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. O

    I Calculating Cooling Effect in Gas Cylinder Expansion

    I'm building a gas supply system that will dump half the contents of a compressed gas cylinder of nitrogen in 10 minutes. I need to ensure the output delivery pressure doesn't fall below a certain limit because of cooling during the gas expansion. If the cooling effect is excessive, I will...
  2. JD_PM

    Software advice on fitting an orifice within a cylinder

    I have a stp file (PF does not support it so I cannot upload it here. If there is a way I can share it please let me know) of an orifice and I want to create a new file where the orifice is fit inside a cylinder. What software do you recommend me to use? Thank you! :)
  3. guyvsdcsniper

    Change in internal energy of a cylinder

    I believe I got the first part of this questions solved. For part b, we are asked to find the change in internal energy. We know ΔE=Q+W. The cylinder,gas and piston head are the system. The cylinder and piston head are well insulated, so there will be no head transfer, therefore Q=0. So now...
  4. Istiak

    Velocity along the cylinder axis

    Since the question says that "velocity along the cylinder axis" and "magnetic field perpendicular to the cylinder axis". So cross product of velocity and magnetic field becomes their magnitude. ##\vec v\times \vec B=||v|| \\ ||B||## So ##\vec F=qvB## ##mg=qv\frac{\mu_0 nI}{4\pi r}## At first...
  5. L

    An iron cylinder inside a solenoid

    From ##\oint_{\Gamma}\vec{H}\cdot d\vec{l}=\sum I## by Ampere's Law which gives ##H \Delta l=\Delta N\cdot i\Leftrightarrow H=n i## where ##n=## number of turns per unit length so ##i=\frac{H}{n}=\frac{10^3 A / m}{\frac{200}{0.2m}}=1 A##. Since ##\vec{H}=\frac{\vec{B}-\mu_0\vec{M}}{\mu_0}## we...
  6. M

    Torque exerted on rolling cylinder

    Hello, i have tried to calculate the acceleration (COM) of the cylinder (even though in the question they asked about the angular acceleration) and the answer is: 𝑎(𝑐𝑜𝑚)=𝐹(𝑟/𝑅−𝑐𝑜𝑠(𝑡ℎ𝑒𝑡𝑎))/(𝐼/𝑅2+𝑀) and my answer is with minus (I/R^2 - M) . in their solution they wrote in the torque equation-->...
  7. chwala

    Find the greatest and least values of Volume of cylinder

    $$V=πr^2h$$ $$V=πr^2(6-r)$$ $$\frac {dV}{dr}=12πr-3πr^2$$ For max/min value, $$\frac {dV}{dr}=0$$ $$12πr-3πr^2=0$$ $$3πr(4-r)=0$$ ##r=0## or ##r=4## $$⇒V_{max}= 32π$$ $$⇒V_{min}= 0$$, I do not think there is another way of doing...
  8. The Bill

    Thermal insulating materials suitable for making piston and cylinder?

    What materials would be suitable for a cylinder and piston that is thermally insulating, reasonably durable for low speeds and very slow cycle rates, and not be a carbon or silicon based polymer? I've been looking at manual lever operated espresso machines lately. Particularly ones that are...
  9. B

    I Surfaces wrapped around a cylinder for 3d printing

    Hi All, I am looking to determine how these Vases where modeled using maths on this webpage https://www.3dforprint.com/3dmodel/sine-wave-vase-generator/2116. It looks like the surface is parametrically defined and wrapped around a cylinder. Interestingly he mentions "Sine waves combine to...
  10. F

    I Electric field of uniformly polarized cylinder

    Hi all, I have a doubt when calculating the electric field of a uniformly polarized cylinder P along its longest axis. The cylinder has length L and radius a. Using Gauss's law: $$\int D\cdot ds = \rho_{f} =0 \, \, (eq .1)$$ The electric field inside of cylinder would be: $$E =-...
  11. T

