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.
Homework Statement
So we have a compound cylinder, 100 mm internal diameter, 200 mm common diameter and an outer diameter of 300 mm. The pressure created by shrinking the outer cylinder on the inner cylinder is 30 MPa.
If the maximum hoop stress on the outer cylinder is 110 MPa, what is the...
Homework Statement
Construct a complex potential in the w-plane which corresponds to a charged metallic cylinder of unit radius having a potential Vo on its surface.
The Attempt at a Solution
I'm a bit confused on how to start deriving a complex potential for the cylinder. If I was given the...
Homework Statement
rho of a hollow cylinder can be found with 4 measured quantity by the folowing formula, proof this formula
Homework Equationsρ= 4.m
∏.(d²-D²).h
d is the outside diameter and D the inside
The Attempt at a Solution
since it's my first time...
Homework Statement
Using a value of n of 1.1, calculate the final pressure and temperature when the cylinder is compressed rapidly with a compression ratio of 15.
Starting pressure = 101.325 kPa
Starting temp = 298 K
Homework Equations
(V2/V1) = 15
The Attempt at a Solution...
Hi, I'm trying to solve this, but I keep getting both sides of the equation to be the same >.<
A solid cylinder is initially moving along a flat surface without rotating. Due to the action of friction, it eventually begins rolling without slipping. The coefficient of friction is 0.22, the...
This is an even-numbered problem in my textbook that I'm looking at early though it hasn't been taught by my lecturer yet, because I need to know the concepts underlying it for a similar problem. Cld someone help me?
Homework Statement
Consider the case of a hollow cylinder rolling down a...
Homework Statement
Hi I was reviewing for my final and I came across this problem:
Problem:
Basically there is a 6in long cylinder with dia = 24in
Given weight density: 490 lb/ft^3
Each Hole is drilled symmetrically, each has 6in dia and equally space around a 10in dia circle concentric with...
Hi I was reviewing for my final and I came across this problem:
Problem:
Basically there is a 6in long cylinder with dia = 24in
Given weight density: 490 lb/ft^3
Each Hole is drilled symmetrically, each has 6in dia and equally space around a 10in dia circle concentric with the cylinder...
Homework Statement
Cylinder of radius a and a cylindrical hole b < a is displaced a distance d in x-direction. Current density \textbf{J}=J_z\textbf{e}_z. Show that a uniform magnetic field inside the hole is
\textbf{B}=\frac{\mu_0}{2}J_zd\textbf{e}_y
Homework Equations
Using previous...
Homework Statement
A cylinder rotating uniformly about the x' axis of S' will seem twisted when observed instantaneously in S, where it not only rotates but also travels forward. If the angular speed of the cylinder in S' is ω, prove that in S the twist per unit length is yωv/c(squared)...
Homework Statement
A lawn roller in the form of a thin-walled, hollow cylinder with mass M is pulled horizontally with a constant horizontal force F applied by a handle attached to the axle.
a)If it rolls without slipping, find the acceleration.
b)If it rolls without slipping, find the...
Homework Statement
A cylinder is initially at rest, how long will it take for the cylinder to turn one revolution?
Homework Equations
(Theta)f=(Theta)i+(alpha)(deltaT)
The Attempt at a Solution
I know that the distance of the cylinder to turn one revolution is 2Pi over speed. My...
Homework Statement
A solid cylinder is pivoted about a frictionless axle as shown. A rope wrapped around the outer radius of 2 m exerts a downward force of 3N. A rope wrapped around the inner radius of 0.7 m exerts a force of 8 N to the right. The moment of inertia of the cylinder is 8 kg m^2...
Homework Statement
A long, cylindrical conductor of radius R carries a current I. The current density, J, is not uniform and is given by the equation J = br, where b is a constant. Find an expression for the magnetic field magnitude B at distance r < R and at distance r > R.
Homework...
Homework Statement
Consider two long coaxial metal cylindrical tubes, with radii a and b and length L. (You may assume a,b<<L. Also a<b.) Suppose the inner cylinder is given a charge +Q and the outer cylinder a charge -Q.
Using Gauss' Law, compute the electric field for all r between a and...
Homework Statement
A hollow cylinder of radius r and height h has a total charge q uniformly distributed over its surface. The axis of the cylinder coincides with the z axis, and the cylinder is centered at the origin, as shown in the figure.
What is the electric potential V at the...
