Cylindrical Definition and 761 Threads

Homework Statement I fill a cylindrical tank of length 50 ft and diameter 90 ft with water (to the brim). What is the force the bottom 1 ft band of water exerts on the lining? Homework Equations The Attempt at a Solution My main doubt is whether i should integrate from 0 to 1 and...

Homework Statement Construct a triple integral in cylindrical coords to find the volume of the cone r=z, where the height (z value) is limited by z=L. Should be in the form => {int[b,a] int[d,c] int[f,e]} (r) {dr dtheta dz} (Sorry for weird formatting above, brackets purely to make terms...

Homework Statement A uniform magnetic field B is confined to a cylindrical volume of radius 0.080m. B is directed into the plane of the paper and is increasing at a constant rate of (delta)B/(delta)t=0.300 T/s. Calculate the magnitude and direction of the current induced in a circular wire...

A cylindrical space station of radius r with thin walls and mass M rotates at angular velocity ω such that the apparent gravity on the inner surface of the cylinder is equal to g. 1) Radial spokes of negligible mass connect the cylinder to the centre of motion. An astronaut of mass m climbs a...

Homework Statement Hi I have an expression on the form df(v, \theta, \phi) = v e^{-v^2/C}\cos(\theta)v^2\sin(\theta)\,dv\,d\theta\,d\phi and I am trying to write it in cylindrical coordinates. Note that θ runs from 0..π, v is a velocity and C a real constant. So I wish to write it in terms...

I am trying to work the following problem; A rigid body is rotating about a fixed axis with a constant angular velocity ω. Take ω to lie entirely on th z-axis. Express r in cylindrical coordinates, and calculate; a) v=ω × r b)∇ × v The answer to (a) is v=ψωρ and (b) is ∇ × v = 2ω...

Homework Statement Find the volume of the enclosed by the surfaces z=qx z=0 and x²+y²=2ax Homework Equations This is meant to be done with calculus but can verify my answer with simple geometry - should be \pi a^3q The Attempt at a Solution So the top of the wedge will be when x=2a...

Homework Statement In cylindrical coordinates, sketch the surface defined by z=6 The hand drawn sketch shown in the answer I have appears to be a rectangular or square plane at z=6 Should the plane be square/rectangular or should it be circular? To illustrate, the blue plane in the diagram...

Homework Statement I need to calculate the integral where the region is given by the inside of x^2 + y^2 + z^2 = 2 and outside of 4x^2 + 4y^2 - z^2 = 3 Homework Equations The Attempt at a Solution So far, I think that in cylindrical coordinates (dzdrdtheta): 0 <= theta <= 2pi sqrt(3)/2 <=...

The cone centre is the z-axis and has base ρ=1 and height z=1, I'm looking at the lecture notes and it says the limit φ=0 to 2pi, z=0 to 1, ρ=0 to (1-z). Could someone tell me where the (1-z) comes from please? Why is it not 0 to 1?

Homework Statement Given the tensor F_{\mu \nu }= \left[ \begin{array}{cccc} 0 & -E_{x} & -E_{y} & -E_{z} \\ E_{x} & 0 & B_{z} &-B_{y} \\E_{y} & -B_{z} & 0 & B_{x} \\E_{z} & B_{y} & -B_{x} & 0 \end{array} \right] F^{\mu \nu }F_{\mu \nu }=2(B^2-\frac{E^2}{c^2}) and metric tensor n_{\mu \nu...

Homework Statement Calculate the electric field of a cylindrical capacitor comprised of a smaller cylindrical conductor of radius ##a## enclosed within a larger cylindrical conductor of radius ##b## where ##b>a##. The smaller cylinder has charge ##+Q## and the larger cylinder has charge...

I can find the metric tensor in cylindrical coordinates to be [1,-1,-1/r^2,-1] but how about the electromagnetic field tensor and thus the energy stress tensor? Is it just change the Ex,Ey,Ez to Eρ,Eθ,Ez? Is FσρFσρ still equal to 2(B^2-E^2)

Problem: Calculating the eddy current distribution inside an infinitely long cylindrical conductor inside a straight and infinitely long solenoid energized by an alternating sinusoidal current. The problem has a perfect summery and we know that magnetic field and the eddy current depend on...

For fluid with viscosity \mu our stress strain relationship takes the form \sigma_{ij} = -p \delta_{ij} + 2 \mu u_{ij}. I was wondering how to express this in cylindrical coordinates. The strain tensor I can calculate in cylindrical coordinates (what I get matches eq 1.8 in [1]). But how...

A very long insulating cylindrical shell of radius 6.40 cm carries charge of linear density 8.90μC/m spread uniformly over its outer surface. What would a voltmeter read if it were connected between the surface of the cylinder and a point 4.00 cmabove the surface? λ=dq/dr V=k∫dq/r...

So, I'm trying this problem and just want to make sure my attack is correct. We have an infinitely long cylindrical hole in an infinitely long cylindrical wire, like in this picture: (Here, they call the radius of the hole 'a'. I'm going to call it r.) There's an electric current I in...

find the geodesics on a cylinder, where R^2 = x^2 + y^2 ---------------------------- so the goal is to find a function F, that gives the minimum distance between any two points on the cylinder. in cylindrical coordinates, dl = sqrt( ds^2 +(sdθ)^2 +dz^2 ) since we are on the surface...

Homework Statement Rotate around the y-axis the region above the graph of y=x3 that is bounded by the lines x=1 and y=8 Homework Equations dV= (2pix)(y)(dx) The Attempt at a Solution dV = (2pix)(y)dx dV = (2pix)(x^3) dx = 2pix^4 I integrated from y = 1 to y=8 and I...

Consider the attached picture, where they express the unit vectors in cartesian coordinates with the unit vectors in a cylindrical coordinate system: The questions might be a bit loose, but try to get what I mean and answer as well as you can please :) 1) I find the expression for i, j and k a...

Homework Statement If the scalar electric potential v in some region is given in cylindrical coordinates by [SIZE="4"] v (r, \phi, z) = r^2 sin \phi e^{\frac{-3}{z}} , what is the electric field \vec{E} in that region? Homework Equations E = -\nabla v The Attempt at a Solution...

Homework Statement An infinitely long solid conducting cylindrical shell of radius a = 3.1 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 = -0.49 μC/m. Concentric with the shell is another...

Homework Statement You have two concentric cylinders. The inner cylinder has radius a and the external cylinder has radius b. Find the electric potential in the region between the cylinders. [Hint: The final equation takes the form V(r) = constant1 - constant2 ln(something) ]...

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...

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...

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 =...

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...

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...

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?

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...

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...

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...

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...

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...

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...

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...

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...

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

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...

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...

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...

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...

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)...

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

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

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...

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

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...

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...

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...