Cylindrical Definition and 821 Threads

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

    Need help getting started Cylindrical centrifuge

    A cylindrical centrifuge of radius 1m and height 2m is filled with water to a depth of 1m. As the centrifuge accelerates, the water level rises along the wall and drops in the center. (a) Find an equation of the parabola when the water level rises in terms of h, the depth of water at its...
  2. J

    Cylindrical Coordinate System. Please check my answer

    Homework Statement (a) In cylindrical coordinates , show that \hat{r} points along the x-axis is \phi = 0 . (b) In what direction is \hat{\phi} if \phi = 90° Homework Equations The Attempt at a Solution here is my solution. for a. \vec{r} = \rho cos \phi \hat{i} + \rho...
  3. J

    Solving cylindrical coordinates system, just want to check my answer

    Homework Statement .. Here is the question; In cylindrical coordinate system , (a) If r = 2 meters , \varphi = 35° , z = 1 meter , what are x,y,z? (b) if (x,y,z) = (3,2,4) meters, what are (r, \varphi, z) Homework Equations x = r cos \varphi y = r sin \varphi z = z r =...
  4. M

    Electric field outside a long cylindrical shell

    Homework Statement A long cylindrical shell of radius R = 12.3 cm carries a uniform surface charge 4.60E-6 C/m2. Using Gauss's law find the electrical field at a point p2 = 16.5 from the center of the cylinder. Homework Equations EA=q/epsilon0 The Attempt at a Solution This is what...
  5. J

    Volumes By Cylindrical Shells (2 questions)

    Homework Statement HEY EVERYONE! Sorry for putting up another quesiton, but I'm almost done my assignment for the week. I understanding volumes by cylindrical shells, but i get confused when rotating about a line that's not the x or y axis. I have uploaded the two questions. Homework...
  6. C

    Chain rule and cylindrical coordinates

    I'm trying to understand this one derivation but this one part keeps messing me up; theta = tan^-1 (y/x) r^2 = x^2 + y^2 d theta/ d x = y/ (x^2 + y^2) how did they get this line?
  7. M

    Thermodynamics: cylindrical figures contains a gas

    Homework Statement A cylindrical figures contains a gas and we have a piston that is capable of changing the gases volume. Initial state: V0=1l P0=10^5p T=300°K We pressurize on the piston that has a mass m=300g and a surface S=20cm^2. The new temperature T1=540°K...
  8. N

    Six cylindrical magnets arranged N-S-N-S-N-S formed into a ring hold shape?

    I was wondering why, when I arrange six cylindrical magnets, about 1inch long and 1/5th inch wide each (neodymium magnets) in a hexagon shape by arranging them into a chain of N-S-N-S-N-S (top or bottom... with the other end obviously being opposite in arrangement) and connecting them into a...
  9. Q

    Consider a long cylindrical dielectric shell of inner cross-sectional

    Homework Statement consider a long cylindrical dielectric shell of inner cross-sectional radius a , outer radius b, and constant volume charge density raw zero . THe potenials of the ineer and outer surfaces of the cylindrical shell are held at potentials 0 and V respectively as shown in the...
  10. J

    Forces on multiple cylindrical magnets stacked

    I am trying to calculate the forces between ten small cylindrical magnets stacked (inside a tube so they cannot flip/shift) so that consecutive magnets are repelling. The bottom magnet is attatched to the bottom of the tube with, let's say, the positive pole facing up. Then the second has a...
  11. K

    Triple integral & cylindrical coordinates

    Homework Statement When you are doing a triple integral and convert it to cylindrical co ordinates, how do you find the new ranges of integration? I understand the new range of z, if z is between f(x,y) and g(x,y), you just sub in x = r cos θ and y = r sin θ to find the new functions...
  12. P

    A 2cm diameter cylindrical solenoid of 10 loops and 20cm long

    Homework Statement A 2cm diameter cylindrical solenoid of 10 loops and 20cm long is in a perpendicular magnetic field of 0.7Tesla directed away from you. The field increases to 2.7Tesla in 100ms. The loop has 8Ω. What is the EMF? What is the current? What is the magnetic field of the...
  13. I

    Spherical & Cylindrical Coordinates

    Are spherical and cylindrical coordinate systems only a physical tool or is there some mathematical motivation behind them? I assume that they can be derived mathematically, but multivariable calculus texts introduce them and state their important properties without much background information...
  14. M

