Cylindrical Definition and 821 Threads

Homework Statement An object slides along the ground at speed v at the base of a circular wall of radius r. The object is in contact with both the wall and the ground, and friction acts at both contacts. The wall is vertical and provides no force in the vertical direction. (i) Show that the...

I'm at it again today. Helping the same friend (plus another) study for their final calculus exams; it's a good refresher for me as well. (I'm a senior industrial engineering major so I'm "done" with calculus, and it isn't used much in our upper level classes nor professionally to the best of...

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. $x=1+{y}^{2}$, $x=0$, $y-1$, $y=2$ https://www.physicsforums.com/attachments/4237 The answer is $\frac{21\pi}{2}$ but I couldn't get it using...

Hey everyone, I'm new to this site and I figured this would be the best place to ask this question. We've been using maple to solve two specific problems on the time it would take two tanks to drain. One being cylindrical, and the other conical. They have the same height, the same volume...

Homework Statement Plotting a point in spherical coordinates means using the format ##(\rho, \theta, \phi)## in place of ##(x, y, z)##. Taking a triple integral means replacing ##dV## with ##\rho ^2 sin(\phi) d\rho d\theta d\phi ## As you can see, ##\rho, \theta, \phi ## are all in the same...

Homework Statement Evaluate ## \int \int \int_E {x}dV ## where E is enclosed by the planes ##z=0## and ##z=x+y+5## and by the cylinders ##x^2+y^2=4## and ##x^2+y^2=9##. Homework Equations ## \int \int \int_E {f(cos(\theta),sin(\theta),z)}dzdrd \theta ## How do I type limits in for...

Homework Statement Find the electric field between the conductor and ground. The conductor is at: Potential = +V0, radius a distance d from the ground plane. Homework Equations I used image theory to create a conductor at -V0 at distance -d from the ground plane. Laplace's equation: ∇2V = 0...

Homework Statement An infinitely long hollow cylinder of radius (a) carries a constant current (i). Use Biot - Savart's law and show that the magnetic field at the centre of the cylinder is zero. Also show, using symmetry arguments and Ampere's law, the magnetic field is zero in any point...

Homework Statement Q. A cylindrical cavity resonator has diameter of 24 mm and length 20 mm. The dominant mode and the lowest frequency band are operated as ? I am providing a picture of problem to show the options given to me. I solved the problem by calculating resonant frequency for cavity...

Hi everyone, I am new to the physics forums and I need your help :) I understand that depending on the symmetry of the problem, it may be easier to change the coordinate system you are using. My question is, how would I convert the electric field due to a point charge at the origin, from...

Hey! :o Using cylindrical coordinates and the orthonormal system of vectors $\overrightarrow{e}_r, \overrightarrow{e}_{\theta}, \overrightarrow{e}_z$ describe each of the $\overrightarrow{e}_r$, $\overrightarrow{e}_{\theta}$ and $\overrightarrow{e}_z$ as a function of $\overrightarrow{i}...

Homework Statement A cylindrical distribution of charge ρ = α/sqrt(r) where α = 2 µC/m^(5/2) extends from 0 cm to 9.3 cm (has radius 9.3 cm). Concentric with this is a dielectric shell with k = 5.44 of inner radius 16.6 cm and outer radius 24.9 cm. What is the electric field at 3.53 cm, 12.6...

Homework Statement The question and my attempt are attached as pics Homework EquationsThe Attempt at a Solution I can't seem to find r¨ and θ¨. Assuming I already got r˙ and θ˙ (the answers are written after the question). The idea I tried was to get the acceleration equation in cylindrical...

Homework Statement A solid sphere sphere (radius = R) rolls without slipping in a cylindrical trough (radius = 5R) as shown in the following figure. Show that, for small displacements from equilibrium perpendicular to the length of the trough, the sphere excuses simple harmonic motions with a...

Homework Statement [/B] We need to use the equation for the E field of a ring to set up the integral for calculating the E field of a cylindrical shell with a charge density of σ and a radius of R and a height of H, at a point P that is D distance away from the cylinder.Homework Equations [/B]...

Hello All, I would like to start learning how to ray trace but the tracing through a tube with a thickness of t has got me stumped. If I have an n1 (outside tube), n2 (Tube), and n3 (inside tube). n1≠n2≠n3. Knowing Θ1 (the angle of incidence in relation to the normal), I can calculate Θ2 from...

