

Hello all , I need to estimate the time it would take for the inside of a hollow cylinder to reach a limit temperature (detailed data below), in order to adjust the wall thickness and choose an insulating material to delay heating as much as possible. Being a total beginner in thermodynamics, I...
2. ### A Superconductor in a hollow cylinder -- two different end states. Why?

When a magnetic field is applied to a SC during cool down, the field goes through the hole of the hollow cylinder. When the cool down first takes place and then later a magnetic field is applied, the magnetic field does not go through the hole of the hollow cylinder but rather is expelled to the...
3. ### Releasing a hollow cylinder on a rotating disk

There is no net external torque since the cylinder is slipping (no friction), so the angular momentum should be conserved. $$L_f=\frac 12MR^2\omega_i=\frac 12\times3.8\times0.52^2\times50\times\frac{2\pi\times0.52}{60}$$
4. ### Torque required to spin a hollow cylinder

Hello all and thanks for viewing this, I am in need of some assistance to solve a problem to size an AC motor rotating this load (power transmission will be trough belt & pulley). I have a hollow cylinder (pipe) that needs to spin 25 RPM: - OD = 50 mm - ID = 48 mm - M = 200 kg - Total length...
5. ### Electric field of a hollow cylinder

I uploaded a diagram of the problem. I treated this as many thin rings and integrated it over the length. I placed my origin as in the same place as the uploaded picture. Finding the electric field due to one small ring: ##\vec r =\langle w-x, 0, 0 \rangle## where ##x## is the distance of the...
6. ### Torque required to rotate a hollow cylinder containing chips

I am designing a prototype to remove cutting oil from waste metal chip during Gun Drilling. My prototype consists of a netted(meshed) metal cylinder rotating horizontally about its axis with help of shaft and a pressurised air blown from above. The metal chips will be put inside netted cylinder...
7. ### Velocity of a hollow cylinder at the bottom of an incline

Homework Statement I was looking at the idea that a hollow cylinder will have less velocity than a solid cylinder at the bottom of an incline. I can find the velocity of the hollow and solid cylinder from the following: PE = Translational KE + Rotational KE From that equation I find v and I...
8. ### Hollow cylinder magnet making contact with the circuit

Homework Statement 1. Circuit moves downward while cylinder magnet is fixed. 2. Cylinder magnet moves upward while circuit is fixed. Gain emf in circuit. Homework Equations All those maxwell equations... F=v x B The Attempt at a Solution [/B] So first question is not that hard...
9. ### Electric Field from Long Hollow Cylinder

Homework Statement Consider the hollow cylinder from Exercise 1.59. Use Gauss’s law to show that the field inside the pipe is zero. Also show that the field outside is the same as if the charge were all on the axis. Is either statement true for a pipe of square cross section on which the...
10. ### Inertia of a hollow cylinder and hollow sphere

Homework Statement Consider a hollow cylinder of mass M with an outer radius R_out = 10 cm and an unknown inner radius R_in. If the hollow cylinder is to roll down an incline in the same time as a spherical shell of the same mass and the same outer radius, calculate R_in. Homework Equations...
11. ### How to calculate the weight of a submerged hollow cylinder?

A hollow cylinder (2 tons) is dipped in a chemical tank using hoist crane for treatment purpose. Can anyone please help me to show how to calculate the maximum weight of the submerged hollow cylinder when it is being pulled up because I need to choose the correct lifting capacity for the crane...
12. ### 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...
13. ### A block placed in a horizontal hollow cylinder

Homework Statement A block is placed inside a horizontal hollow cylinder. The cylinder is rotating with constant angular speed one revolution per second about its axis. The angular position of the block at which it begins to slide is 30° below the horizontal level passing through the center...
14. ### Moment of inertia of a hollow cylinder derivation

Homework Statement Show that a hollow cylinder of radius R_1, outer radius R_2, and mass M, is I=1/2M(R_1^2+R_2^2) if the rotation axis is through the center along the axis of symmetry. Homework Equations $$dm = \rho dV$$ $$dV = (2 \pi R)(dR)(h)$$ The Attempt at a Solution I was mainly...
15. ### Moment of Inertia: Non Uniform Rod

Homework Statement Hello, I am looking to determine the moment of inertia for the cantilever beam pictured below. I want I to be a function of L1 and T1. Known variables: L, D, P, t Dependent variables: T2, L2 Design variables: T1, L1 Homework Equations L2 = L - L1 T2 = T1 - t Standard...
16. ### 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...
17. ### 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...
18. ### 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!
19. ### I A diamagnet inside a magnetized hollow cylinder

