What is Cylindrical: Definition and 821 Discussions
A cylinder (from Greek κύλινδρος – kulindros, "roller", "tumbler") has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. It is the idealized version of a solid physical tin can having lids on top and bottom.
This traditional view is still used in elementary treatments of geometry, but the advanced mathematical viewpoint has shifted to the infinite curvilinear surface and this is how a cylinder is now defined in various modern branches of geometry and topology.
The shift in the basic meaning (solid versus surface) has created some ambiguity with terminology. It is generally hoped that context makes the meaning clear. Both points of view are typically presented and distinguished by referring to solid cylinders and cylindrical surfaces, but in the literature the unadorned term cylinder could refer to either of these or to an even more specialized object, the right circular cylinder.
1. This is not a question from the book but i think if i can get the answer to this it will clear the idea i am confused about
can i covert a cylindrical vector such as
P(1 ar, 1a\theta)
into cartesian
after using the matrix
i got
Px = cos \theta - sin \theta
Py = sin \theta + cos...
1. IM very confused about the meaning of these cylindrical vectors
for Cartesian vectors if i say A = 1ax + 2ay + 3az
I know i mean a vector with a magntiude of 1 in the x direction 2 in the y direction and 3 in the z direction and i make a line from the origin to point (1,2,3).
Now for...
Note: This is my first time using LaTeX. Any formatting advice would be appreciated.
Homework Statement
Consider a homogeneous sphere of radius R_s made of a material that exerts a force obeying the inverse r-squared law (i.e. a particle of this material exerts a force on a test particle...
Symmetry Arguments--a finite cylindrical can
Homework Statement
Consider a finite cylindrical can shape that has charge uniformly distributed on its surface. Symmetry does allow us to say some things about the electric field of this distribution
A) at points along the can's central axis
B) At...
Hi,
I've been searching the internet for useful information regarding this but I cannot find anything that helps me completely. I am working on a project on my own where I have identical cylindrical objects (standing up on their flat sides like hockey pucks on ice - so from a 2D "overhead"...
Help!
I trying to improve momentum eq for cylindrical element coordinate by using vector method or may other methods
Please give me response v.ergent . Thanks! =)
If a cylindrical magnet with a uniform magnet field were to be rotated at high speed along its polar axis (assuming the poles to be at either end of the cylinder) would there be any change or distortion to the shape (ie pattern of field lines) of the magnetic field?
Please help me with the following simple and dumb questions:
First, assumptions:
- Ignore atmospheric pressure.
- The liquid in the tanks is water with uniform density = 1g/cc.
- all tanks are sealed at the bottom and are vertically positioned.
- cross sections of the tanks are circular...
A frictionless cylindrical flywheel, of diameter 250mm and mass 30kg, has a string attached/wrapped on the outside diameter, with a mass of 10kg on the other end.
What is the radius of gyration of the flywheel?
If the mass starts 1.5m form the floor, what will its speed be when the mass is...
hi,
I have this problem I've been stuck with for a long time and i can't figure out what to do.
if spherical coordinates are denoted (r,θ,ϕ) and cylindrical coordinates are denoted (ρ,ϕ,z), how do i express the radial unit vector in cylindrical coordinates, e(ρ), in terms of the spherical...
1. Homework Statement
This is a question in my classical mechanics book, and i am not very good with polar coordinates. I am suppose to fine r, phi, z in terms of x,y,z.
Basically I need to derive the cylindrical polar coordinates from the Cartesian coordinates.
The question specifically...
Homework Statement
This is a question in my classical mechanics book, and i am not very good with polar coordinates. I am suppose to fine r, phi, z in terms of x,y,z.
Basically I need to derive the cylindrical polar coordinates from the Cartesian coordinates.
The question specifically asks...
Homework Statement
\int\int_{Q}\int(x^4+2x^2y^2+y^4)dV where Q is the cylindrical solid given by \{(x,y,x)| x^2+y^2 \leq a^2, 0\leqz\leq\frac{1}{\pi}\}Homework Equations
When I convert to cylindrical I get f(r,\theta,z) = r^4\cos^2\theta + 2r^4\cos^2\theta\sin^2\theta + r^2\sin^2\theta, but I...
Homework Statement
Use Cylindrical Coordinates.
Find the volume of the solid that the cylinder r=acos\theta cuts out of the sphere of radius a centered at the origin.
Homework Equations
Sphere = x2+y2+z2=a3
The Attempt at a Solution
I think that the limits are from -pi/2 to...
Homework Statement
This is my last question about triple integrals in cylindrical coordinates.
Evaluate the integral by changing to cylindrical coordinates:
\int _{-3}^3\int _0^{\sqrt{9-x^2}}\int _0^{9-x^2-y^2}\sqrt{x^2+y^2}dzdydx
Homework Equations
In cylindrical coordinates...
