Ring Definition and 1000 Threads

Three forces are applied to a ring (as shown in the photo) that lies on a frictionless surface in the xy plane. The ring has a mass of 100 kg. Fa=200N, Fc=240N and the angle between Fa and Fb is 135°. What is Fb if: The system is stationary? The system accelerates at .5 m/s2? For...

Homework Statement Let R be a commutative ring with 1. What are the units of M_n(R)? Homework Equations N/A The Attempt at a Solution If R is a field, then I know that we can characterize the units as those matrices with non-zero determinant (since those are the invertible...

Homework Statement Solve Laplace's equation on a ring in the plane with r_1<r<r_2. And arbitrary functions on the edges of the ring.The Attempt at a Solution After separation of variables the solution to the radial factor is an often-seen problem. It's eigenvalues are λ=n² the eigenfunctions...

Homework Statement Hi, Having some trouble with answering this question: A thin nonconducting rod with a uniform distribution of +'ve charge 'Q' is bent into a circle of radius R. There is an axis, 'z' which originates in the center of this ring. In terms of 'R', at what +'ve value of...

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...

In my Abstract Algebra course, it was said that if E := \frac{\mathbb{Z}_{3}[X]}{(X^2 + X + 2)}. The basis of E over \mathbb{Z}_{3} is equal to [1,\bar{X}]. But this, honestly, doesn't really make sense to me. Why should \bar{X} be in the basis without it containing any other \bar{X}^n...

Hello, I have a question about two particles in a ring. Okay, so as far as I know the wavefunction of a particle in a ring is cos(kθ) with k=0,1,2,3... So, what is the wavefunction (total one) for the two particles? I am guessing it must be the multiplication of the two: totalphi=...

Homework Statement A metal ring of radius a is located in a region with the homogenous magnetic flux density: \hat{B} =\hat{z}B_0 cos(\omega t) The metal ring coincides with the plane z=0. The frequency w is very low. Use Faraday´s Law to determine the electric field where the metal ring...

Hello, I am hoping someone can give me some advice. I am playing about with the design of a ring oscillator in an electronics simulations package. The ring has 5 inverters. As part of the assignment we were asked to ad in an extra inverter to the output of the ring and see if there was a...

How do you find all the distint ideals of any ring? I am able to find may ideals but how do you prove that there are no more ideals. Eg Let R = Z[1/n] = {x/n^i | x \in Z, n is a natural number} I can see that x/n is an ideal for every x \in Z. Is that right?

It is desired to slip an aluminum ring over a steel bar. At 7.00° C the inside diameter of the ring is 4.000 cm and the diameter of the rod is 4.080 cm. (b) Find the temperature of the ring at which it fits over the bar. The bar remains at 7.00° C. ---- It is desired to slip an aluminum...

Help me understand a homework solution -- intro to ring theory -- ideals problem: solution: The first paragraph is just saying the ideals generated by the units in the ring is the whole ring correct? Also, the principal ideals generated by 2, 4 and 8 are all the same correct? So...

Household physics question: Before I left town for 3 weeks the lock on my apartment door was loose in its encasement. I had to hold it in place while turning the key or the inner disc would rotate uselessly inside the outer ring: http://scott-shepherd.com/share/forums/lock.jpg When I came...

Homework Statement Homework Equations The Attempt at a Solution

Homework Statement Exhibit two examples of a ring homomorphism \phi from Z4 to Z8, one that is one-to-one and another that is not. For each case, find ker(\phi) and describe Z4/ker(\phi) 2. The attempt at a solution Let \phi : \mathbb{Z}_4 \longrightarrow \mathbb{Z}_8 be the identity mapping...

Homework Statement Consider a circular ring of wire of radius a that resides in the x-y plane through the origin. The center of the ring coincides with the origin and you can regard the thickness of the wire to be infinitesimal. a. Given that a current I flows in the ring, find an...

Hello, This is my first post on this forum, and I'm not used to the english mathematical vocabulary, I'll try my best to explain what is my problem. Let (A,+,x) be a ring, ans S be the subset of the indempotents of A, i.e S={x\in A , x^2=x} . I must show that if S is a finite set, then S has...

