Cylindrical Definition and 761 Threads

In Rc Stephen's book Strength op materials, the longitudinal stress in a cylinder(see) attachment caputure.jpeg. My question is how is the area(pi X d X t ) is derived as my calculations show that this area should equate to (pi x d x t + t x t)

Homework Statement Not really a homework question, but more of a concept question which I'm unfamiliar with. So as we know, equations can be in any coordinate, but how do you convert them from one to another? For example, a few equations from fluid mechanics. the first equation is the vector...

Homework Statement Write the vector D_{p}=2\partial/ \partial x-5\partial/ \partial y+3\partial/ \partial z \in T_{p}\Re^{3} in cylindrical and spherical coordinates Homework Equations NA The Attempt at a Solution x=r cost y=r sint z=z ...

Hello everybody! Although this may sound like a homework problem, I can assure you that it isn't. To prove it, I will give you the answer: 40pi. So.. I'm self-studying some electrodynamics. I'm using the third edition of Griffiths, and I have a quick question. For those who own the book and...

I don't understand what's wrong with it:

Homework Statement Find the volume of curved wedge that is cut from a cylinder of radius 3m by two planes. One plane perpendicular to the axis of the cylinder, the other plane crosses the first plane at a 45 degree angle at the centre of the cylinder. (Hint: let the line of intersection of the...

Hi. Sorry my spelling, because I am not English. Homework Statement In a sphere truncated sector with an angle of 60 degrees, there is a uniform charge distribution, \rho. Calculate the electric field in (0,0,0). The sector starts in z=a and ends in z = b. The sphere center is in (0,0,0)...

Make the indicated change of variables (do not evaluate) (Not sure how to write an iterated integral with bounds so I will try and explain by just writing the bounds) (I also tried using the symbols provided, but everything I tried just put a theta in here so I gave up) \int\int\intxyz...

Homework Statement Use cylindrical coordinates to find volume... Homework EquationsInside: x2+y2+z2=16 Outside: z=sqrt(x2+y2) The Attempt at a Solution Cylindrical coordinates have always been a problem for me, so I initially tried to put them into spherical and then convert them over, but...

Homework Statement do we only use spherical and cylindrical coordinates for triple integrals? or for double too? thanks for your replies in advance

Hi there, I'm trying to determine the radial component of a velocity vector in a disk. The vector doesn't (necessarily) start from the centre of the disk and can be pointed in any direction. I've attached a .pdf with the schematics - it seems like a simple problem but it has me stumped...

Homework Statement A long, hollow conducting pipe of radius R and length L carries a uniform current I flowing around the pipe. Find expressions for the magnetic field (a) inside and (b) outside the pipe. Hint: What configuration does this pipe resemble? Homework Equations Ampere's Law...

Homework Statement Given \textbf{F} = x\textbf{i} + y\textbf{j} + z\textbf{k}, what is the flux of \textbf{F} through the cylinder x^2 + y^2 =1 bounded by the planes z=0, x+y+z=2. The Attempt at a Solution By Gauss' Theorem, \int\int_{S}\textbf{F}\cdot d\textbf{S} =...

Homework Statement Two coaxial cylinders, radii {a,b} where b>a. Find the potential between the two cylinder surfaces. Boundary conditions: V(a,\phi) = 2 \cos \phi V(b,\phi) = 12 \sin \phiHomework Equations Solution by separation of variables: V(r,\phi) = a_0 + b_0 \ln s + \sum_k \left[...

Homework Statement I have three problems and I could really use some help. 1. Integrate the function f(x,y,z) = y over the part of the elliptic cylinder x^2/4 +y^2/9 = 1 that is contained in the sphere of radius 4 centered at the origin and such that x≥0, y≥ 0, z≥0. 2. Find the total...

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) differential equation governing z(p) please help!

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...

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...

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 =...

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...

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...

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...

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} -...

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...

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...

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...

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...

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 =...

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} -...

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 =...

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...

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}...

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...

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

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?

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

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...

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}...

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...

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...

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

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...

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...

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...

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...

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...

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...

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...

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...

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...