Ring Definition and 1000 Threads

This is more of a practical question - what is the proper way to remove the retaining ring shown below? Note that it does not contain lug holes, so I am not sure whether retaining/snap-ring or circlip pliers would be capable of removing the ring.

How to calculate the deflection in ring, fixed at center, with a radial point force acting at some point(let say at theta=0) ? I have derived complete set of equations. Now how to apply boundary conditions ? to get a complete solution of 4th order equation, I need 4 B.C's, but here...

Let R be a commutative ring with 1. If there exists a non-zero R-module M such that every submodule of M is free, then R is a PID. I remember proving something similar to this, assuming submodules of all R-modules are free, but I'm not too sure about this question. The direction I am headed in...

I have got a doubt regarding the situation when a ring rolls in a non-uniform magnetic field. We can see that the flux linkage is increasing (considering dB/dt to be positive). So EMF should be induced in the loop. But if we join any two points, say the instantaneous axis of rotation and the...

http://today.msnbc.msn.com/id/44002915/ns/us/_news-crime_and_courts/#.TjmjfGFKO_I There was over 100 terabytes of child pornography swapped here. From the indictment I've read the rules required to be in the site. Here's the indictment document...

Homework Statement Consider \frac{\mathbb Z_2[X]}{X^2+1}, is this ring isomorphic to \mathbb Z_2 \oplus \mathbb Z_2, \mathbb Z_4 or \mathbb F_4 or to none of these? Homework Equations / The Attempt at a Solution - \mathbb F_4 No, because \mathbb Z_2[X] is a principle ideal domain...

As we know for the average Undergrad attempting to grasp (and understand) these abstract mathematical concepts can be challenging to say the least. I was (and still am in some sense :P) in that boat. Does anyone have any Analogies or creative ways of explaining these and getting their meaning...

Hello, I have to find the maximum rpm of the shaft that has ring mounted on the shaft with interference fit of 0.002". I want to know at what rpm the ring will come loose from the shaft? and If I run the shaft at 7000rpm at 400 degree Celsius, is the interference fit of 002" enough...

Homework Statement There is a vertical ring with a bead strung on it. The vertical ring spins at 4 revolutions per second, and the the bead moves up the ring at what angle from the bottom of the ring will the bead be at equilibrium? Is it possible for the bead to make it all the way up to the...

Homework Statement A massive ring (radius = a and mass = M) lies on the xy plane. Calculate the force F on a test mass m at position z on the z axis. Now assume a = 1 and GMm/a2 = 1 in some system of units. (a) What is the force on m at z = 0? I got the answer for this its 0 (b) What...

large number of magnets attached to a fixed non magnetic circular ring. Another non magnetic smaller radius ring with equal number of magnets is taken. Here magnets are attached such a way that like polls of the magnets of bigger and smaller rings are facing each other. Due to repulsive force...

Homework Statement A circular metal ring, as shown on the diagram below, is constructed so as to expand or contract freely. In a region with a constant magnetic field Bo oriented perpendicular to it, the ring expands, with its radius growing with time as r=r0(1+\alphat2). As the ring expands...

I got this question from another forum and it's driving me crazy. Find all triples of odd primes, p,q,r such that p^2+1 is divisible by q, q^2+1 is divisible by r and r^2+1 is divisible by p. Two such triples are 5,13,17 and 17,29,421. If we assume p<q<r, then there are no other such triples...

Hi, All: Could someone please tell me or give me a ref. on the basic properties of Gl(n,R) ; R a ring; possibly a division ring, and Gl(n,R) the group (under composition) of matrices invertible over R ? (I imagine we need a ring R with 1 , to talk about invertibility). I...

It may seems like simple homework question but it is industrial question with actual condition & I am struggling for the answer & also asked this question on other website but not get any reply. So ,please help me 'O' ring Internal Diameter(ID) ID=4 mm with tolerance is + & - 0.15mm...

Hi there, I'm attempting a science experiment to create a magnetic suspension field that can hold magnetic objects in place in mid air. Since a Magnetic field isn't flat a single magnet would be pointless as the opposing object is continually sliding off it, so I looked at creating a ring...

