Cylindrical Definition and 761 Threads

So I'm trying to find out what the procedure is to convert a cartesian unit vector to a cylindrical unit vector. Any thoughts?

i am having trouble with finding inductance and capacitance of a cylindrical shell with gap. say inner radius is a, outer radius is b, and filling dielectric between a and b, and its not a exact circle which have a small gap say d. its like a split ring but only one shell. How can i...

if a point in cylindrical cordinates is A=(r1,\theta1,z1) and another point is B=(r2,\theta2,z2) (if ar,a\theta,az are unit vectors) then the position vector of A is = r1<ar>+\theta1<a\theta>+z1<az> and the position vector of B is = r2<ar>+\theta2<a\theta>+z2<az> so vector BA=...

1. Homework Statement cylindrical space station - large diameter, thin walled - radius r, mass M rotating in deep space, no gravity 1)radial spokes of negligible mass connect the cylinder ti the centre of motion. Astronaut mass m climbs a spoke to the centre. What is the fractional change...

Homework Statement A circular disk of radius r and thickness d is made of material with resistivity p . Show that the resistance between points a and b (Fig. attached)is independent of r and is given by R=πp /2d Homework Equations R= p L / A where L and A are length and section...

Homework Statement Hi I am converting from Cartesian co-ordinates to cylindrical co-ordinates systems and can do the conversion fine, but am unsure about how to convert the limits. Q) Region V is given in Cartesian by: F(x,y,z) = xi+yj+z(x^{2}+y^{2})k Where x^{2}+y^{2} \leq 1...

Dear all, here's my first request for a little help (maybe also in finding the proper subforum...) I'm working as developer and scientific consultant in a lab for Nuclear Magnetic Resonance at high field (> 21 Tesla), and I have to create a suitable probe for checking the stability of a...

Homework Statement Question Attached Homework Equations The Attempt at a Solution So here I'm attempting b), I know \nabla \times \vec F\ is the curl, which in this case is defined by the matrix \left[ \begin {array}{ccc} x&y&z\\ \noalign{\medskip}{\frac {d}{{\it dx}}}&{\frac {d}{{\it...

I have seen the derivation for the formula: h2(pi)rdr used in math textbooks. However, earlier today I had a physics problem where I needed to use the volume of a cylindrical shell of inner radius r and outer radius dr+r and length h. without remembering the formula I tried to derive it...

Use cylindrical coordinates to evaluate the triple integral , sqrt(x^2+y^2) where the region integrated is the solid bounded by the circular paraboloid z=9-16(x^2+y^2) and the xy-plane. I'm having trouble deciding what the bounds for r would be.

Homework Statement A non-conducting, infinitely long, cylindrical sheath has inner radius r=10 m, outer radius r=15 m and a uniform charge density of 9 nC/m^3 spread throughout the sheath. Magnitude of electric field at r=5, r=12, r=17? Homework Equations Q=rho(Volume) and phi=EA...

it's not homework but it's something I can't make any sense with it why when we transform from cylindrical 2 cartisian or the inverse we take the unit vector in our consideration and transform it also not just transform the function and relate it to the other unit vectors ??. for example ...

I have tried to solve the cylindrical case of the heat equation and reached the second order differential equation for the function R(r): R'' + (1/r)*R' + (alfa/k)*R = 0 (alfa, k are constants) I couldn't find material on the web for non-constant coefficients, does anyone know how to...

Just trying to do a problem to find the minimum volume for a homogeneous, bare cylindrical reactor, and my main question is if the radial and axial bucklings are equal to one another at min. V or if there is some other condition that would be helpful. Thanks.

Homework Statement Describe the following vector field: \bold v (\bold x)=\frac{\bold a \times \bold x}{(\bold a \times \bold x)(\bold a \times \bold x)} with \bold a = \text{constant}. Calculate its divergence and curl. In what region is there a potential for \bold v? Calculate it. Hint...

Homework Statement An isolated cylindrical capacitor consists of two concentric conducting cylinders of length L and radii a and b. The inner and outer conductors carry +Q and -Q, respectively. a. Determine the electric field between the conductors. b. Determine the electric potential...

Homework Statement Two infinite coaxial metal cylindrical tubes of radius a and b (a < b) are charged with charge per unit length (unit [C/m]) \lambda and -\lambda respectively. Calculate the electric field between the tubes (i.e. for a < r < b) Where \epsilon_{0} is the permittivity...