    Solving Cylindrical Coordinate Equation with $\delta$ Functions

    Homework Statement Solve in cylindrical coordinates -m\delta(z)\delta(\rho-a)=\partial^2_z A(z,\rho)+\partial^2_\rho A(z,\rho)+\frac{1}{\rho}\partial_\rho A(z,\rho)-\frac{1}{\rho^2}A(z,\rho) Where \partial_i is the partial derivative with respect to i. Homework Equations It is...
  15. M

    Orthogonality Relationship for Legendre Polynomials in Cylindrical Coordinates

    Hello everyone, Sorry if this is in the wrong sub-forum, I wasn't sure exactly where to place it. I was wondering if there is an orthogonality relationship for the Legendre polynomials P^{0}_{n}(x) that have been converted to cylindrical coordinates from spherical coordinates, similar to...
  16. C

    Why Does the Cylindrical Wall Heat Equation Solution Include Logarithms?

    I'm a little bit rusty with my differential equations, and can't seem to see how solving for 1/r d/dr (r dT/dr)=0 has the solution T(r)=C_1*ln⁡(r)+C_2
  17. H

    Combination of cartesian and cylindrical coordinate system

    Hi, I have to solve a numerical problem namely how air is flowing first through a porous medium followed by streaming of the air coming out of the porous medium in a very narrow channel flowing to the ambient (journal porous air bearing). This problem can be described with the use of two...
  18. I

    Surface Integral of a Cylindrical Surface

    Homework Statement What is the integral of the function x^2z taken over the entire surface of a right circular cylinder of height h which stands on the circle x^2 + y^2 = a^2 Homework Equations The Attempt at a Solution My problem is writing the equation in cylindrical form if...
  19. M

    Maxwell 3D eddy current simulation for a cylindrical wire

    Hi, I am trying to do a simulation for the current distribution in a cylindrical conductor wire using MAXWELL 3D. I used eddy current solver and assigned excitation of current 1A at both ends of the round wire. (I set length L=2mm, radius R=1mm) The field plot seems ok, having highest current...
  20. M

    A frog is riding on the top of a cylindrical piece of wood floating in

    A frog is riding on the top of a cylindrical piece of wood floating in still water. Half of the wood, with a diameter of 4 cm and length 20 cm, is immersed in water. The density of water is 1 gm/cc. What is the mass of the wood along with the frog? After the frog slowly goes into the...
  21. H

    Magnetic Field in a Cylindrical Conductor

    Homework Statement A cylindrical conductor of radius R = 2.49 cm carries a current of I = 2.17 A along its length; this current is uniformly distributed throughout the cross-section of the conductor. Calculate the magnetic field midway along the radius of the wire (that is, at r = R/2)...
  22. Q

    How to visualize in spherical and cylindrical coordinates

    Homework Statement i just want to know how to visualize in spherical and cylindrical coordinates I am really having a rough time doing that for example why is that when we keep r constant we get a sphere and θ constant a cone why?? Homework Equations The Attempt at a Solution
  23. K

    Another change in unit vectors (d(r-hat)/d(theta)) in Cylindrical

    Homework Statement Does anyone know what d(r-hat)/d(theta) in Cylindrical coordinates is? Homework Equations The Attempt at a Solution I'm pretty sure its -(theta-hat) but I'm not sure, any help? Thanks so much
  24. K

    Finding the volume using cylindrical coordinates

    Homework Statement Use cylindrical coordinates to find (a) the volume and (b) the centroid of the solid S bounded above by the plane z=y and below by the paraboloid z=x2+y2. Homework Equations V= ∫∫∫dv x= r cos θ, y=sin θ, z=z The Attempt at a Solution For the first integral I got...
  25. D

    Cylindrical Coordinates Domain

    Homework Statement Let W be the region between the paraboloids z = x^2 + y^2 and z = 8 - x^2 - y^2 Homework Equations The Attempt at a Solution for each domain, 0 ≤ z ≤ 8 0 ≤ r ≤ 2 0 ≤ θ ≤ 2\pi So... \int^{2\pi}_{0}\int^{2}_{0}(8-2r^{2})r drdθ
  26. E