Homework Statement Let \phi: R \to S be a ring homomorphism from R to S. What can you say about \phi if its image \text{im}\phi is an ideal of S? What can you say about \phi if its kernel \ker \phi is a subring (w unity) of R? The Attempt at a Solution I think the second one...

Homework Statement Let R be a ring and S be any set. Let R^S be the set of set-functions S \to R . Endow R^S with a ring structure such that if S is a singleton, then R^S is just a copy of R. The Attempt at a Solution It seems to me that the obvious (and perhaps only?) way to...

Homework Statement Ok I'm going through last year's practice exam for electrodynamics and I'm stuck on a particular problem. For problem statement see attachment. q5a part i is fine but I'm confused with the other parts. Homework Equations...

Some Japanese tech company called shimizu is parading this new idea of solar energy generation. The Luna Ring it is called. Links http://news.cnet.com/2300-11386_3-10003698.html" http://www.youtube.com/watch?v=TUL_rDeKIeU" I think there are some serious issues with said idea WRT...

Homework Statement Determine whether the indicated operations of addition and multiplication are defined (closed) on the set, and give a ring structure. If a ring is formed, state whether the ring is commutative, whether it has unity, and whether it is a field: The set of all pure...

Homework Statement Describe all the units (if any) in each given ring: 2Z X Z with addition and multiplication by components; and Z X Q X Z with addition and multiplication by components Homework Equations The Attempt at a Solution I do not know how to begin, I am not sure how...

Homework Statement Give an example of a commutative ring R with a 1 and nonzero prime ideal P of R such that P = P2 Homework Equations The Attempt at a Solution Letting R be an integral domain and look at the ideal 0xR in RxR. is all i got but not sure how to show this or what to...

Hi all, I'm trying to answer the following questions related to a project on smoke rings. We are in an introductory class, so this project is more for fun and just applying the little we have learned about point, rigid body, and fluid motion to something less understood like vortex rings...

Hi, given a polynomial ring R=\mathbb{C}[x_1,\ldots,x_n] and an ideal I=\langle f_1, f_2 \rangle, \quad f_1, f_2 \in R, is it always true that R/I \cong (R/\langle f_1 \rangle)/\phi(\langle f_2 \rangle), with \phi: R \rightarrow R/I being the quotient map? That is, is quotienting by I always...

Homework Statement A metal ring 4.50cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. These magnets initially produce a magnetic field of 1.12T, but are gradually pulled apart, causing the field to remain...

Hi everyone. I want to derive for fun the stationary state wave functions for FREE a particle of mass m on a ring of radius R. The question seems trivial, but I am getting hung up on something silly. What I think I know: Since \psi can be written as a function of the radial angle \phi ...

1)Problem statement A translating and rotating ring of mass 1 kg, angular speed of 500 rpm, and translational speed of 1 m/s is placed on a horizontal surface. The coefficient of friction between the ring and the surface is 0.35. Outside radius is 3 cm. This is a problem from a FE...

Homework Statement A thick cylindrical ring of inner radius 29.0cm and thickness 2.8cm has a mass of 10.0kg. What is the moment of inertia of this cylinder about its central axis? Homework Equations I = (.5)(m)(ri^2+ro^2) The Attempt at a Solution I tried to use hollow cylinder...

Homework Statement There wasn't a figure given. All that was given was that the figure is a circular ring. Theta is the angle between the electric field direction and a unit vector normal to the surface area of the ring. Flux versus costheta was plotted and a slope was found to be m = 0.172. E...

Homework Statement The ring (m), which weighs 5Kg, is sliding along a frictionless arc (Shown in the draw). Arc radius - 1.2 meters. There are 2 forces applied on the ring: 1) F - 40N and always tangent to the circle. 2) F' - 150N, 30 degrees above the horizon. Calculate the total...

I have a question about Ring Laser Interferometry. A couple of years ago I contributed some text and several pictures to the http://en.wikipedia.org/wiki/Sagnac_effect" . Ever since I have been curious about the quantum interpretation of Ring laser interferometry. The special thing about...

Homework Statement A long circular solenoid of radius a and N turns per unit length has its axis in the z direction. A small highly conducting ring, or area A, resistance zero but self inductance L, is place with its plane horizontal and its centre on the axis and near the top of the...

1. Prove that a ring which is left Artinian and right Noetherian is right Artinian. The Attempt at a Solution I can't figure it out. Can anyone help?

