What is Cylindrical: Definition and 821 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. A

    First Order Differential Equation in Cylindrical Coordinates

    Consider cylindrical coordinates p = (x^2 + y^2)^.5  angle = arctan(y=x). Consider your curve to be specifi ed by z(p). Write down a ( first order) diff erential equation governing z(p) please help!
  2. G

    Potential of Dipole in Cylindrical coordinates

    Homework Statement I have been given the problem of finding the potential of a dipole in cylindrical coordinates. The only way that comes to my mind is to extract the dipole term from the multipole expansion of the potential of an arbitrary charge distribution in cylindrical coordinates. But I...
  3. B

    Triple integrating cylindrical coordinates?

    Homework Statement Integrate the function f(x,y,z)=−4x+3y over the solid given by the figure below, if P = (5,1,0) and Q = (-5,1,2). [PLAIN]http://img259.imageshack.us/img259/958/sfig1681g1.gif Homework Equations x=rcos(\theta) y=rsin(\theta) r=sqrt(x^2+y^2)The Attempt at a Solution i...
  4. D

    Related Rates - Cylindrical Pools

    Homework Statement 2 Cylindrical pools are filled simultaneously at the same rate, 1m3/min. The smaller pool has radius 5m and the water level rises at a rate of 0.5m/min. The larger pool has a radius 8m. How fast is the water level rising in the larger pool? Homework Equations V =...
  5. P

    Divergence in cylindrical coordinates

    Homework Statement Calculate the divergence of the vector function f = a/s^2 (s hat) where s is the radial distance from the z axis, expressed in cylindrical coordinates. Homework Equations The Attempt at a Solution Using the divergence theorem I relate the volume integral of...
  6. D

    Converting vector in cartesian to cylindrical coordinates

    Homework Statement This seems like a trivial question (because it is), and I'm just not sure if I'm doing it right. I have vector in cartesian coordinate system: \vec{a}=2y\vec{i}-z\vec{j}+3x\vec{k} And I need to represent it in cylindrical and spherical coord. system Homework...
  7. T

    SHM on a cylindrical trough

    SHM on a cylindrical trough (solved?) Homework Statement A solid sphere of radius R rolls without slipping in a cylindrical trough of radius 5R. Show for small displacement, the sphere executes SHM with period T=2\pi \sqrt{\frac{28R}{5g}}...
  8. A

    Vector fields in cylindrical and spherical coordinates

    I am reading the Wikipedia entry http://en.wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates" . There, in particular I see this: Time derivative of a vector field To find out how the vector field A changes in time we calculate the time derivatives. In cartesian...
  9. Q

    Maximizing the height of a bullet in cylindrical coordinates

    Homework Statement A gun can fire shells in any direction with the same speed v0. Ignoring air resistance and using cylindrical polar coordinates with the gun at the origin and z measure vertically up, show that the gun can hit any object inside the surface z = \frac{v_{0}^{2}}{2g} -...
  10. V

    Force Required to pull a cylindrical cover

    1. Homework Statement A plastic shade cover is almost 290 ft in length and 150 ft in breadth. It is wrapped around a cylindrical wooden rod which is at a height of 7 ft from the ground. The cover is pulled by nylon/plastic ropes to the right to its complete length of 290 ft. Consider the...
  11. V

    Tangential Force to pull a cylindrical plastic cover

    I would like to know views on the force required to pull a cylindrical cover. A plastic shade cover is almost 290 ft in length and 150 ft in breadth. It is wrapped around a cylindrical wooden rod which is at a height of 7 ft from the ground. The cover is pulled by plastic ropes to the right to...
  12. N

    Energy of Coaxial Cylindrical Shells

    Homework Statement Calculate the energy per unit length for two long coaxial cylindrical shells, neglecting end effects. The inner and outer cylinders have radii a and b, and linear charge densities λ and -λ, uniformly distributed on the surface, respectively. 2. The attempt at a solution...
  13. D