The whole problem consists of several parts, but my issue is to come up with a dl for the piece of wire shown. Im trying to find the force on the wire due to a magnetic field produced by another wire running along the x-axis (not shown in pic). \vect{B} = \frac{\mu_0I}{2\pi s}\hat{\phi}...

Homework Statement A hole is drilled through the center of a ball of radius r, leaving a solid with a hollow cylindrical core of height h. Show that the volume of this solid is independent of the radius of the ball. Homework Equations V = \int_{a}^{b} 2\pi x (f(x) - g(x))...

Hello I have a local stress acting radial on a thin cylindrical plate (see illustration), how can I calculate if the plate will deform/bend? I can only find equations for uniform external pressure (Marcel Dekker), but will it be okay when the stress is only local?

Homework Statement A conical container with radius 1, height 2 and with its base centred on the ground at the origin contains food. The density of the food at any given point is given by D(r) = a/(z + 1) where a is a constant and z is the height above the base. Using cylindrical polar...

Homework Statement A cylindrical shell of radius 8.1 cm and length 247 cm has its charge density uniformly distributed on its surface. The electric field intensity at a point 20.3 cm radially outward from its axis (measured from the midpoint of the shell ) is 41800 N/C. Given: ke =8.99×10^9...

Homework Statement Two very long hollow conducting cylindrical shells are situated along the x-axis. The shells are concentric and have negligible thickness. The inner shell has a radius a and a linear charge density +lambda, while the outer shell has a radius b and a linear charge density...

Hi, The following is a general question which doesn't have to do with any particular problem. (therefore I am not including the template). I understand that when a circular object (e.g: a hoop) rolls on a *flat* surface without slipping with angular speed \omega, its contact point, and thereby...

Homework Statement A very long insulating cylindrical shell of radius 6.00 cm carries charge of linear density 8.90*10^-6 C/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 4.70 above the surface...

.A very long insulating cylindrical shell of radius 6.00 cm carries charge of linear density 8.90*10^-6 C/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 4.70 above the surface. and What would a...

Homework Statement A coaxial cable used in a transmission line has an inner radius of 0.15 mm and an outer radius of 0.65 mm. Calculate the capacitance per meter for the cable. Assume that the space between the conductors is filled with polystyrene. (Also assume that the outer conductor is...

Can anyone please explain the stress fields in cylindrical coordinates? What is the difference between \sigma_{rz} and \sigma_{\theta z}? What is the difference between stress in the r axis and stress in the \theta axis? Thanks

Homework Statement An infinitely long conducting cylindrical rod with a positive charge lambda per unit length is surrounded by a conducting cylindrical shell (which is also infinitely long) with a charge per unit length of -2 \lambda and radius r_1, as shown in the figure. What is E(r)...

OK, having some trouble wrapping my head around this so would appreciate some clarification. Let us say I had a long, thin wall metal tube of radius R with a uniform charge per unit length. Would there be some magnitude of E of the electric field at a radial distance of R/2? I understand...

Homework Statement Inside the sphere x2 + y2 + z2 = R2 and between the planes z = \frac{R}{2} and z = R. Show in cylindrical and spherical coordinates. Homework Equations \iiint\limits_Gr\,dz\,dr\,d\theta \iiint\limits_G\rho^{2}sin\,\theta\,d\rho\,d\phi\,d\theta The Attempt at a...

Homework Statement Plate in the shape of the circular halo (inner radius a, outer radius b>a), the inner edge is being kept at a constant temperature T_0, and the outer at the temperature given by the function f(\phi)=T_0\cos(2\phi). Find the equilibrium distribution of the heat everywhere...

Homework Statement This problem is at Griffiths 4.13. A very long cylinder of radius a with a uniform polarization perpendicular to the axis. The question is to solve for the field inside the cylinder. Homework Equations \rho_b=P\cdot\hat{n} and \sigma_b=-\nabla\cdot P The Attempt...

Im new to finding volume using the cylindicral shell method so what should i do. I know I will eventually plug equations into the integral 2piX(f(x)-g(x))dx x=y x+2y=3 and y=0 revolve about the x axis

Homework Statement Use cylindrical coordinates to evaluate the triple integral (over E) sqrt(x^2+y^2) dV , where E is the solid bounded by the circular paraboloid z=9−16(x^2+y^2) and the xy plane. The Attempt at a Solution This is really bugging me... Is this the correct setup for the...