Homework Statement If s is a ring with the property that s=s^{2} for each s\in S, which of the following must be true? I. s + s = 0 for each s in S. II. (s+t)^{2}=s^{2}+t^{2} for each s,t in S. III. S is commutative Homework Equations none The Attempt at a Solution The answer is I, II...

Hello Experts, Again a Q and what I did, please tell me what I am doing wrong: Given that there is a ring of matrices above Z (integers) Mn(Z) and 2 ideals I, J of this ring. I need to prove that they are commutative: IJ = JI What I did is that: For all i in I and for all M in...

Hello Experts, Here is the question, and what I did: Q: Given a ring with division D char(D) != 2, F = Centralizer of D (means that F becomes a field). Given that x in D isn't in F but x^2 is included in F. Needed to prove that there exists y in D and y*x*y^(-1) = -x and also that y^2...

Homework Statement A total charge q is distributed uniformly along a ring of radius b. The ring is in the x-y plane centered on the origin. The multipole expansion is not valid for r<b. Find an expansion for the potential valid in this regionHomework Equations The charge density is just...

Homework Statement A uniform circular ring of charge Q= 6.40 microCoulombs and radius R= 1.30 cm is located in the x-y plane, centered on the origin as shown in the figure. Homework Equations 1.What is the maximum value of E on the z-axis? 2.What is the frequency of the small...

Homework Statement Determine the nilpotent, idempotents and units in a) F[x]/<x2-x> b) F[x]/<x2> Homework Equations The Attempt at a Solution How do I do this without a specified Field? For a) the elements in R would be {a+bx: a,b are in F; x2=x} b) {a+bx: a,b in F; x2...

Show \mathbb{Z} [ \sqrt{2} ] = \{ a + b \sqrt{2} | a,b \in \mathbb{Z} \} has infinitely many units. I started by taking an element: a + b \sqrt{2} \in \mathbb{Z} [ \sqrt{2} ] and finding an inverse \left( a + b \sqrt{2} \right) ^{-1} such that the product gives zero and...

Homework Statement Given a commutative ring R with a prime characteristic p, show that the mapping phi:R-->R defined by phi(a)= a^p is a isomorphismHomework Equations Fermat's little theorem(I think)The Attempt at a Solution I'm pretty sure Fermat's theorem must have something to do with this...

Homework Statement a) Calculate the electrostatic force on an uniformly charged rod of length 2L and charge q, which lies along the axis of an uniformly charged ring of radius R and charge q'. The centers of the charged rod and the rings are displaced at a distance z= z0. b)Show that if z0 >>...

I was asked to decide if Z_9 and the direct sum of Z_3 and Z_3 are isomorphic. Do I check to see if they are 1-1 and onto?

Homework Statement Let R = Z[x] be a polynomial ring where Z is the integers. Let I = (x) be a principal ideal of R generated by x. Prove I is a prime ideal of R but not a maximal ideal of R.Homework Equations The Attempt at a Solution I want to show that R/I is an integral domain which...

My professor gave us this query at the end of class, it contained two parts. 1. Show a ring is idempotent 2. Consider the degree one polynomial f(x) is an element of M2(R)[x] given by f(x) = [0 1 ______0 0]x + B (so f(x) = the matrix []x + B). For which B is an element of M2(R), if any...

Homework Statement A wire with uniform charge density λ per unit length is bent into a ring of radius a and rotates with angular velocity ω about an axis through its centre and perpendicular to the plane of the ring. Find the magnetic field on the axis at a distance z from the ring...

Homework Statement Let (X,T) be a normal topological space. Let R be the ring of continuous real-valued functions (with respect to the given topology T) from X onto the real line. Prove that the that T is the coarsest Topology such that every function in R is continuous. Homework...

Homework Statement I am try to prove : Let R be a ring, I be a ideal of R. Then N is a maximal in R/I if and only if N=M/I where M is a maximal ideal in R that contains I. Homework Equations The Attempt at a Solution First I'm not 100% sure that the statement is true, but I'm...

I'm working with elementary rings, and my professor gave me about ten of these to start but it seems like a lot of work with how he managed it. I know you guys don't answer homework so I chose so I can do the others. Any help would be greatly appreciated, the groups were easy but the rings are a...