I am currently helping one of my old physics professors and his Phd student designing a pressure vessel for ultra-sciencey detector (still figuring out the theory behind it all). So far we have the general vacuum tank that opens on the ends, with the pressure difference holding the ends on...

Homework Statement Using Cylindrical coordinates, find the total flux through the surface of the ellipsoid defined by x2 + y2 + ¼z2 = 1 due to an electric field E = xx + yy + zz (bold denoting vectors | x,y,z being the unit vectors) Calculate ∇⋅E and then confirm the Gauss's Law Homework...

A twisted cylindrial rod has the cross sectional symmetry so that it's not posible to tell whether it is twisted or not without knowing if there is any torsional energy. now drawing a line on the surface of it can tell us whether or not it's twisted. It might not be a straight line.. there are...

Hello PF, I have a problem to solve in the following form: Given a vector with Cartesian components, V={Vx,Vy,Vz}, find its components in circular cylindrical coordinate. Given the actual vector components, it'd be very easy to convert. But I have no idea where to start on this. Any guide to...

plane wave is represented as exp (ik.r) and the cylindrical wave as 1/sqrt(r) *exp(ik.r) and the spherical wave as 1/r*exp(ik.r) Have anyone tried to plot these waves? How to do it? Attempt: in Matlab assuming k=1 >> x=linspace(-1,1,100); >> for(ii=1:100) fp(ii)=exp(i*x(ii)); end >>...

r\rightarrow r-2qz and \psi\rightarrow\psi+q\cdot(r-qz), I don't know how to derive it, anybody know? This question results from the book "Optical Solitons: From Fibers to Photonic Crystals [1 ed.]" section 6.5

I have a question, to use cylindrical coordinates to find the volume of the ellipsoid ${R}^{2}+{3z}^{2}=1$. I know for cylindrical coordinates the Jacobian is $r$ so I have some integral: $$\iiint (r)dzdrd\theta$$ However I am struggling to work out the bounds of the integral for $z,r,\theta$...

Homework Statement An infinite cylindrical wire of radius ##R## carries a current per unit area ##\vec{J}## which varies with the distance from the axis as ##J(s)=ks^2\hat{z}## for ##0<s<R## and zero otherwise where k is a constant. Find the magnetic field ##\vec{B(s)}## in all space. Homework...

Homework Statement Problem 1c from here: http://web.phys.ntnu.no/~ingves/Teaching/TFY4240/Exam/Exam_tfy4240_Dec_2013.pdfHomework Equations Maxwell's equations The Attempt at a Solution According to the solutions, the electric field is ZERO everywhere because it's "magnetostatics" and because...

This is not a homework problem this is just a problem I was thinking about whether or not it would be possible to solve without cylinderical shells The region bounded by y=1/(x^2) x=e x=e^3 and the x-axis Rotated around y axis.. I did cylindrical shells and got 4pi and then wondered if I...

Hello friends, I am new for numerical methods and programming. i have been trying to devolop a program in 2D poisson heat equation in cylinder (r,angle) by finite difference method ∂2u/∂r2 + 1/r * ∂u/∂r + 1/r2 * ∂2u/∂θ2 = Q(u,θ)discritized equation :- ui+1,j − 2uij + ui−1,j/(∆r)2 + 1/ri *...

I seek to build a vacuum chamber for shipping radon contamination sensitive samples. The cylinder will have a height of approximately 2 inches, and needs an inner diameter of 10 inches. The plan is to weld stainless steel pipe to a plate on the bottom, and to have a lid bolt on to the pipe with...

Homework Statement Proper way to graph xy = 1 for a Cylindrical Shell problems. Homework Equations V = ∫^b_a 2πy f(y) dy The Attempt at a Solution I am rotating around the x-axis, so I am integrating with respect to y, but should I choose x = 1/y, or y = 1/x to solve my problem? How are...

Homework Statement A hollow cylinder with radius ##a## and height ##L## has its base and sides kept at a null potential and the lid on top kept at a potential ##u_0##. Find ##u(r,\phi,z)##. Homework Equations Laplace's equation in cylindrical coordinates...