Hi! Suppose I have a cylinder of pyrolytic carbon graphite (strong diamagnet) that's vertically placed inside a hollow cylinder made out of approximately radially magnetized neodymium. Assume the graphite is frictionlessly held into place vertically somehow (so gravity can be ignored) but can...
20. ### Kinetic energy of a hollow cylinder

Hello 1. Homework Statement In a uniform solid cylinder of radius r, mass m and height h we emptied a cylindrical cavity of radius r/4 tangent and parallel to the symmetrical axis z of the original cylinder. The cylinder is rolling without slipping on a horizontal plane. Find the kinetic energy...
21. ### Rotational Forces on a Hollow Cylinder

Homework Statement I am trying to model a hollow cylinder of known radius r, length l and density rho. The cylinder is fixed on a horizontal axle along its longest axis (l) and will have a force F applied tangentially to its surface and perpendicular to its axis, with negligible frictional...
22. ### Volume of a Hollow Cylinder vs Cylindrical Shell

In my physics lab, I am asked to calculate the volume of a hollow cylinder. The equation for the volume hollow cylinder below was given. Then, my curiosity made me wonder, is the volume of the hollow cylinder the same as the volume of a cylindrical shell used in calculus? At first though you...
23. ### Mechanics of Materials: Deformation of a Hollow Cylinder

Homework Statement Hollow Circular tube of Length (L) 600 mm is compressed by forces P (axially). Outside diameter (d2) is 75 mm. Inside diameter (d1) is 63 mm. Modulus of Elasticity (E) is 73 GPa Poisson's ratio (v) is 0.33. axial strain (ε) is 781 x 10-6 Find shortening of tube (δ). (This...
24. ### How to determine how much torque a hollow cylinder can take?

I'd like to calculate how much torque a hollow cylinder along its axis can take before it will start to buckle. The cylinder is held at one end, and the torque is applied equally in discrete intervals along the length of the cylinder. In the example image above, the hollow cylinder is mounted...
25. ### Electron's trajectory in positively charged hollow cylinder

How an electron moves when it is released from rest to a positively charged hollow cylinder? The hollow cylinder is finite and insulating. The electron is constrained to move only in z direction (into the center of the hollow cylinder). My thinking is that there is no electric field inside the...
26. ### Finding potential difference in a very long hollow cylinder

A very long hollow cylinder has inner radius A and outer radius B. It has a known unit charge per unit volume p. Find the difference in the electric potential a point on the axis and a point a distance A+D assuming A+D<B The diagram is in the url. It is #3...
27. ### Determination of moment of inertia of a hollow cylinder

Hi! I got the task to determine the moment of inertia of a hollow cylinder, however it's not about just measuring the mass and the inner and outer radius and putting it into the right formula, instead I should roll it down an inclined plane. 1. Homework Statement I'm only allowed to use the...
28. ### Magnetic field of hollow cylinder

Homework Statement A hollow cylinder with thin walls has radius R and current I, which is uniformly distributed over the curved walls of the cylinder. Determine the magnetic field just inside the wall and just outside, and the pressure on the wall. Homework Equations F = IL×B The Attempt at a...
29. ### 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...
30. ### Eccentrically hollow cylinder - Lagrangian (external forces)

Homework Statement I am providing a solution up to the point when I'm having a little issue with defining the generalized force. An eccentrically hollow cylinder of radius r rolls down a plane of inclination angle \alpha. Inside the cylinder, there is a cylinder-shaped hole of radius...
31. ### Ball performing small oscillations within a hollow cylinder

Homework Statement A small ball of radius r performes small oscillations within a hollow cylinder of radius R. What would be the angular frequency of the oscillations given that the rolling is without slipping? The angle between the radius connecting the center of the hollow cylinder to the...
32. ### Magnetic field of a hollow cylinder

Homework Statement Find an expression for the magnetic field of a hollow finite solenoid carrying uniform current with n turns (there is no top or bottom surfaces and the turns a very closely winded) at a point arbitrary P both inside and outside. Let's just say windings around a hollow pvc...
33. ### Magnetic field of a wire within a hollow cylinder.