Are there standard algorithms for calculating stresses (axial, radial) in pressure vessels? I have found pages detailing circular cylindrical, thin- and thick-walled pressure vessels. However, what about other shapes? Are there some equations I can use to integrate to find stresses for e.g...

Homework Statement In cyclindrical coordinates we can represent points as (\rho,\phi,z) We define a vector in cyclindrical coordinates as follows A = A\rhoa\rho + A\phia\phi + Azaz I'm having some problem with subscripts. Anyway I don't understand this. If I am given a point say ( 5, 20...

Homework Statement Nevermind the rough picture, the shaft is cylindrical. Knowing that the post has a diameter of 60mm, determine the principle stresses and the maximum shearing stress at point K. Homework Equations These are equations for your reference: \sigma = My/I \tau = Tc/J Where...

Homework Statement Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. Sketch the region and a typical shell. y = 4x - x^2, y = 3; about x = 1 Homework Equations ? The Attempt at a...

Why the term "cylindrical functions" for the states in LQG? I just can't find a any reference that explain the why of the term "cylindrical" for the states in LQG. Thanks in advance for any comment. Z.

Homework Statement Convert to Cylindrical Coordinates from Cartesian 1st int(-2 to 2), 2nd int(-sqrt(4-x2) to sqrt (4-x2)), 3rd int((x2+y2) to 4) X dz dy dx. I changed the integrals to Cylindrical 1st int(0 to pi), 2nd int(-2 to 2), 3rd int(r2 to 4) and the X to r cos(theta). r dz dr...

Homework Statement The conductor is cylindrically shaped with a radius of R. The hole on the inside is also cylindrically shaped with a radius of R/2. If a cross-section of this conductor is placed on an x-y coordinate plane, the hole would be centered on the x-axis at a distance of R/2 from...

I'm doing an investigation where I am trying to find the repulsion force of cylindrical magnets. For this I have two ferromagnetic disk magnets on their sides, so that the curved sides face each other. In the investigation I push one of the magnets with a constant force towards a stationary one...

Homework Statement http://img688.imageshack.us/img688/5277/loopb.jpg A cylindrical shell is released from rest and rolls down an incline without slipping. Find speed of shell at the top of the loop. h(incline) = 2.0m h(loop) = 1.3m The Attempt at a Solution vf = sqrt(g * yi)...

1. A cylindrical open tank needs cleaning. The tank is filled with water to a height meter, so you decide to empty it by letting the water flow steadily from an opening at the side of the tank, located near the bottom. The cross-sectional area of the tank is square meters, while that of the...

If a cylindrical tank of radius 1m rests on a platform 5m above the ground. Initially the tank is filled with water up to a height 5m. A plug whose area is 10-4m2 removed from an orifice on the side of the tank at the bottom.(density of water = 103kg/m3, g= 10m/s2). i wanted to ask what would...

Evaluate by changing to cylindrical coordinates \int from 0 to 1 \int from 0 to (1-y^2)^1/2 \int from (x^2+y^2) to (x^2+y^2)^1/2 (xyz) dzdxdy I came to an answer of integral from 0 to pi integral from 0 to 1 integral from r^2 to r (rcos\thetarsin\thetaz) r dzdrd\theta Is this the correct answer?

Hi all! I was trying to figure out how to find the volume of a cone with radius R and height h using integration with cylindrical coordinates. I first tried to set the the integral as: \int_{0}^{2\pi}\int_{0}^{h}\int_{0}^{R}\rho d\rho dz d\phi ...but I think that this is setting up the...

Homework Statement evaluate : \int\int\int_{E} e^z DV where E is enclosed by the paraboloid z = 1 + x^2 + y^2 , the cylinder x^2 + r^2 = 5 I just need help setting this up. I know that theta is between 0 and 2pi Now is z between 0 and 1 + r ? and r is between 0 and sqrt(5)...

Homework Statement can you explain this conversion, I am not sure. Rectangle coord : \int^{2}_{-2}\int^{sqrt(4-x^2)}_{-sqrt(4-x^2)}\int^{2}_{sqrt(x^2 + y^2 )} F(x) dzdydx = cylindrical coord : \int^{2\pi}_{0}\int^{2}_{0}\int^{2i}_{r} r*dzdrd\theta I see that x^2 + y^2...