    Computation of forces of liquid sloshing inside a cylindrical tank

    Hello, I am trying to develop a formula to calculate the force of water sloshing against the inside of a cylinder. While there has been a lot of development of baffles and structures designed to minimize the effect of sloshing liquids in tanks, we are doing some studies of liquids in small...
  14. J

    Concentric Cylindrical Conducting Shells Potential Difference

    Homework Statement An infiinitely long solid conducting cylindrical shell of radius a = 4.5 cm and negligible thickness is positioned with its symmetry axis along the z-axis as shown. The shell is charged, having a linear charge density λinner = -0.35 μC/m. Concentric with the shell is another...
  15. F

    Electric Field in Cylindrical Insulator

    Homework Statement We have a solid cylinder of radius R0, and it has a uniform charge density p. The length is much greater than its radius, so it appears almost infinite. Homework Equations Find the electric field inside the cylinder where r<R0 and outside the cylinder where r>R0...
  16. R

    Charged particles and cylindrical coordinate system

    A charged particle in a magnetic field is spiralling along a path defined in cylindrical coordinates by r = 1 m and θ = 2z rad (where z is in meters). The speed along the path is constant at 3.87 km/s. What is the z-component of the velocity, vz, in cylindrical coordinates? My attempt...
  17. S

    Potential of Concentric Cylindrical Insulator and Conducting Shell

    Potential of Concentric Cylindrical Insulator and Conducting Shell...Please Help Homework Statement An infinitely long solid insulating cylinder of radius a = 3.6 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ =...
  18. M

    Simple Projectile in Cylindrical Coordinates

    Homework Statement A gun can fire shells in any direction with the same speed v_{0}. Ignoring air resistance and using cylindrical polar coordinates with the gun at the origin and z measured vertically up, show that the gun can hit any object inside the surface z = \frac{v^{2}_{0}}{2g} -...
  19. W

    Line Charge and Charged Cylindrical Shell

    Homework Statement 1. Homework Statement An infinite line of charge with linear density λ = 7.5 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.9 cm and outer radius b = 4.9 cm. The insulating shell is uniformly charged with a volume density of ρ =...
  20. A

    What is the linear charge density of the insulating shell in this problem?

    Homework Statement An infinite line of charge with linear density λ = 7.5 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.9 cm and outer radius b = 4.9 cm. The insulating shell is uniformly charged with a volume density of ρ = -612 μC/m3. What is λ2...
  21. Telemachus

    Cylindrical coordinates to cartesian coordinates

    Homework Statement Hi there. Hi have in cylindrical coordinates that \theta=\displaystyle\frac{\pi}{3}, and I must make the graph, and take it into cartesian coordinates. How should I do? I've tried this way: \begin{Bmatrix}x=r\cos\displaystyle\frac{\pi}{3}\\y=r\sin\displaystyle\frac{\pi}{3}...
  22. P

    Hamiltonian in cylindrical coordinates

    Hi, I'm trying to find the Hamiltonian for a system using cylindrical coordinates. I start of with the Lagrangian L=\frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2+\dot{z}^2)-U(r,\theta,z) From that, using H=\sum p\dot{q}-L...
  23. S

    Divergence operator in cylindrical & sherical

    look for some proof for the formula of the divergence operator in cylindrical & spherical coordinate is there any on the net ? TNX ! the formula here: http://hyperphysics.phy-astr.gsu.edu/hbase/diverg.html
  24. S

    Confirming Gauss Theorem with Cylindrical Co-ordinates

    How would you go about confirming the Gauss theorem using cylindrical co-ordinates? Could it be just like Cartesian co-ordinates, or what is the transformation?
  25. S

    Differential Cartesian Coordinates Into Cylindrical Coordinates

    Has to convert B6-1 into B6-2 Source Transport Phenomenon 2nd ed -
  26. N

    Cylindrical shells question

    1. From Stewart Calculus and Concepts 4th edition, page 454 #15 Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. 15. y=4x-x^2, y=; rotate about x=1 Homework Equations 3. I was able to...
  27. C