Homework Statement
Problem is described in the picture
I do not understand how can \alpha^{'}R=a^{'}.
The dimensions do not seem correct. Angular velocity x distance from the origin = tangential velocity, is that correct ? How can this equal acceleration then ?
3. Attempt to solution
I...
Homework Statement
A cylinder of radius a has a hole drilled through it of radius b, the hole is parallel to the axis of the cylinder but is displaced from it
by a distance d in the x-direction where d < a - b. The asymmetric hollow cylinder has a uniform current density J = Jzez
Show that...
Hi,
the problem isn't written in English originally, so there might be some slight mixing up in the terminology
A cylinder with mass M = 2 kg is attached to a spring and lying on a horizontal plane. (Imagine looking at it from the side, with the wall where the spring is attached forming a...
Homework Statement
A long, non conducting, solid cylinder of radius 4.2 cm has a nonuniform volume charge density ρ = Ar^2, a function of the radial distance r from the cylinder axis. A = 2.5 µC/m5.
(a) What is the magnitude of the electric field at a radial distance of 3.2 cm from the axis...
It is told, that all homework-like threads should be posted there. So, here I go.
Imagine such a situation: there is a vertical rod and a cylinder, with the hole diameter sightly larger than the diameter of rod. There is also a second rod, attached to the cylinder perpendicularly. There is a...
Imagine such a situation: there is a vertical rod and a cylinder, with the hole diameter sightly larger than the diameter of rod. There is also a second rod, attached to the cylinder perpendicularly. There is a friction between the main rod and the cylinder. It is known, that if we put a...
Hey all,
I've been trying for a while now to derive the following solution, for a circular cylinder under uniform flow:
φ(r,θ)=U(r+\frac{R^2}{r})cos θ
where φ is the flow potential that satisfies Laplace's equation, as defined in this article...
The flow of an inviscid incompressible fluid around a circular cylinder is commonly studied in fluid dynamics courses. There's a wikipedia article about it here: http://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder.
However, what about a square cylinder? There seem to be...
Homework Statement
Develop a source-panel computer program to numerically calculate the potential flow pressure distribution on a right circular cylinder with and without circulation.
1.) Tabulate and plot your numerical results for the pressure coefficient distribution on the cylinder...
Hey Guys, I'm fairly new to this forum.
I would just like to know is their a way to allow for a four cylinder engine to produce for more engine gas to spin 2 turbos. As I researched on forced induction, I've found that Twin turbos on a four cylinder might be one turbo too many, though I...
Hi,
My knowledge is not too good and I'm trying to help my son find out how we would go about determining the equation of the volume of the cyclinder V(r), expressed in terms of r alone? We do not know how we would go about this without using l or h?
Any help would be really appreciative (Smile)
Homework Statement
A viscometer consists of two concentric cylinders, 10.20cm and 10.60 cm in diameter. A liquid fills the space between them to a depth of 12.0cm. The outer cylinder is fixed, and a torque of 0.024 N*m keeps the inner cylinder turning at a steady rotational speed of 57...
Hey everyone,
First I'd like to say my thanks to the community for all the information I managed to glean while lurking on the forum and doing my schoolwork over the last year or so. It's been an invaluable resource to me!
Now, on to my question. (I see that it says not to post homework...
Homework Statement
The cylindrical drum of a copy machine is .38 m long with .05 m radius. If charge is uniformly distributed over the cylindrical surface (the top and bottom flat circular ends of the drum have no charge) and the electric field very close to this surface midway along the...
Hey all,
I am using the Joukowski transform to calculate the electrostatic potential and streamlines around an elliptical cylinder. The flow is caused by two point charges (one positive, one negative). My idea was, of course, to first solve the problem for a circular cylinder, and then...
Homework Statement
Particle of mass m constrained to move on the surface of a cylinder radius R, where R^2 = x^2 + y^2. Particle subject to force directed towards origin and related by F = -kx
Homework Equations
L = T - U
H = T + U
The Attempt at a Solution
So I have the solution, but...
1. Homework Statement
(a) Calculate the electric field at an axial point z of a thin, uniformly charged cylinder of charge density ρ , radius R, and length 2L. z is the distance measured from the center of the cylinder. (b) What becomes of your result in the event z >> L ?