    Changing rectangular to cylindrical

    Change (-3,3,3) to cylindrical coordinates. I'm doing r^2 = x^2 + y^2, which I find r = sqrt(18) = 3radical(2) tan(theta) = 3/-3 = 1, so theta = -pi/4 = 7pi/4. z = 3 Cylindrical coordinates are (3sqrt(2),7pi/4,3). Is this right? Correct answer to the homework says 3pi/4 for the angle, for...
  27. X

    Center of mass of cone using cylindrical coordinates

    Homework Statement Set up intergral expression for center of mass of a cone using cylindrical coordinates with a given height H and radius R Homework Equations rdrddθdz is part of the inter grand. M/V=D volume of cone is 1/3π(r^2)H The Attempt at a Solution dm=Kdv dv=drdθdx K...
  28. K

    Cylindrical Container Minimum Cost

    Homework Statement An industry is to construct a cylindrical container of fixed volume V, which is open at the top of. Find the quotient of the height by radius of the base of the container so that manufacturing cost can be minimal, given that the unit area of the base costs (b) twice the...
  29. V

    Cylindrical to rectangular coordinates

    Hi sorry,I still need some help on converting coordinates >.< Set up an integral in rectangular coordinates equivalent to the integral ∫(0 ≤ θ ≤ \frac{∏}{2})∫(1 ≤ r ≤ \sqrt{3})∫(1 ≤ z ≤ √(4-r2)) r3(sinθcosθ)z2 dz dr dθ Arrange the order of integration to be z first,then y,then x. I...
  30. M

    Triple Integral converting from cylindrical to spherical

    Homework Statement Convert the following integral to an equivalent integral in spherical coordinates. Do NOT evaluate the integral. ∫∫∫ r^3 dz dr dtheta limits of integration pi/4<theta<pi/2 0<r<2 0<z<√(2r-r^2) Homework Equations z=pcos(theta) r^2=x^2 +y^2 p^2=x^2 +y^2...
  31. D

    Triple Integrals with Cylindrical Coordinates

    Homework Statement Evaluate the integral, where E is the solid in the first octant that lies beneath the paraboloid z = 9 - x2 - y2. ∫∫∫(2(x^3+xy^2))dV Homework Equations x=rcosθ y=rsinθ x^2+y^2=r^2 The Attempt at a Solution θ=0 to 2π, r=0 to 3, z=0 to (9-r^2)...
  32. T

    Infinitely extended cylindrical region in free space has volume charge density

    Homework Statement An infinitely extended cylindrical region of radius a>0 situated in free space contains a volume charge density given by: [ ρ(r)= volume charge density ρo=constant=initial volume charge density radius=a>0 ρ(r)=ρo(1+αr^2); r<=a ] with ρ(r)=0 for r>a Questions...
  33. S

    Finding Volume with Cylindrical Shells

    Homework Statement Using cylindrical shells, find the volume obtained by rotating the region bounded by the given curves about the x-axis. x= (y^2) +1 x= 0 y=1 y=2 Homework Equations 2∏ ∫ rh The Attempt at a Solution 2∏ ∫ from 1 to 2 (y^2) + 1 I'm not sure...
  34. S

    Volume using Cylindrical Shells

    Homework Statement Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves y = 4+3x-x^2 and y+x=4 about the y-axis. Below is a graph of the bounded region. Homework Equations V = ∫ a to b 2 pi x f(x) The Attempt at a Solution...
  35. I

    Volumes with Cylindrical Shell Method

    Homework Statement Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. y= 4x2, y=-2x+6 Homework Equationsy= 4x2, y=-2x+6 These 2 equations meet at x= -3/2 and x=1 integral from a to b of...
  36. I

    A closed cylindrical can of fixed volume V has radius r

    (a) Find the surface area, S, as a function of r. S = 2*pi*r^2 + 2*pi*r*h I know how the 2pi(r)^2 is found, but where does the 2*pi*r*h come from? (b) What happens to the value of S as r goes to infinity? S also goes to infinity. As r increases, S increases. (c) Sketch a graph of...
  37. S

    Ferromagnetism, what's happening in cylindrical magnets?