    Hom. heat equation in cylindrical coordinates using Fourier & Laplace transforms

    I'm trying to solve the homogeneous heat equation of a semi-infinite cylinder in cylindrical coordinates for a semi-infinite cable (no theta dependence): \frac{\partial U}{\partial t}=D\left(\frac{\partial^{2} U}{\partial r^{2}}+\frac{1}{r}\frac{\partial U}{\partial r}+\frac{\partial^{2}...
  28. Q

    Water valve for a cylindrical container

    I need help designing a mechanism for quickly releasing water through a tiny hole on one end of a thin cylindrical pole by a switch/button/etc on the other end. I have thought of one way to do this and drew an illustration, which is in the attachment. But I'm not sure if when the bar is covering...
  29. D

    Cylindrical Surface Charge Density

    Homework Statement The figure shows a portion of an infinitely long, concentric cable in cross section. The inner conductor carries a charge of 6 nC/m and the outer conductor is uncharged. (part 5 of 6) What is the surface charge density inside the hollow cylinder? Answer in units...
  30. S

    Understanding the Stress Induced in Cylindrical Nanowires: Equations 12-13

    Hi, I came across a piece of maths with which I am struggling to find info on. It has to do with the stress induces in a cylindrical shaped wire (nanowire to be precise). The article where the maths appear is attached. The specific problem is in equations 12 through 13. Thanks
  31. A

    Cylindrical coordinate convertion

    Homework Statement cylindrical coordinates: r=2cscƟ, give both rectangular and spherical cordinates Homework Equations I know this: From rectangular to cylinder z=z r2=x2+y2 tanƟ=y/x From Cyl to rectangle x=cosƟ y=sinƟ z=z From cyl to spherical Ɵ=Ɵ...
  32. J

    What is the Intensity of Light from a Cylindrical Source?

    I'm working on a project and don't have access to a physics book so I'm asking for help. I need to find the intensity of light at a certain distance over a given rectangular area from a cylindrical light source. The source is 18in long, 1in in diameter, and outputs 2.6watts. I need the light...
  33. J

    The cylindrical chamber electric field

    In the cylindrical chamber, the voltage is applied to a very thin wire, a few mills of an inch in diameter, stretched axially at the center of the cylinder. The cylinder wall is usually grounded. The electric field is, in this case, E=\frac{V_{0}}{Ln(b/a)r} where a = radius of the central...
  34. C

    Converting Frenet TNB Coordinates to Cylindrical Coordinates

    Hi all, I have a circular helix with any point on the helix defined using the Frenet tnb triad. t- tangent, b- binormal and n-normal acting towards the axis of the host circular cylinder. The tangent of the helix t is oriented at angle A with respect to the base of the cylinder. Now...
  35. N

    Cylindrical coordinate sysyem-Gambit

    hi, i am doing a simulation of 3D problem.i want to draw it cylindrical coordinate sysyem(r,z, o).but gambit shows X , Y , Z Coordinate . how to do in cylindrical co ordinate , will it show r, z and o axis ? i opened the Tools command button then i changed the co ordinated system to...
  36. T

    If you spin a cylindrical magnet will anything happen to its magnetic field?

    If the magnetic poles are at the ends of a perfectly symmetric permanent magnet cylinder and and you spin the cylinder around its central axis, will anything happen to the magnetic field? I feel like something should happen since the magnetic domains are revolving around, but the field is...
  37. M

    Evaluate the integral by changing to cylindrical coordinates.

    I wish I knew how to type this out with the proper symbols but here it goes. It says to change the following to cylindrical coordinates and evaluate (x^2 + y^2)^(1/2) dz dy dx where -3<=x<=3, 0<=y<=(9-9x^2)^1/2, 0<=z<=9-x^2-y^2Homework Equations The Attempt at a Solution I got 162pi/5 Would...
  38. F

    What is the Pressure on the Circular Side of a Cylindrical Drum of Molasses?