2. Homework...
Homework Statement
How might I show that the map (in cylindrical polar coordinates) given by f:(1,\phi,z)\to(\sqrt{1-z^2},\phi,z) does not change the area?Homework Equations
The Attempt at a Solution
I can see this is like having a sphere in a cylinder and we shine "light" on the cylinder...
Homework Statement
Positive charge is distributed throughout a solid non-conducting cylinder of radius 'b ' and infinite length. The charge density increases with radius according to ρ = {ρ}_{o}({r}{^2}/{b}{^2}), where {ρ}_{o} is a constant (evidently equal to the charge density at the surface...
I came across this formula by Blevins for calculating the natural frequency of a hollow cylinder and was hoping that someone could answer a question I have for calculating the mass per unit length (m). Here's the formula:
f = A/(2*pi*L^2)*sqrt(E*I/m)
A= 9.87 for first mode
I = Area Moment of...
Homework Statement
Evaluate the surface integral ∫A\bullet\hat{n}dS where A = z\hat{x}+x\hat{y}+3y^2z\hat{z} and S is the cylinder x^2+y^2=16 for the range of x\geq0,y\geq0, 0\leqz\leq5
Homework Equations
I used this page as an example way to do this. I'm not good with surface integrals...
Homework Statement
Two coaxial cylindrical conductors are shown in perspective and cross-section above. The inner cylinder has radius a = 2 cm, length L = 10 m and carries a total charge of Qinner = + 8 nC (1 nC = 10-9 C). The outer cylinder has an inner radius b = 6 cm, outer radius c = 7...
Homework Statement
In an infinitely large evenly charged dielectric cylinder(charge density is \rho ) there is an infinitely large cylindrical void. Prove that the electric field inside the void is homogenous and find its value. (picture)
http://img513.imageshack.us/img513/5747/61734727.png...
Homework Statement
I have a solid cylinder of uniform charge density whose axis is centered along the z-axis. I am trying to calculate the electric field at a point on the z-axis.
What I'm trying to do is to start by first calculating the field of a disk centered on the z-axis at a point on...
I am conducting an experiment where I have a cylinder heated from the outside and a fluid flowing through the inside. I know the heat flux into the cylinder and I know the temperature at two points within the cylinder wall. However, I am not confident on the radial position of the temperature...
Homework Statement
An infinite line of charge with charge density λ1 = 2.9 μC/cm is aligned with the y-axis as shown. a = 7.9 cm. h = 8.8 cm. λ2 = -8.7 μC/cm. Another infinite line of charge with charge density λ2 = -8.7 μC/cm parallel to the y-axis is now added at x = 3.95 cm as shown...
Hello,
My name is Jason, I am a senior high school student (new at using Physics forums), and am currently looking into alternative fuels, specifically a substitute for the popular leaded aviation fuel in use today, 100LL.
100LL contains lead to prevent engine knocking, (pre-detonation of...
Homework Statement
You have been assigned to design brass pistons to slide inside steel cylinders. The engines in which these pistons will be used will operate between 20.0 degrees Celsius and 150.0 degrees Celsius. Assume that the coefficients of expansion are constant over this temperature...
Hi, I'm trying to locate a formula for determining the radial breathing mode of a hollow cylinder.
The dimensions of the cylinder of interest are approximately .5" OD x .4" ID x .5" L
Any help would be greatly appreciated. Thanks!
Homework Statement
This is from a worksheet. I had to find the volume myself
"A large number of spheres are poured into a graduated cylinder and gently vibrated until the occupy a minimum volume of 40 mL (or 40 cm^3). Use the information about close packing and the data you found to...
1. Homework Statement [/b]
this is griffiths 6.8 fyi.
a long cylinder of radius R carries magnetization M=ks^2 \hat{∅}, k is a constant and s is the distance from the axis. \hat{∅} is the azimuthal unit vector. find the magnetic field inside and outside the cylinder.
Homework Equations...
I am writing a science fiction story, and would like some help from the PH community.
Details:
There is a cylindrical spaceship which is rotating to create artificial gravity.
The cylinder has a circular radius of 10km and a length of 30km.
The rotational period is 3 minutes and 20...
Find the mass of the solid bounded by the cylinder (x-1)2 + y2=1 and the cone z=(x2+y2) 1/2 if the density is (x2+y2) 1/2
I know that I have to substitute for cylindrical co-ordinates x=rcos(theta), y=rsin(theta), and z=z, and then use the change of variables formula to get the mass by...