Derivation Definition and 1000 Threads

Hi, I am likely just missing something fundamental here, but I recently just revisited series and am looking over some notes. In my notes, I have written that if ## \lim_{x \to +\infty} \frac{a_{n+1}}{a_n} = L ## Then ## | x - x_o | = 1/L ## But shouldn't the correct expression be $$ | x -...

How did they derive equation (6)? I don't like how they say -Φm instead of Φm, but that aside, I get that both rays 1A and 2A' travel the same distance, but AC incurs a phase change due to total internal reflection (-Φm) and it travels AC from there. Meanwhile, A'C is the distance the other...

Homework Statement Hi, so confused abou this question that I probably haven't even posted it in the correct section.Here's the question. A wheel of radius ,r, is situated at the top of a ramp having an angle θ = π/6 rad. At t= 0 the wheel is at rest with its centre at coordinates (0,r) and...

Hello, I am new here, glad I found this Forum :0) I am german and english is not my mother-tongue, so sorry in advance for any language-related mistakes 1. Homework Statement i don't know how to make a vector arrow on a letter so I declare a v for vector as the following...

For a Gaussian beam, which has 86% of its power within its beam diameter (spot size 2w0), I've read that beam (angular) divergence is given by 2θ = 4λ/(π[2w0]) Where does this come from? I hate memorizing equations. It makes me feel stupid.

In the integration of Force with respect to displacement (W=∫F.dx), is that true if the rate of change of displacement approaches to zero? My teacher said the one which approaches to zero is the rate of change of time. But If I arrange the formula, I will get F=dW/dx then F= lim Δx→0 ΔW/Δx...

I'm confused on how you get the formula v=root(2GM/R²). I know you can use work=forcexdisplacement (W=Fd) so F=W/d. W=½mv² and R=d. Hence, F=½mv²/R Equate that to F=GmM/R² and rearrange to get v=root(2GM/R²). That makes sense as it involves the kinetic energy needed/work done in reaching orbit...

general equation of q in terms of S,T $$q=d(ST)=SdT+TdS$$deivation of ΔS at constant pressure(in terms of heat cap C_p: $$dq=C_{p}dT=TdS$$ $$\frac{C_{p}}{T}dT=dS$$ $$C_{p}ln(T_{f}/T_{i}=ΔS$$ why do we keep T constant on TdS side?

Homework Statement A police car is parked 50 feet away from a wall. The police car siren spins at 30 revolutions per minute. What is the velocity the light moves through the wall when the beam forms angles of: a) α= 30°, b) α=60°, and c) α=70°? This is the diagram...

Might be simple but I couldn't see. We can easily derive momentum operator for position space by differentiating the plane wave solution. Analogously I want to derive the position operator for momentum space, however I am getting additional minus sign. By replacing $$k=\frac{p}{\hbar}$$ and...

I have noticed many of the thrust derivations in textbooks I have seen do not do a straightforward derivation of rocket thrust. The all seem to use the same trick with infinitesimals in a sort of binomial form. For reference: Taylor, "Classical Mechanics" Pg. 85. I am working on a rigorous...

Homework Statement Statistical Mechanics by Pathria. Problem 3.1 Homework Equations (1) <(△nr)2>=<nr2>-<nr>2=(wrd/dwr)(wrd/dwr)lnΓ, for all wr=1 How to derive above equation from these equations? <nr>=wrd/dwr(lnΓ), for all wr=1 <nr2>=(1/Γ)(wrd/dwr)(wrd/dwr)Γ, for all wr=1 (2) Also, if you...

Bell's 1971 derivation The following is based on page 37 of Bell's Speakable and Unspeakable (Bell, 1971), the main change being to use the symbol ‘E’ instead of ‘P’ for the expected value of the quantum correlation. This avoids any implication that the quantum correlation is itself a...

Homework Statement Hi, need some help trying to understand calculus derivation of the rocket equation. If someone who be so kind as to look at the attachment where it is all laid out. Homework Equations All equations are listed in the attachmentThe Attempt at a Solution I have had a good go...

In Einstein's paper section 6 (I'm reading an English version online: https://www.fourmilab.ch/etexts/einstein/specrel/www/), it's said that one of the Maxwell Equations in frame K \frac{1}{c}\frac{\partial X}{\partial t} = \frac{\partial N}{\partial y} - \frac{\partial M}{\partial z}, where <X...

