Convention Definition and 184 Threads

I understand the simplest application of the summation convention. x_{i}y_{i} I create a sum of terms such that in each term the subscripts are the same i.e. x_{1}y_{1}+x_{2}y_{2}+x_{3}y_{3}+... But now when I look at understanding summation convention applied to the generalised Hooke's law...

I thought passive sign convention is obeyed when you have a positive current flowing into the positive terminal of the element first. But how about this case? While it is drawn that way, the positive terminal is actually the NEGATIVE terminal because the voltage is negative, so you have to flip...

Homework Statement What is sign convention, and how is it applied to vectors? I was reading an economics paper when I came across this term. There's a ":" sign between the vector in question and an entry, which is all supposed to output a real number. What exactly is sign convention, and how...

Hi all. I'm studying deep inelastic cross section in parton model. In particular I'm referring to Halzen-Martin's "Quarks and leptons" section 8.5, but I think this is a quite generale procedure. In studying the deep inelastic scattering by e- on proton it cuts off the electron part and work...

Hello, I believe this is a really stupid question but I can't seem to figure it out. So given a Minkowski spacetime one can choose either the convention (-+++) or (+---). Supposedly it's the same. But given the example of the four momentum: Choosing (+---) in a momentarily comoving...

Greetings, How do we decide on which sign to take when using the momentum operator? The question may be very simple but I need a push in the right direction. Many thanks.

Homework Statement Compute the surface integral for F = [3x^2, y^22, 0] and S being a portion of the plane r(u,v)=[u,v,2u+3v], 0≤u≤2, −1≤v≤1.The Attempt at a Solution I managed to get the correct answer, because with some luck I defined the normal in the correct direction. I am just confused...

I keep reading through the course textbook but no matter how many times I read it I just can't see the understanding of it? There are activities asking me to solve problems, and I have a book of exercises to do, but the main book supposed to be designed to give some information to the student...

Frictional force-- sign convention For a horizontal spring mass system is the frictional force considered negative (-μmg)? i guess it will be negative; the minus sign used to convey the force is trying to impede the motion of block then with that guessing work; i think friction force will be...

Hi! I'm having some trouble with optics. When we have convex, planoconvex, concave, planoconcave, and meniscus lenses, I don't understand how to substitute with the sign for R1 and R2. How do I determine whether the radius of a side is negative or positive? A book that I'm using said to take...

I read through all of the previous sign convention posts on this forum (and googled a lot and checked a bunch of textbooks) before posting this question. I don't understand the sign convention properly for geometric optics. There are two conventions that I've understood so far, and I've got a...

If a mass was hanging vertically from a spring under its own weight. In the static equilibrium position, using up as positive, the spring force is +kx and gravity is -mg. Add them up to get: kx - mg = 0. Using down as positive, the spring force is -kx and gravity is +mg. Add them: -kx + mg =...

Homework Statement The handle of the hammer is subjected to the force of F = 20. Determine the moment of this force about the point A. http://s3.amazonaws.com/answer-board-image/3214a2db-1a55-4648-b582-5f36f0f34451.jpeg Homework Equations Principle of moments: Mo = FxY - FyX The...

if a gas is expanding,what will be the sign of the work done by it?

I have just started on a course in Tensor calculus and I'm absolutely new to it, so I read that according to the summation convention, if an index appears twice, it means that the expression is summed over that index, but if it appears more than twice then the expression is meaningless. I want...

Until today I learned in geometric optics that Object distance +ve for real object else -ve Image distance +ve for real image else -ve Radius of curvature +ve for if light comes to the surcace from the side lying center of curvature else -ve On the basis of this the lens formula...

Electric potential --- doubt in sign convention Homework Statement Revered members, I know dV = -E.dx so E = -dV/dx So E should be E = -V/x . But while deriving capacitance of a parallel plate capacitor when dielectric medium is introduced we use E = V/x. But how E = V/x? Homework...

Hi, not sure if this is the right forum.. pls move if not. Almost 30 years ago, I was studying engineering and my math tutor spoke about 0 (zero) being special. We talked about how nothing can be divided by zero, and sure enough, enter 1/0 into a calculator produces an error. (I vaguely recall...

