Cylindrical Definition and 761 Threads

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...

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...

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)...

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...

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...

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...

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...

(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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

This is calculus question, but I don't think calculus really cover this topic in either multi-variables or even vector calculus classes. This is really more common problem in electrodynamics. Let R be position vector that trace out a circle or radius a with constant velocity. In rectangular...

I have some problems using this definition, maybe because it's not valid in every coordinate system: T^{\mu\nu} = (\epsilon + p) \frac{dx^{\mu}}{ds} \frac{dx^{\nu}}{ds} -p g^{\mu\nu} since in cylindrical coordinates x^0 =t \qquad x^1 =\rho \qquad x^2 = \phi \qquad x^3 =z using weyl metric...

How would I go about calculating the hydrostatic force on the walls of an upright Cylindrical Tank. To keep it simple, it is completely full of water, is 1m tall, has a diameter of 1m. Many thanks for anyone that can help.

Homework Statement the tank has a radius of 2m, containing an initial water level of 3m. A hole at the very bottom (underneath) of the tank has radius .005m. How long will it take to empty the tank? Homework Equations Bernoulli's principle. A=radius at top of tank a=radius of...

Homework Statement I took a picture of the problem so it would be easier to understand. All I need to know is what the bounds are. Homework Equations In cylindrical: x=rcos(theta) y=rsin(theta) z=z The Attempt at a Solution I don't know why we should change this to...

Homework Statement A thick cylindrical ring of inner radius 29.0cm and thickness 2.8cm has a mass of 10.0kg. What is the moment of inertia of this cylinder about its central axis? Homework Equations I = (.5)(m)(ri^2+ro^2) The Attempt at a Solution I tried to use hollow cylinder...

I am researching water clocks through history. At some point, it was realized that for the container the water drips from, a conical container with the hole at its point was superior to a cylindrical container with the hole in its side. Could someone explain to me why conical containers are...

Homework Statement Hi there. I haven't used iterated integrals for a while, and I'm studying some mechanics, the inertia tensor, etc. so I need to use some calculus. And I'm having some trouble with it. I was trying to find the volume of a cone, and then I've found lots of trouble with such a...

Homework Statement Question 3 (a)A long metal cylinder of radius a has the z-axis as its axis of symmetry.The cylinder carries a steady current of uniform current density J = Jzez. Derive an expression for the magnetic field at distance r from the axis,where r<a. By resolving the...

Homework Statement The figure shows a section of a cylindrical surface, height h and radius R. The curved surface extends from the z-axis to the y-axis only and has a charge density given by σ(z)= σ0z where σ0is some constant. ind the electrostatic potental at a. (a is at the origin) I'm...

How would I go about working out the Electric Field E(X) in cylindrical coordinates? The question is, Suppose pho = pho(r) find E^pho. Suggestion to use Greens & Gauss theorem

1. Homework Statement +attempt at solution+equations In Cartesian coordinates, x translate into x=r \cos \theta into cylindrical coordinates, y=r \sin \theta and z=z . However dx=\cos \theta dr - r \sin \theta d\theta. This is what I don't understand. Since x is a function of both...

Homework Statement Find the potential of a cylindrical capacitor Radius of both cylinder plates, x and y where x<y Height of the cylinder: h Charge on the plates: qHomework Equations E = \frac{q}{A\epsilon_0} = \frac{q}{2\pi r h \epsilon_0} \Delta V = \frac{\Delta U}{q} = - \int_a^b E drThe...

Homework Statement Hey everyone, I'm just studying some physics, and came across this question where I don't know why I'm wrong =( It's from Physics (5th Ed.) by Halliday, Resnick and Krane - Chapter 27, Exercise 22 Positive charge is distributed uniformly throughout a long, nonconducting...

Hello, Homework Statement My problem regards the disk|washer, and cylindrical shell methods for finding volumes in single variable calc. My problem is basically am I understanding these two methods and their relationships properly. Fundamentally, these methods are indentical, as we can...

Homework Statement Hi, i am trying to find the div, grad and curl in cylindrical polar coordinates for the scalar field \ phi = U(R+a^2/R)cos(theta) + k*theta for cylindrical polar coordinates (R,theta,z) I have attempted all three and would really appreciate it if someone could tell me...

Mathematica: Div in Cylindrical and "Shadowing" I have a vector given in cylindrical coordinates. I know that the divergence of the vector should be zero. However, I am not sure why Mathematica is not returning zero. Also, the Div operator is showing up red (Div) and it is saying something...

Homework Statement Find the volume of the solid bounded by the paraboloids z=x^2+y^2 and z=36-x^2-y^2. Answer is: 324\pi \\ Homework Equations r^2=x^2+y^2 x=rcos0 y=rcos0 The Attempt at a Solution 36-x^2+y^2=x^2+y^2\\ 36=2x^2+2y^2 18=x^2+y^2 r^2=18 V=\int_{0}^{2\pi} \int_0^{3\sqrt{2}}...

Homework Statement A cylindrical shell of radius 9.9 cm and length 286 cm has its charge density uniformly distributed on its surface. The electric field intensity at a point 23 cm radially outward from its axis (measured from the midpoint of the shell ) is 44800 N/C. Given: ke = 8.99 × 10^9...

Homework Statement A cam has a shape that is described by the function r = r_0(2 - cos \theta), where r_0 = 2.25 ft. A slotted bar is attached to the origin and rotates in the horizontal plane with a constant angular velocity (\dot{\theta} dot) of 0.85 radians/s. The bar moves a roller...

Homework Statement I'm given 2 unit vectors a_x and a_theta. I need to find the dot product between the two. Homework Equations Conversion from Cylindrical to Cartesian x = r * sin(theta) y = r * cos(theta) z = z Conversion from Cartesian to Cylindrical r = sqrt(x^2 +...

Homework Statement An infinitely long solid insulating cylinder of radius a = 3.2 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 22 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner...

What if you want to rotate around something other than the x/y axis? For example: Homework Statement y=x, y=0, x=1, rotated around the line x=-1 Homework Equations or The Attempt at a Solution V= ⌠(between 0 and 1)π[1+x]^2 dx = π(1/3(x)^3+x^2+2x),x=0, x=1...

Homework Statement An infinite line of charge with linear density λ = 8.8 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.9 cm and outer radius b = 4.1 cm. The insulating shell is uniformly charged with a volume density of ρ = -659 μC/m3. What is λ2, the...

Homework Statement Funky, all the surrounding exercises are quite easy, so I assume this is too... my brain's just not catching it... Use cylindrical shells to find the volume of the shape formed by rotating the following around the y-axis. The (x,y) graph before rotation: use the area...

I do not understand when we are given a vector at point P(x,y,z) or in different forms cylindrical and spherical. What does it mean at point?? I mean aren't vectors supposed to start at origin, even if they don't how will that make a difference in their magnitude or angle between them. For...

Homework Statement On the afternoon of January 15, 1919, an unusually warm day in Boston, a 26.0 m high, 27.4 m diameter cylindrical metal tank used for storing molasses ruptured. Molasses flooded the streets in a 9 meter deep stream, killing pedestrians and horses and knocking down buildings...

This is something I have zero familiarity with. Anyways, I was given the equation: r=2asin(theta)+2bcos(theta) and had to prove that it was a circle, and then state its center in cartesian and cylindrical coordinates. After making the appropriate substitutions and completing the square...