    Homework Statement A cylindrical drum of molasses is 25% full and laying on its side. The dimension sof the drum are 4 ft. height and 1.5 ft. radius. Find the pressure on the circular side (end) of the drum) created by the molasses. Weight density of molasses = 100 lb/ft^3 Homework...
  39. F

    Calculating a volume through cylindrical coordinates

    Just a question. Say you have a function, which in cylindrical coordinates it gives that \int\int\int \sqrt{x^2 + y^2} dx dy dz which is \int\int\int r^2 dr d/theta dz i want to find in cylindrical coordinates, in the area limited by the functions : x^2 + y^2 = z^2 z is greater or equal than...
  40. T

    How to find the unit vector in cylindrical coordinates

    So I'm trying to find out what the procedure is to convert a cartesian unit vector to a cylindrical unit vector. Any thoughts?
  41. I

    Capacitance and inductance of cylindrical shell

    i am having trouble with finding inductance and capacitance of a cylindrical shell with gap. say inner radius is a, outer radius is b, and filling dielectric between a and b, and its not a exact circle which have a small gap say d. its like a split ring but only one shell. How can i...
  42. B

    Vector analysis in cylindrical coordinate system

    if a point in cylindrical cordinates is A=(r1,\theta1,z1) and another point is B=(r2,\theta2,z2) (if ar,a\theta,az are unit vectors) then the position vector of A is = r1<ar>+\theta1<a\theta>+z1<az> and the position vector of B is = r2<ar>+\theta2<a\theta>+z2<az> so vector BA=...
  43. B

    Exploring Changes in Gravity: Cylindrical Space Station

    1. Homework Statement cylindrical space station - large diameter, thin walled - radius r, mass M rotating in deep space, no gravity 1)radial spokes of negligible mass connect the cylinder ti the centre of motion. Astronaut mass m climbs a spoke to the centre. What is the fractional change...
  44. A

    Resistance of Cylindrical Conductor

    Homework Statement A circular disk of radius r and thickness d is made of material with resistivity p . Show that the resistance between points a and b (Fig. attached)is independent of r and is given by R=πp /2d Homework Equations R= p L / A where L and A are length and section...
  45. F

    Convert Cartesian To Cylindrical Limits

    Homework Statement Hi I am converting from Cartesian co-ordinates to cylindrical co-ordinates systems and can do the conversion fine, but am unsure about how to convert the limits. Q) Region V is given in Cartesian by: F(x,y,z) = xi+yj+z(x^{2}+y^{2})k Where x^{2}+y^{2} \leq 1...
  46. _maxim_

    Cylindrical glass boll (sealed, containing solvent) for RF detector

    Dear all, here's my first request for a little help (maybe also in finding the proper subforum...) I'm working as developer and scientific consultant in a lab for Nuclear Magnetic Resonance at high field (> 21 Tesla), and I have to create a suitable probe for checking the stability of a...
  47. G

    Solving a Cylindrical Curl Integral Question

    Homework Statement Question Attached Homework Equations The Attempt at a Solution So here I'm attempting b), I know \nabla \times \vec F\ is the curl, which in this case is defined by the matrix \left[ \begin {array}{ccc} x&y&z\\ \noalign{\medskip}{\frac {d}{{\it dx}}}&{\frac {d}{{\it...
  48. M

    Problem Deriving Volume of a Cylindrical shell

    I have seen the derivation for the formula: h2(pi)rdr used in math textbooks. However, earlier today I had a physics problem where I needed to use the volume of a cylindrical shell of inner radius r and outer radius dr+r and length h. without remembering the formula I tried to derive it...
  49. K

    Calc 3- Triple Integral using cylindrical coordinates

    Use cylindrical coordinates to evaluate the triple integral , sqrt(x^2+y^2) where the region integrated is the solid bounded by the circular paraboloid z=9-16(x^2+y^2) and the xy-plane. I'm having trouble deciding what the bounds for r would be.
  50. A

    Gauss' Law: Cylindrical sheath

    Homework Statement A non-conducting, infinitely long, cylindrical sheath has inner radius r=10 m, outer radius r=15 m and a uniform charge density of 9 nC/m^3 spread throughout the sheath. Magnitude of electric field at r=5, r=12, r=17? Homework Equations Q=rho(Volume) and phi=EA...
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