    A Cylinder Rolling in a V-Groove

    I am confused because according to my solution the disk is already rotating at constant angular velocity. I have written the translational equilibrium on the horizontal and vertical component: ##N_1## and ##f_2## will have a positive horizontal contribution, while ##N_2## and ##f_1## will have a...
  12. Y

    B Terminal Velocity Equation in vertical cylinder with some fluid

    I just have a question that could you guys make an equation that expresses the terminal velocity based on followed condition? - When diameter increase, velocity decrease - velocity should change depending on both cylinder and sphere's diameter - We know every variable - The sphere is in...
  13. A

    Semi-circular cylinder and line charge

    Hi! I think I solved the problem but I would like you to take a look at it please, is it right? is there a better way to solve it?
  14. V

    Energy transformations in an IC engine cylinder

    A drop of fuel is ignited in an engine cylinder, that produces heat, light and sound energies from the chemical energy stored in the drop of oil. What I am not clear about is how heat energy gets transformed into mechanical work? I think the heat energy produced from ignition flows from burnt...
  15. A

    I Falling in an O'Neill Cylinder

    So I'm working on a project that involves the design of an O'Neill Cylinder, and there was a consideration that I had never made before. Say you are in a cylinder that is generating enough force for 1G in its spin. This means that while you are spinning, the motion means that your body is being...
  16. L

    A slanted cylinder full of liquid about to fall

    The cylinder will cease to be in equilibrium when the sum of the torques on the cylinder calculated with respect to the rightmost point of contact of the cylinder with the plane will be unbalanced. Now, the liquid is homogeneous and the cylinder has negiglible mass so the forces (normal force of...
  17. Istiak

    How to find coordinates of a system (I am taking cylinder now)?

    A person wrote that ##L=\frac{1}{2} m (\dot{r}^2+r^2 \dot{\phi}^2 +\dot{z}^2)## But, how to find equation of that coordinate system?
  18. LCSphysicist

    Motion of Rolling Cylinder in Fixed Cylinder: Confusing Constraint Condition

    The problem is a classical one, basically to find the equations of motion of cylinder of radius a inside a fixed cylinder of radius b, the cylinder that rolls rotate about its own axis in such way that it does not skid/slip. Now, the thing that is making myself confused is the constraint...
  19. V

    Electric flux through ends of an imaginary cylinder

    When I look at this question, I can see two possible values of electric flux depending on how I take the normal area vector for either ends ##A \text{ and } A^{'}##. What is wrong with my logic below where I am ending up with two possible answers? The book mentions that only ##2E\Delta{S}## is...
  20. A

    MHB Calculate Volume & Surface Area of a Cylinder Without Lid

    how to find volume and surface area of this without using the upper lid
  21. Istiak

    Calculate the volume change with gas temperature for this piston in a cylinder

    Solution attempt : Option : I am sure that my work is wrong. But, I must add solution attempt in PF that's why I just added that. How can I solve the problem?
  22. P

    Someone stole an argon cylinder today

    It is my fault. The cage/cabinet where all the cylinders are stored on the side of the building all have dial locks and I know it sounds really bad but my success rate with dial locks is close to zero. I was trying to swap out the 3/4 full argon cylinder for nitrogen but couldn't unlock it so I...
  23. LCSphysicist

    Magnetic field of a permanently magnetized cylinder

    I need to find the magnetic field of a permanently magnetized cylidner: In calculating the magnetic field, i find that it should be $M_{0} \mu / 2$ and $H = M_{0} / 2$ inside. I just want to make sure that i understand the concepts in this type of problems. Since $M = H \chi (1)$, does this...
  24. G

    Find the center of gravity of a combined cone and cylinder

    Could I please ask for help with the following: Given: The centre of gravity of a uniform solid right circular cone of vertical height h and base radius a is at a distance 3h/4 from the vertex of the cone. Such a cone is joined to a uniform solid right circular cylinder of the same material...
  25. uni98