I've learned that a vector in coordinate system can be expressed as follows: A = axAx+ayAy+azAz. ai, i = x, y, z, are the base vectors. The transformation matrix from cylindrical coordinates to cartesian coordiantes is: Ax cosΦ -sinΦ 0 Ar Ay = sinΦ cosΦ...

please someone explain me the following expression for Cartesian unit vectors expressed by the cylindrical unit vectors: http://web.mit.edu/8.02t/www/materials/modules/ReviewB.pdf at page B-8 line B.2.4 i would like to know which steps led to it. thanks, Chen

An infinitely long solid insulating cylinder of radius a = 5.2 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 23 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 14.2 cm, and...

The potential on the side and the bottom of the cylinder is zero, while the top has a potential V_0. We want to find the potential outside the cylinder. Can I use the same boundary conditions as for case of inside cylinder potential? What is different?

Homework Statement (a)The current density across a cylindrical region of radius R varies according to the equation: J=J0(1-r/R), where r is the distance from the axis of the cylinder. The current density is the maximum J0 at the axis r=0 and decreases linearly to zero at the surface r=R...

I'm working on a prototype device, and I'm currently figuring out the form factor. On the turn indicator of my car, there is a ring with several positions that will control the lights. I'm thinking that something similar would work well on the handle of my device, and I'm looking to purchase...

I Need to design a Vertical cylindrical water tank to be build by Fiberglass. I need to calculate the tank also for 7.5 m bar pressure and 2.5 m bar vacuum pressure. Tank Dimensions to be 4m Dia, 5 m High (60000 Liters). I have Fiberglass laminate of 6 mm Thk and Modules is 1470000 psi. I have...

on road? and why not cuboidal ones?

Hi all, I am trying to describe/understand how to define a 2-plane distribution in R^3 , i.e., an assignment of a 2-plane at each tangent space, when the distribution is given in terms of the basis of a plane in (R^3, cylindrical). It has just been a while since I have worked with cylindrical...

I am trying to find out if I could substitute a Plano-convex cylindrical microlens array with a Double-convex (fly's eye) cylindrical microlens array for laser beam homogenization in 1 dimension. Assuming that the lens parameters are the same, how would the quality of performance be affected...

Homework Statement An infinitely long solid insulating cylinder of radius a = 2.5 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 30 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of...

Hello, I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows: 2W = σijεij Where σ and ε are symmetric rank 2 tensors. For cartesian coordinates it is really easy because the metric is just the identity matrix, hence: 2W = σxxεxx +...

Dear kind helpers, actually I am not 100% sure whether this is the right place to post, as it is not a homework in the sense of an exercise sheet. But I think it could be because it feels pretty basic and that I should be able to solve it. Though I really searched for a solution but could not...

I am setting up a numerical simulation from a 2D discretization of the heat equation in cylindrical coordinates. my spatial variables are radius (r), height (z), and azimuth (ø). The assumption is that there is no gradient along the azimuth direction (if temperature is T then dT/dø = 0)...

I know the capacitance of cylindrical shell formula if both cylinder length is same.If cylinders length differs between which the dielctric is sandwitched what is the formula to calculte the capacitance?

Homework Statement Homework Equations Possions Equation and boundary conditions... The Attempt at a Solution First Part that I think is right... However when I try and apply the boundary conditions ie V(a)=V(r)=0... I can't get the answer! And for the last...

So the problem statement is: A conducting solid sphere (R = 0.167 m, q = 6.63·10–6 C) is shown in the figure. Using Gauss’s Law and two different Gaussian surfaces, determine the electric field (magnitude and direction) at point A, which is 0.00000100 m outside the conducting sphere. (Hint: One...

Homework Statement 1. Use Gauss' Law to calculate the electric field at a radius of 5.0cm from the z-axis 2. Use Gauss' Law to calculate the electric field at a radius of 8.0cm from the z-axis 3. What is the surface charge density σmetal on the outer surface of the metal cylinder...

I'm confused why when using cylindrical coordinates three unit vectors are needed. My book says that the three unit vectors are one for the radial direction which is bound to the xy plane and then a unit vector in the z direction. It goes on to say that there is another unit vector associated...

I am working on a home made electromechanical actuator to replace the vacuum actuator on the front axle of my Jeep Cherokee. The vacuum actuator isn't the greatest and I have replaced it and the system lines few times. SO I figure, I know what force the vacuum actuator is putting out, I...