Homework Statement
Find the mass and center of mass of the solid S bounded by the paraboloid z=4x^2+4y^2 and the plane z=a\;\;(a>0) if S has constant density K.
Homework Equations
In cylindrical coordinates, x^2+y^2=r^2.
The Attempt at a Solution
In order to find the mass, I tried...
Homework Statement
I have a question to find Scalar factors of parabolic cylindrical coords and element dV with provided tranformation equations. I know the values for both of them and that the product of the scalar factors is the dV, but how do i derive those scalar factors? I don't even know...
Homework Statement
Evaluate \int \int \int_E x^2 \, dV where E is the solid that lies within the cylinder x^2+y^2=1, above the plane z=0, and below the cone z^2=4x^2+4y^2.Homework Equations
In cylindrical coordinates, x^2+y^2=r^2 and x=r\cos{\theta}.The Attempt at a Solution
I tried \int...
Homework Statement
1. The expression F = [x,y,z] defines a vector field. Given the parametric representation of a surface S:[u cos v, u sin v, u^2] = r (u,v), where the parameters cover the ranges 0 ≤ u ≤ 2 and 0 ≤ v ≤ 2π, calculate the flux F through the surface S.Homework Equations
How do i...
A hole of radius \sqrt{3} is bored through the center of a sphere of radius 2. Find the volume removed4\pi\int\intx\sqrt{a^{2}-x^{2}}dx from \sqrt{3} to 2\sqrt{3}?
And then subtract this from the volume of the sphere?
Homework Statement
The one dimensional steady-state heat conduction equation in a medium with constant conductivity (k) with a constant volumetric heat generation in three different coordinate systems (fuel rods in a nuclear power plant) is given as:
\frac{d^2 T}{dx^2}=-\frac{\dot{q}}{k}...
1. A thick conducting cylindrical shell has an inner radius Rsub1 and outer radius Rsub2. It has a net excess charge = Q, and it is L long. Find electric field at certain points given.
Ok, when r is less than Rsub 1, the electric field is zero. And when r is greater than Rsub2, it is easy to...
i need MAJOR HELP!
this is the problem:
The can do tin can company minimizes costs by construckting cans from the least possible amount of material. this company suppplies many different sizes of cans to packing firms. a designer with the company needs to determine the radius that gives...
Homework Statement
Represent the surface in space, identify the surface-
r=2cos(theta)
Homework Equations
Uhh...
The Attempt at a Solution
My main thing here is this... how does r tell me anything about the graph of the function in a 3-D plane? i see that...
Say we are looking at a positively charged rod with uniform charge density and a radius of R.
When using Gauss' law and taking a cylindrical surface we use the formula
E = lambda/2*pi*epsilon*r
When we derive this equation we are assuming R is significantly smaller than L and so we...
Homework Statement
An empty cylindrical canister 1.50 m long and 94.0 cm in diameter is to be filled with pure oxygen at 30.0 C to store in a space station. To hold as much gas as possible, the absolute pressure of the oxygen will be 21.5 atm . The molar mass of oxygen is 32.0 g/mol ...
1. Homework Statement
A cylindrical centrifuge of raidus 1 m and height 2 m is filled with water to a depth of 1 meter. As the centrifuge accelerates, the water level rises along the wall and drops in the center; the crossection will be a parabola.
a) Find the equation of the parabola in...
Homework Statement
Capacitor plates are length L with radii a,b a<b are co-axial and intially covering each other with line charge density of the inner plate Q/L.
determine the force between plates as the inner plate is partially withdrawn along the axis.
i) if cylinders charged to...
Homework Statement
Cylin. surfaces \rho = 1 , 2 , 3, cm have uniform surface charge density of 20, -8, 5 nC/m^2.
What is the total electric flux that passes through the closed surface rho = 4 cm and z(from 0 to 1 m)?
And what is \vec{D} at the point \rho= 4 cm , \phi= 0 , z = .5 cm...
Could someone tell me what I'm doing wrong? thanks!
Homework Statement
Write the equation is cylindrical coordinates
7x2 + 7y2 = 2y
r = ? (has to be in the r = ? format)
Homework Equations
r2 = x2 +y2
x = rcos(θ)
y = rsin(θ)
The Attempt at a Solution
7x2 + 7y2 = 2y...
Homework Statement
Convert the following cylindrical coordinate vector to a Cartesian vector:
\overrightarrow{A}\,=\,\rho\,z\,sin\,\phi\,\hat{\rho}\,+\,3\,\rho\,cos\,\phi\,\hat{\phi}\,+\,\rho\,cos\,\phi\,sin\,\phi\,\hat{z}
Homework Equations...