Homework Statement Homework Equations H=-k A \frac{\Delta T}{\Delta x} kconcrete = 1.0 W / m K (approx) The Attempt at a Solution H=\frac{-1.0 (8 * 12) (10-20)}{0.23} = 4.17 kW My problem is that the book (Essential University Physics, Wolfson) has the answer as -4.17 kW, but...

Homework Statement I've just started to study group theory, and i keep encountering questions where no operators are specified so i was wondering if there was a conventional operator that was meant to be used. For instance I had a question to prove that a cyclic group of order 14 is isomorphic...

My understanding of the Einstein Summation convention is that you sum over the repeated indices. But when I look at the metric tensor for a flat space I know that g^{λ}_{λ} = 1 But the summation convention makes me think that it should equal the trace of the matrix g_{μσ}. So it should...

I have seen in various locations different conventions regarding the location of a prime symbol denoting a tensor represented in a new frame. For example, if the position four-vector is x^{\mu} then this four-vector in a different frame is often written as either x'^{\mu} or...

Suppose they threw a Constitutional Convention Party and all of PF came as delegates. What rights, powers, or limitations on government, the market, or the People, (if any) would you espouse. In submitting your ideas, please don’t just say “the US Constitution – it’s perfect!” Specify a single...

Hi folks, When you arrange to meet someone at a restaurant and you may arrive at different times, what is the social protocol in terms of where to wait? Should I go inside, grab a table and wait or should I stand outside the restaurant and wait for the person to arrive? Will doing one or...

general equation of parabola is y^2=4*a*x. it's parametric equation is ((a*t^2),(2*a*t)) [as in my book] but i think there can be other kind of parametric equations also like( ((t^2)/4*a),t) it defines a parabola easily. is using ((a*t^2),(2*a*t)) as parametric equation of parabola is convention...

I have a question about Garrity's formula at the top of p. 125, here, for a function from the set of 2-form fields to the set of tangent vector fields, together with the formula on p. 123 for the exterior derivative of a 1-form field and Theorem 6.3.1 on p. 125 (Garrity: All the Mathematics you...

At first I thought that roman d was reserved for the exterior derivative and italic d for scalar differentials. That is, one would have df for the exterior derivative of function f but write dy/dx in regular calculus. But the author of the wikipedia article...

From what I understand: P=+iv (current enters through the positive polarity of the voltage, implying that the element is absorbing power) and P=-iv (current enters through the negative polarity of the voltage, implying that the element is releasing or supplying power) I remember reading that...

Hi there PF How does mathematicians usually prove differential equation (I am just speaking of the ordinary differential equations). We are going through proofs of differential equations in my high school math class at the moment, and in our books there are usual proofs, where one derives...

[I meant "what's actually happening"]The convention is that the electrons flow from + to - But in reality they flow from - to +I don't get it. Why don't we just mark it like it happens in reality? Why decided to do it otherwise? Isn't it just confusing, esp. to new students?

Okay I realize that stars emit at least some radiation outside the visual range but I have seen stars with positive BC when I thought that most values are negative due to the radiant flux over all wavelengths being greater than its flux over a certain wavelength. Is the sign of the BC the same...

Homework Statement Determine the polarity of the induced voltages in L1 and L2. [PLAIN]http://img406.imageshack.us/img406/730/31761140.jpg According to the dot convention rule, when current enters the dotted terminal of a coil,the polarity of the voltage it induces in the other coil is...

Hey guys, So the sign convention for power is really confusing me. According to my knowledge, if a positive current is entering the positive terminal of an element, the voltage drops across the element and power is hence absorbed. Why does the question solution change the sign of the current...

definition \{\vec{A},\vec{B}\}\cdot \vec{C}=\vec{A}(\vec{B}\cdot\vec{C}) \vec{C}\cdot \{\vec{A},\vec{B}\}=(\vec{C}\cdot\vec{A})\vec{B} I have a question. I found in some books that definition of tensor is \hat{T}=\{\vec{T}_k,\vec{e}_k\} where \hat{\T} is tensor! Is here...