    I've a question on ferromagnetism. I've been trying to simulating the field around a rod shape magnet, cylindrical in shape and N on one end and S on the other. I just wonder if one would expect the the B, the magnetic flux density, to be uniform in magnet. I used comsol to simulate and get...
  38. jegues

    Flux out of a Cylindrical Cable

    Homework Statement A coaxial transmission line has an inner conducting cylinder of radius a and an outer conducting cylinder of radius c. Charge ql per unit length is uniformly distributed over the inner conductor and -ql over the outer. If dielectric \epsilon_{1} extends from r=a to r=b and...
  39. D

    Potential of Concentric Cylindrical Insulator and Conducting Shell

    An infinitely long solid insulating cylinder of radius a = 5.3 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 45 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 14.2 cm, and...
  40. D

    Electric Flux through Cylindrical Surface

    An infinite line of charge with charge density λ1 = -5 μC/cm is aligned with the y-axis as shown. I am pretty sure you are supposed to use Gauss' Law so I tried just calculating the total enclosed charge and dividing it by epsilon naught, but it's not working. I think maybe I have to use...
  41. B

    Using Gauss' theorem ande exploiting the cylindrical symmetry of the system, show

    Homework Statement A wire of length L and negligible transverse dimensions, made of an insulating material, is placed on the x-axis between the origin and the point (L,0). The wire has a uniform line charge density lambda. using Gauss' theorem and exploiting the cylindrical symmetry of...
  42. S

    Magnetic field of cylindrical magnet

    Hi, I wanted to calculate the magnetic field of a cylindrical magnet at a point P (r,ɵ,z). The magnet can be at the origin or anywhere convenient. Preferably the axis of the magnet is aligned with the z axis. The magnet is of radius r_m and height h_m. The remanent flux density of the...
  43. H

    Gradient of a tensor in cylindrical coordinates

    Hi all, I have been struggling (really) with this and hope someone can help me out. I would just like to compute the gradient of a tensor in cylindrical coordinates. I thought I got the right way to calculate and successfully computed several terms and check against the results given by...
  44. A

    Electric field in a cylindrical capacitor

    Homework Statement A very long question. First let's solve the case for E-field between outer and inner capacitor. Homework Equations The Attempt at a Solution Since there is no charge between the 2 capacitors, the charge density is zero. By Gauss's law, the integral is zero...
  45. C

    Currents in a Wire and a Cylindrical Shell

    Homework Statement Hello PF, first time poster here. I don't normally ask for help on the internet, especially for homework, but I've visited this website several times and I've seen nothing but good as I've looked at everyone else being helped, so I decided it'd be worth a try. :) So here's...
  46. fluidistic

    Cross product expressed in the cylindrical basis

    Homework Statement It's not a homework question but a doubt I have. Say I want to write \vec A \times \vec B in the basis of the cylindrical coordinates. I already know that the cross product is a determinant involving \hat i, \hat j and \hat k. And that it's worth in my case...
  47. G

    Increase dielectric strength of a cylindrical capacitor

    Homework Statement You have a co-axial cylindrical capacitor placed in vacuum. The two co-axial cylinder tubes are made of copper. The outside tube radius a1 and inside tube radius a2, with overlapping length L; both tubes have a thickness of t. Say, the capacitor was designed to withstand 5...
  48. R

    Godel's metric in cylindrical coordinates

    Hello, In Godel's paper: an example of a new type of cosmological solutions of einstein's field equations of gravitation, he passes from his original metric to cylindrical coordinates by giving some transformation formulas. Can someone tell me how is this transformation obtained, or at least...
  49. Y

    Clarification on curl and divergence in cylindrical and spherical coordinates.

    Divergence and Curl in cylindrical and spherical co are: \nabla \cdot \vec E \;=\; \frac 1 r \frac {\partial r E_r}{\partial r} + \frac 1 r \frac {\partial E_{\phi}}{\partial \phi} + \frac {\partial E_z}{\partial z} \;=\; \frac 1 {R^2} \frac {\partial R^2 E_R}{\partial R} + \frac 1 {R\;sin...
  50. S

    Curl in Cylindrical Vector Fields: Exploring Zero Curl

    If a vector field has any component in a circular direction how can its curl be zero? If I imagine a vortex of water, it makes sense that it will be easier to go with the water in a circle than it would be to go against the water in a circle. Or more mathsy: A vector field in cylindrical...
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