    Electric field of wire and cylinder at one point in space

    I can calculate the fields generated by the cylinder and the wire but I don't know how to calculate their vector sum to evaluate it at point A. Cylinder field inside: ρR^2/2rε Cylinder field outside: ρr/2ε Field generated by the wire: λ/2πr I should break the fields into components but I don't...
  26. S

    Volume of the smaller part of a sliced cylinder

    I imagine the shape will be like this: and I need to find the volume of the shaded part. I am planning to use: ##V=\int A(y) dy## I tried to take the cross-sectional area A(y) to be triangle: and the base of the cylinder to be: So it means that the base of the triangle will fulfill the...
  27. Kaushik

    Find the frictional force acting on a solid cylinder

    This was the answer key provided: My questions are the following: if the force required for rotational equilibrium is more than the limiting static friction, then the body will rotate aka slip over the surface. When it slips, the frictional force will be kinetic and not static, right? If I...
  28. lenilein

    Massflow of steam to be supplied to a drying cylinder

    Good afternoon, I am trying to calculate the massflow of steam required in a cylinder used for paper drying but I think there is a bug in my calculation and I would love to get your help to find where the issue is! Saturated steam is continuously supplied to a cylinder. The steam condenses in...
  29. A

    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...
  30. H

    Comparing the kinetic energies among a solid sphere, a cylinder and a hoop

    I did the question as attached, so I think A and D are correct but the given answer is E. Where am I wrong? Thanks.
  31. J

    Electric Potential of point outside cylinder

    Edit: Below is my work but i believe i have chosen the wrong values of the separation vector in the s direction. Any ideas as to what it should be?
  32. davidgruty

    Friction of a rope around a cylinder

    Hi, We have a cylinder held by a rope . The rope holds it around its lower half. If the center of mass of the cylinder is not in the middle, but towards a side, a distance "a". How does this offset affect to the friction on the rope? or How big does "a" have to be so the cylinder starts...
  33. C

    Fire protection -- Water in a cylinder pressurized with Nitrogen

    I wondered if anyone could help, I work in the fire protection industry. We currently have a project using a pressurised cylinder. The cylinder hold 200 lites of water plus 40 litres of nitrogen gas as a propellant at 10.0 bar. I’m trying to work out once the 200 litre water volume has been...
  34. M

    Electric field of non-conducting cylinder

    a) I have calculated (1) λ = ρA = ρπr^2 = 2.49 * 10^-10 C/m and placed it into (2) yielding E = λ / (2πεx^2) = 106.73 N/C. This doesn't seem to be correct by the feedback, however. b) Here just to consider the proportion of the cylinder mass constrained by y.
  35. rxh140630

    Optimization problem - right circular cylinder inscribed in cone

    Please I do not want the answer, I just want understanding as to why my logic is faulty. Included as an attachment is how I picture the problem. My logic: Take the volume of the cone, subtract it by the volume of the cylinder. Take the derivative. from here I can find the point that the cone...
  36. Y

    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...
  37. Marilyn67

    I Unravelling the Mysteries of the Kerr Black Hole Ergosphere

    I have a problem understanding what is going on in the region called the ergosphere of a "fast" Kerr black hole. - Relativity teaches us that no frame of reference can have relative displacements greater than the speed of light, ok. - The ergosphere of a fast Kerr black hole can contain light...
  38. ezfzx

    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...
  39. ricles

    Cylinder rotating on a support

    This comes from a list of exercises, and setting ##m_1 = 5.4kg##, ##m_2 = 9.3kg## and ##F=5N##, the answer should yield ##2.19m/s^2## (of course, supposing the answer is right). If I knew the radius ##R## of the cylinder, I could find its momentum and use it to find the linear acceleration...
  40. C