Imagine a thick cylinder with a retaining ring groove cut in the ID. I'm replacing the retaining ring with a split ring pressed into the groove. The split ring I'll have made along with the tool to install it. What I would like to determine is the amount of interference and the force...

Is it true that polynomials of the form : f_n= x^n+x^{n-1}+\cdots+x^{k+1}+ax^k+ax^{k-1}+\cdots+a where \gcd(n+1,k+1)=1 , a\in \mathbb{Z^{+}} , a is odd number , a>1, and a_1\neq 1 are irreducible over the ring of integers \mathbb{Z}...

I am taking a first course in algebra and I am having issues with a detail in this proof that every finite domain is a division ring. The argument that I used is that (because of cancellation in domains) left & right multiplication by a nonzero element r in a domain R gives a bijection from R...

Most introductory physics textbooks derive the following formula for the gravitational field for a point mass on the on the axis of the ring: g_{x} = -\frac{Gmx}{(x^2 + a^2)^{1.5} } where, m = total mass of ring x = distance from point mass to ring center a = radius of ring Is...

Homework Statement A ring can rotate about a horizontal axis(x), and a diameter placed on the x-axis. A uniform field is perpendicular to the ring -B0*y. The diameter of the ring is D. it spins with constant angular velocity ω around the x-axis. At at time t = 0 the ring is entirely in the xy...

This is about the electric field of a ring with radius r, at a distance z from center, along the axis of the ring. The ring carries a uniform line charge λ . We always say that the radial component of the field cancels out due to symmetry. Can somebody tell how to prove it mathematically...

A statement in a book of analysis I have says: (Q,+, .) is a commutative ring with an identity element. I assume by its notation (Q,+,.) is a tuple.(correct?) There are several questions that come to mind: 1. Why is there an order between Q,+ and . ? 2. As far as I know, a tuple is an...

Homework Statement What is the centre of the ring of the quaternions defined by: \mathbf{H}=\{ \begin{pmatrix} a & b \\ -\bar{b} & \bar{a} \end{pmatrix} | a,b \in \mathbf{C} \}? Homework Equations The definition of the centre of a ring: The centre Z of a ring R is defined by Z(R)=\{A...

hi i need the schrödinger equation for a particle(electron) in a ring under the influence of a magnetic field that goes through perpendicular to the plane of the ring and i want to consider the spin too. Well, the particle in the ring is pretty easy: - \frac{ \hbar^2}{2mr^2}...

Homework Statement Write down the Schrödinger equation for a particle inside a circle of radius R Homework Equations - Gradientψ(r,θ)=Eψ(r,θ) The Attempt at a Solution Take the gradient in spherical form and set r = R; θ=90;∅ as 0 Then you are left with the first two...

Homework Statement Consider the bead threaded on a cicular hoop of example 7.6 (pg 260), working in a frame that rotates with the hoop. find the equation of motion of the bead, and check that your result agrees with eq 7. 69. Using a free body diagram explain the result 7.71 for...

Homework Statement [PLAIN]http://img695.imageshack.us/img695/3864/unled1dxu.jpg Homework Equations F=(mv^2)/r The Attempt at a Solution NetForce=0 N-W=0 === A free body diagram of the car at the bottom would just incorporate a downwards W force and an upwards N force together equalling 0...

Homework Statement A point charge Q is located at point P(0,-4,0) while a 10nc charge is uniformly distributed along a semicircular ring as shown in the figure. find the value of Q such that E(0,0,0)=0 Homework Equations Q=ρLdl dl = ρd∅ (because ρ and z are constant)...

1. Homework Statement A ring of mass M and radius R lies on its side on a frictionless table. It is pivoted to the table at its rim. A bug of mass m walks around the ring with speed v, starting at the pivot. What is the rotational velocity of the ring when the bug (a) is halfway around and...

Hi everyone, Homework Statement Let a charge Q be uniformly distributed on a circular ring defined by a < \rho < b. Find D at (0,0,h). Homework Equations E = kQ/r2 ar D = \epsilono E The Attempt at a Solution Well I thought I had this figured out, but I was wrong and I still...