1. Problem statement. 2. Known equations Amperes law, biot-savart law 3. Attempt. Just taking steps 1 at a time, I first drew a diagram then I found Jo in terms of I and R, and since it is a non uniform current I know that to find the current I use J = I / A substitute A for 2(pi)rdr, and...
34. ### Electric field at a radius outside of a hollow cylinder w/ a rod in it

Homework Statement Consider a hollow cylinder of radius 10 m., length 50 m., and charge 6 C., and a rod with radius 4 m., length 50 m., and charge -4 C. The rod is uniformly placed inside the center of the hollow cylinder. What is the electric field at radius = 15 m.?Homework Equations...
35. ### How do I calculate the maximum rotational speed of a hollow cylinder?

Hello! How do I calculate the maximum possible rotational speed of a thin walled hollow cylinder? In other words, at what rotational speed will it explode due to centripetal force? This picture shows the plane of rotation...
36. ### Is There a Magnetic Field Inside the Hollow Cylinder?

A few of my classmates and I are in a debate about whether or not there would be a magnetic field within a hollow cylinder. The problem has a solid cylinder with current running (throughout the solid) along its axis. Slightly off-center is a hollowed out 'hole' that runs the length of the...
37. ### Heat transfer via conduction from hollow cylinder to Bitumen

Hey all, not sure if this is where I'm supposed to post this question, but it is all about heat transfer. So this is part of my design project for my 4th year of chemical engineering. Problem Statement: A hollow cylinder 400 m long has hot combustion gases T = 500 Celsius flowing through...
38. ### 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...
39. ### 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...
40. ### 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...
41. ### Find Rho of Hollow Cylinder: Explaining Formula & Solving

Homework Statement rho of a hollow cylinder can be found with 4 measured quantity by the folowing formula, proof this formula Homework Equationsρ= 4.m ∏.(d²-D²).h d is the outside diameter and D the inside The Attempt at a Solution since it's my first time...
42. ### Magnetic field in asymmetric hollow cylinder

Homework Statement Cylinder of radius a and a cylindrical hole b < a is displaced a distance d in x-direction. Current density \textbf{J}=J_z\textbf{e}_z. Show that a uniform magnetic field inside the hole is \textbf{B}=\frac{\mu_0}{2}J_zd\textbf{e}_y Homework Equations Using previous...
43. ### Electric Potential of a hollow cylinder

Homework Statement A hollow cylinder of radius r and height h has a total charge q uniformly distributed over its surface. The axis of the cylinder coincides with the z axis, and the cylinder is centered at the origin, as shown in the figure. What is the electric potential V at the...
44. ### Radial Breathing Mode for hollow cylinder - formula needed

Hi, I'm trying to locate a formula for determining the radial breathing mode of a hollow cylinder. The dimensions of the cylinder of interest are approximately .5" OD x .4" ID x .5" L Any help would be greatly appreciated. Thanks!
45. ### Experiment testing Rotational Kinetic Energy with a hollow cylinder

1. I'm doing an experiment where I have a brass hollow cylinder, and I roll it down an inclined plane, and after each trial, I add fish weights to the inside of it to increase the mass. I'm testing the proportionality between mass and angular velocity, with my hypothesis being an inverse...
46. ### Find inner radius of hollow cylinder given inertia

Homework Statement A roll of toilet paper ( a partially hollow cylinder with R2=7.0 cm, M=320 g, I=6.0x 10 ^(-4) kg m is mounted on an axle. initially at rest, until a child grabs the end and starts running at a constant linear acceleration. part a) what is the inner radius (R1)Homework...
47. ### Electric field in a hollow cylinder

An infinitely long thick hollow cylinder has inner radius Rin and outer radius Rout. It has a non-uniform volume charge density, ρ(r) = ρ0r/Rout where r is the distance from the cylinder axis. What is the electric field magnitude as a function of r, for Rin < r < Rout? for this problem, when...
48. ### How friction affects rotational inertia of a hollow cylinder

How does friction affect the rotational inertia and angular velocity of a hollow cylinder rolling down an inclined plane? Assuming the cylinder isn't slipping
49. ### Exploring the Path of an Object in a Hollow Cylinder in Zero Gravity

My applied maths teacher proposed this question while we were having a discussion about gravitational effects. We do not know the answer. Given a hollow cylinder with a mass large enough to have its own gravitational effects, placed in zero gravity. If you propel an object into to an...
50. ### Moment of inertia of hollow cylinder, axis orthogonal to length

Hi, I am working through the Feynman lectures on physics and trying to calculate the moment of inertia stated in the title. (the taxis of rotation going through c.m., orthogonal to length). My approach is to slice the cylinder into thin rods along the length, using the parallel taxis theorem...