    Moment of Inertia of a Solid Cylinder With a Wedge Removed

  41. archaic

    Cylinder rolling due to magnetic force

    Hello! The magnetic force is to the right. ##I_c## is the moment of inertia of the cylinder. For the net force on the centre of mass, I have the frictional and magnetic forces ##F=F_B-f##. I know that ##F_B## is ##IdB##. I also know that ##rf=I_c\alpha=I_c\frac ar##, so that...
  42. Hamiltonian

    B Volume of paraboloid in a cylinder

    the equation of a parabola that is obtained by taking a cross-section passing through the center of the paraboloid is ##y = ax^2## breaking the paraboloid into cylinders of height ##(dy)## the volume of each tiny cylinder is given by ##\pi x^2 dy## since ##y = ax^2## we have ##\pi (y/a) dy##...
  43. K

    Surface integral: Calculate the heat flow from a cylinder

    Hi, I am trying to calculate the heat flow across the boundary of a solid cylinder. The cylinder is described by x^2 + y^2 ≤ 1, 1 ≤ z ≤ 4. The temperature at point (x,y,z) in a region containing the cylinder is T(x,y,z) = (x^2 + y^2)z. The thermal conductivity of the cylinder is 55. The...
  44. E

    Finding the inductance of a rotating cylinder shell

    First, the correct answer is μ0*π*R^2. I tried to look at the cylinder like it was a solenoid, this technique was used in my class. Then I tried to find the current of the solenoid, to do that I looked at a piece of a solenoid with a legnth of dz, then: I=dq/dt=(2πRσ*dz)/(2π/ω)=ω*R*σ*dz. The...
  45. M

    Why Is Angular Momentum Not Conserved When a Cylinder Moves on a Stopping Board?

    I've been trying to solve it mainly through conservation of momentum and angular momentum, appareantly it's not correct. My idea was: I, Moment of inertia = 0.5*m*r^2 L1, initial angular momentum = I * v/r After a board stops, the change in it's momentum is M*v, so the impulse of torque on the...
  46. karush

    MHB Apc.2.8.1 ap vertical circular cylinder related rates

    $\tiny{2.8.1}$ The vertical circular cylinder has radius r ft and height h ft. If the height and radius both increase at the constant rate of 2 ft/sec, Then what is the rate at which the lateral surface area increases? \een $\begin{array}{ll} a&4\pi r\\ b&2\pi(r+h)\\ c&4\pi(r+h)\\ d&4\pi rh\\...
  47. A

    Ideal gas: two tanks connected by a cylinder

    I ASSUME THAT THE PRESSES OF THE TWO CONTAINERS WILL BE EQUAL IN THE FINAL (STATIONARY REGIME). SO Pa = Pb naRTa/V = nbRTb/V naTa = nbTb Than , I just need to set up a system My question is , so, will the two pressures at the end be the same? And as for the temperatures, can I also say...
  48. Z

    Cylinder in a heat bath @ 0C contains water and ice & is compressed

    You can use the change in volume to find how much ice turned into water, and then find the energy required to melt that ice - that I have no problems with. But then work done by piston = change in internal energy of ice/water combination (which we found) + heat released to the bath. And we...
  49. S

    Number of balloons that can be filled from a gas cylinder

    ##\frac{P_{cylinder}.V_{cylinder}}{P_{balloon}.V_{balloon}}=\frac{n_{cylinder}.R.T}{n_{balloon}.R.T}## ##\frac{n_{cylinder}}{n_{balloon}}=\frac{4 \times 10^4 \times 2.5 \times 10^7}{7.24 \times 10^3 \times 1.85 \times 10^5} \approx 746## But the teacher said I should take the volume of gas...
  50. M

    "KICK" force exerted from a hydraulic cylinder

    Hello,I am building a press that will squeeze hot steel ,back off .5"push hot steel in further and repeat.The cylinder is 4" bore , 1.375"rod and travel is 8" (the majority of squeeze will be at 5"of extension)at a max of 2500PSI. my question is when putting @15 tons straight down what will the...
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