Homework Statement Are chain and ring forms of glucose isomers? They aren't, because they have the same structure, right? Homework Equations The Attempt at a Solution

I researched this some, but could not find a method to calculate the radius of the ring singularity in a Kerr black hole. I would think it is a function only of black hole mass and angular velocity. Please let me know if there is some reports or papers on this.

Hi, I have found many papers using analytical methods to calculate the static twist in piston rings. All the papers that i found have used the results of that analytical tool but no one explained how the tool works. Can anyone find a paper in which the analysis to calculate piston ring twist is...

Homework Statement Solve for the Electric force exerted on a Particle a distance z above a uniform ring of charge Q. Determine the potential energy of the charge where the charge lies directly in the center. Homework Equations F=kq1q1/r^2 The Attempt at a Solution Knowing E=F/q I...

The Problem is as follows: A ring of diameter 7.50 is fixed in place and carries a charge of 5.50 uniformly spread over its circumference. A) How much work does it take to move a tiny 3.80 micro-columb charged ball of mass 2.00g from very far away to the center of the ring? B) What...

Homework Statement A ring falls through a horseshoe magnet. Before reaching the magnet, is the current induced in the ring clockwise or counterclockwise? What about after the ring has passed through the magnet? The answers are clockwise before the ring passes through, and...

Homework Statement I need help specifically with b. The inner diameter of a steel ring is 2.0000 cm, and the diameter of an aluminum disk is 2.0100 cm. Both are at 430 C. At what common temperature will the disk fit precisely into the hole in the steel ring? b) If after the aluminum disk is...

In a token ring LAN (IEEE 802.5) what are the differences between "Single token", "Multiple token" e "Single packet"? Thanks in advance.

Homework Statement \mathbb{Z}[x]/(x^3-x) \rightarrow \mathbb{Z} Show that is ring homomorphism, and count the number of homomorphism..? Homework Equations The Attempt at a Solution the map f is homomorphism if, f(x+y)=f(x)+f(y) f(xy)=f(x)f(y) I think, I must find a...

I have attached a figure with this, to help in understanding the problem. A ring whose circumference is attached to its center by infinite springs. Center is fixed. thickness of ring is h, width is b, Young's modulus E and moment of area I. Now a radial force is applied(shown in the figure...

Homework Statement You have an iron ring, hung near a solenoid which has an iron core inserted within. [PLAIN]http://img843.imageshack.us/img843/1623/imgsole.jpg Below are the questions and answers my book provided. I highly suspect the reasoning and i seek PF members to evaluate how true it...

Homework Statement E=(kqz)/(z^2+a^2)^1.5 Through calculus i found that the max occurs at z=a/sqrt(2) and z=-a/sqrt(2) and I think the negative one is the minimum. That answer was given in the book also. The ring has radius a. It wants me to graph E versus z. I'm a little confused on how to...

Ok, I understand that the liquid crystal structure expands and contracts in response to thermal fluctuations and that the structure is made of layers... and only the wavelengths that mach exactly or are half (or quarter and so on) can have constructive interference, thus, only those wavelengths...

consider the image i have uploaded, it shows 4 ring-shaped magnets of different sizes each pair of concentric magnets are held in position relative to each other, and the lower pair is also affixed to the ground, i.e. the upper pair of magnets is free to move blue and red faces show the...

You just can't make this stuff up. http://news.yahoo.com/greek-police-smash-violent-doughnut-ring-213853411.html

Suppose that there is an integer n>1, such that an=a for all elements of some ring. If m is a positive integer and am=0 for some a , then I have to show that a=0. Please suggest.

I found that the endomorphism group over an elliptic curve is isomorphic to a complex quadratic order: End(E)\simeq \mathbb{Z}[\delta]=\mathbb{Z}+\delta\mathbb{Z}, where \delta=\frac{\sqrt{\Delta}}{2} if \Delta is even \delta=\frac{1+\sqrt{\Delta}}{2} if \Delta is odd Does anyone know where...