Homework Statement
Transform the vector below from Cartesian to Cylindrical coordinates:
Q\,=\,\frac{\sqrt{x^2\,+\,y^2}}{\sqrt{x^2\,+\,y^2\,+\,z^2}}\,\hat{x}\,-\,\frac{y\,z}{x^2\,+\,y^2\,+\,z^2}\,\hat{z}
Homework Equations
Use these equations...
Converting from Cartesian to Cylindrical coords - but division by zero!
Homework Statement
Let's say I want to convert the point P(0, -4, 3) to cylindrical.
To convert from Cartesian to Cylindrical coordinates, one must use the formulas listed below.
Homework Equations...
Homework Statement
Immediately outside a very long cylindrical wire of radius r1 = 1mm, the electric field is 40kV/m directed towards the wire's surface.
A hollow cylindrical metal tube with inner radius r2 = 3mm is now placed around the wire, to form a coaxial cable. What will be the charge...
1. How do we calculate the electric field of a Coaxial Cylindrical Capacitor??
That is one question, the other is:
Is the field strength E the same at all locations of a uniform electric field at any point between the plates or electrodes of a parallel plate capacitor, and or a cylindircal...
Homework Statement
Use a triple integral in cylindrical coordinates to show that the volume of the solid bounded above by a sphere \rho = \rho_{o}, below by a cone \phi = \phi_{o}, and on the sides by \theta = \theta_{1} and \theta = \theta_{2}, \theta_{1} < \theta_{2} is
V = 1/3...
When a problem with a number of equations is given, asking to find its volume, a student has a choice between the cylindrical shell method and the cross-section method. However, regardless of what method is chosen, do both answers end up being EXACTLY the same?
Homework Statement
A cylindrical storage tank 8 feet in diameter and 20 feet long is lying horizontally on the ground. The tank is full of olive oil whose weight density is 57 lb/ft^3. How much work does it take to pump the olive oil to a level of 6 feet above the top of the tank?
Almost...
Homework Statement
Consider an ideal cylindrical solenoid of length L and radius a=L/2 on which a thin wire has been wrapped a total of N turns. A steady current I flows through the wire. Assume the wires are wound so tightly that the solenoid can be thought of as a collection of N parallel...
Homework Statement
Set up triple integrals for the volume of the sphere rho = 2 in (a) spherical, (b) cylindrical, and (c) rectangular coordinates.
Homework Equations
Volume in cylindrical coordinates: Triple integral of dz r dr d(theta) over region D.
Volume in spherical coordinates...
Homework Statement
A long cylindrical insulator has a uniformcharge density of 1.46uC/m3 and a radius of 6cm.a-What is the electric field inside the insulator at a distance of 2cm and 12cm? Answer should be in N/C.
b-How much work must you do to bring a q=0.086uC test charge from 12cm to 2cm...
Question Details:
Convert the following equation into cylindrical coordinates...
x^2 + y^2 + z^2 = 4
It's obvious that r^2 = x^2+y^2... but that would only simplify the equation to:
r^2 + z^2 = 4 ... is there a better way to do this?
Homework Statement
a cylindrical bar of copper has a resistance of 0.02 ohms
a) if the power of the bar is 10000 watts, what is the maximum current the bar can carry?
b) the bar is now stretched to 3 times its original length, while the total volume of the bar remains constant. what is...
My question is about vector addition in cylindrical coordinates:
Let A = 2x + y, B = x + 2y. In rectangular coordinates, AB = B-A = -x+y
In cylindrical coordinates, x=rcosθ + θsinθ, y=rsinθ + θcosθ
A =Axx + Ayy, B =Bxx + Byy
Ar = Ax(x.r) + Bx(y.r)=2.236, Aθ = 0. So A = 2.236r
Br =...
My question is about vector addition in cylindrical coordinates:
Let A = 2x + y, B = x + 2y. In rectangular coordinates, AB = B-A = -x+y
In cylindrical coordinates, x=rcosθ + θsinθ, y=rsinθ + θcosθ
A =Axx + Ayy, B =Bxx + Byy
Ar = Ax(x.r) + Bx(y.r)=2.236, Aθ = 0. So A = 2.236r
Br...
Homework Statement
The problem is :''Resolve the cartesian unit vectors into their cylindrical components(using scale factors)
The Attempt at a Solution
It's simple to do the inverse(resolving cylindricl unit vectors into cartesian components),but I'm having some ''trouble'' with the...
Homework Statement
See attached
Homework Equations
K.E (rotational) = .5*I*omega^2
K.E (translational) = .5*m*v^2
The Attempt at a Solution
v(of rod and translational vel of cylinder) = L * (dαlpha/dt)
Is the angular velocity of the cylinder the same as the angular velocity of...