The two standard conventions for the Minkowski metric are diag(1,-1,-1,-1) and diag(-1,1,1,1). The physics comes out the same either way, but I'm trying to make a list of the things that change depending on the convention you use. The Klein Gordon equation is one - with the "mostly plus"...

Hi everyone, I recently started a course on continuum mechanics. It started with the mathematical background of transforming tensors with contravariant and/or covariant indices. There is one thing I don't understand and it should be really straight forward. I hope you can give me a hint...

Help! Union Labor at Convention Center I was hoping someone could help me figure out the following: If I have a 40 lb trough filled with 250- 12oz sodas and 40 lbs of ice on top of a sico table on wheels that weighs 125lbs...how can i figure out if a union employee can push this to our events...

Hello, I have a doubt regarding dot convention in magnetically coupled circuits. In book A, the following is stated: But in book B, this is stated: In book B, why the inducted voltage of the second mesh (-j w M I1) has that negative sign ? According to dot convention, it is supposed that...

i have started to use dot convention for magnetically circuit. my understanding is that if the currents for primary winding and current in the secondary winding are clockwise and the dots are ontop of the inductors then the mutual inductance value would be negative because the secondary winding...

Homework Statement Ok so I'm meant to answer: To what scalar or vector quantities do the following expressions in suffix notation correspond? (expand and sum where possible). 1) aibjci 2) aibjcjdi 3) dijaiaj 4) dijdij 5) eijkaibk 6)eijkdij Homework Equations The...

Hello, I think I am fundamentally confused with summation convention. For example, if I have \epsilon_{ijk}x_j\delta_{jk} Can I sift the levi civita and get \epsilon_{ijj}x_j=0 or sift x and get \epsilon_{ijk}x_k\not=0 Each gives a different answer. What mistake...

Homework Statement Basically need to use einstein's summation convention to find the grad of (mod r)^n and a.r where a is a vector and r = (x,y,z) Homework Equations The Attempt at a Solution Not sure where to begin really.. :S grad (mod r)^n= (d/dx, d/dy, d/dz) of root (X1^2...

This is just a quick question about the convention used to write units. My assumption is that you wouldn't leave spaces between different units, but i could see this could lead to potential confusion. should i write: kms-1Mpc-1 or km s-1 Mpc-1 I guess it's normally clear from what you're...

Homework Statement Using the Einstein summation convention, prove: A\bulletB\timesC = C\bulletA\timesB Homework Equations The Attempt at a Solution I tried to follow an example from my notes, but I don't entirely understand it. Would it be possible to find out if what I've...

Homework Statement 1) Q. Which of the elements follow the passive sign convention? (psc) http://img401.imageshack.us/img401/3092/pic1r.gif v1 = +5 (V) i1 = +2 (mA) v2 = -10 (V) i2 = +500 (µA) v3 = +1 (V) i3 = -3 (mA) 2) Q. Which of the elements follow the passive sign...

Homework Statement Evaluate the following sums, implied according to the Einstein Summation Convention. \begin{array}{l} \delta _{ii} = \\ \varepsilon _{12j} \delta _{j3} = \\ \varepsilon _{12k} \delta _{1k} = \\ \varepsilon _{1jj} = \\ \end{array} The Attempt at a...

I always tended to think that we ought to use formulae which explicitly remind us that position and momentum are on equal footing in quantum theory (even though this may not be ultimately true) and write my transforms symmetrically f(x)=(2\pi)^{-3/2}\int{F(p)e^{ix\cdot p}d^3p...

Where did the 360 degree for a circle convention come from? By any chance, is it from the ~360 days for the Earth to revolve around the sun?

Hi All, I'm trying to come up with a proper method of naming cables in our machine.( we develop vending machines.) Currently I am using the following structure for cable names: Host-Target-cable Type for example: IPC-NAC-D ; which is Industrial PC - Note Acceptor - Data Cable But...

Question About Shear Stress "Naming" Convention I cannot seem to find this in any of my texts. For a shaft of circular cross-section, how do you name the shear stress \tau_{ij} caused by a Torque? That is, how do you assign the indices i j ? Is it the plane that contains the cross-section...