# 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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40. ### Electrostatics problem related to polarization and a cylindrical dielectric

I understand that the above eqs would be used but I clearly don't know how to use them. I am a bit confussed.
41. ### Determining an object's velocity in cylindrical coordinates

I got the answer for velocity and acceleration. But I don't know how to draw the shape of the particle's motion over time. How to draw it? should we change a,b,c,e into a numbers or not? or we may not to change a,b,c,e? Please help me how to draw the shape of particle's motion over time?
42. ### Stokes' Theorem 'corollary' integral in cylindrical polar coordinates

Hi, I was just working on a homework problem where the first part is about proving some formula related to Stokes' Theorem. If we have a vector \vec a = U \vec b , where \vec b is a constant vector, then we can get from Stokes' theorem to the following: \iint_S U \vec{dS} = \iiint_V \nabla...
43. ### Flux in a rotated cylindrical coordinate system

##\vec F= 2x^2y \hat i - y^2 \hat j + 4xz^2 \hat k ## ## \Rightarrow \vec \nabla \cdot \vec F= 4xy-2y+8xz## Let's shift to a rotated cylindrical system with axis on x axis: ##x \to h, y \to \rho cos \phi, z \to \rho sin \phi ## Then our flux, as given by the Divergence theorem is the volume...
44. ### Modes of laser propagation in cylindrical optics

I saw the solution of the light propagates in cylinder.. so in every solution there is the first order Gaussain function (the slandered one) times another function which gives I think the separation, both of them gives the intensity separation.. So what does that mean?! is it as I draw on the...
45. ### Elliptical facet cylindrical optical fiber - Mathieu equation

Let's say I have three modes in a fiber that is elliptical cylinder shaped (cylinder with elliptical facet), as in the image below (the source:Optical Engineering, 46(4), 045003 (2007)) so what is the equations that describe these fields..
46. ### Cylinder inside a cylindrical track

1) Conservation of energy ## mg(R-r)(1-cos \theta_0) = \frac{1}{2}mv^2 + \frac{1}{2} I \omega^2 ## because of pure rolling ## \omega = \frac{v}{r} ## So i got: ## v = \sqrt{\frac{4}{3} g (R-r) (1-cos(\theta_0))} ## this is how i got normal force: 2) ## N - mg = m \frac{v^2}{R-r} ## where v is...
47. ### Cylindrical Halbach array with a vertical magnetic field?

Similar to what is shown here, except the south side would be the weak side of the array. A link to purchase one of these or at least the magnetic field arrangement would be very helpful. Thanks in advance.
48. ### Cylindrical Conductors Carrying a Current I -- Formula (?)

How can I' be the formula above? Is there any formula to get this same
49. ### Line integral where a vector field is given in cylindrical coordinates

What I've done so far: From the problem we know that the curve c is a half-circle with radius 1 with its center at (x,y) = (0, 1). We can rewrite x = r cos t and y = 1 + r sin t, where r = 1 and 0<t<pi. z stays the same, so z=z. We can then write l(t) = [x(t), y(t), z ] and solve for dl/dt...
50. ### Radiation detector - cylindrical ionising chamber

Let r = position of the electron = 6mm - 36.8μm; λ = mean free path traversed. Integrate E(r) = Q/(2πϵLr) between the two shells gives: V = [Q/(2πϵL)]*log(r/(r-λ)) I know that the question is asking for the voltage at which the electron energy will get to 23eV, but i am unsure how to get rid...