Homework Statement Solve the annuity problem: \frac{dS}{dt} = rS + d S(0) = S_0 Homework Equations Integrating factor method equation Future value of an annuity equation (this should be the final answer): S(t) = S_0e^{rt} + \frac{d}{r}(e^{rt} - 1) The Attempt at a Solution Ok, I am...

I am reading "An Introduction to Mechanics" by Kleppner and Kolenkow (2014). On page 241 is the definition of the angular momentum: "Here is the formal definition of the angular momentum $$\vec{L}$$ of a particle that has momentum $$\vec{p}$$ and is at position $$\vec{r}$$ with respect to a...

Homework Statement Look at the figure below. Derive the formula for the magnitude of the force F exerted on the large block (mC) in the figure such that the mass mA does not move relative to mC. Ignore all friction. Assume mB does not make contact with mC. Homework Equations F = ma...

Homework Statement (The fourth equation is the central one) first, we have \frac{1}{r}=\frac{a}{b^2}(1+ecosθ) and b^2=a^2(1-e^2) now using these two, we transform acosψ=ae+rcosθ into (1-ecosψ)(1+ecosθ)=\frac{b^2}{a^2} we want to find dθ/dψ, and the author performs an inplicit...

Homework Statement This seems like a simple question but I've never asked it and I'm stuck haha For my general relativity course we are asked to derive the change in a vector under parallel transport. My professor references his lecture notes on his course web page in the statement of the...

This is a question for anyone who is familiar with Di Francesco's book on Conformal Field theory. In particular, on P.108 when he is deriving the general form of the 2-point Schwinger function in two dimensions. He writes that the most general form of the tensor is $$S_{\mu \nu \rho \sigma} =...

Homework Statement A physical pendulum, consisting of a uniform rod (of mass M and length L) with an attached blob, can oscillate about an axis that goes through one end of the rod. The mass of the blob is also M. The distance of the blob to the rotation axis is x. The aim is to derive a...

When Planck's law is derive a cubical cavity is often used (for example in: http://disciplinas.stoa.usp.br/pluginfile.php/48089/course/section/16461/qsp_chapter10-plank.pdf) However, the result is applied generally. But in general, it seems like the wave lengths of the standing waves will...

Homework Statement Derive Stefan-Boltzmann Law from Wien's Law. Hint: You can use (without proof) R(T)=∫(-∞ to ∞) R(λ,T)dλ, p(λ,T)= 4/c R(λ,T). Homework Equations Stefan-Boltzmann Law:P=AσT^4 Wien's Law: λmax=(2.898*10^-3 m*K)/T. The Attempt at a Solution Let λmax=(2.898*10^-3...

This is not homework but is part of the solution process of an ODE and I cannot understand how the author made a derivation step. After a change of variable in the original ODE, the ODE in the new independent variable has a standard method of solution. But instead of using this method, the...

In Griffiths section 4.4.3, he derives the energy in a dielectric system as W=0.5∫D.Edτ. Part of the derivation involves the relation 0.5Δ(D.E)=0.5Δ(εE2)=ε(ΔE).E=(ΔD).E for infinitesimal increments, using D=εE. Now the part 0.5Δ(εE2)=ε(ΔE).E loses me so I was wondering if anybody could explain...

The differential form of a stochastic variable can be expressed as $$dx=a(x)dt+b(x)dw(t)$$, here w(t) presents the Wiener process and satisfies ##(dw)^2=dt##. For the function f(x), the derivation of its differential form in the book by Gardiner is...

Hi everyone Homework Statement I'm trying to understand the Laue equation but I have problems unterstanding the derivation, especially one part in my textbook about the path difference (see attachment) The Attempt at a Solution My textbook says that the path difference here is...

I am trying to experimentally derive the drag equation. I have dropped coffee filters with varying masses and determined their resulting terminal velocity. I plotted the data and found that the mass of the coffee filter is proportional to the terminal velocity squared. I was now wondering how I...

I have learned in 1st year that the under-damped simple harmonic motion can be described by the differential equation m \frac {d^2 x} {dt^2} + b \frac {dx} {dt} + kx = 0 where m is the mass, b is the constant of linear drag and k is the spring constant But the derivation is skipped...

The torque contribution due to the uniaxial anisotropy is given by the equation below \frac{\Gamma}{l_m K} = (2 \sin\theta \cos\theta)[\sin\phi e_x - \cos\phi e_y] (3) This contribution can be taken in the LLG equation to derive the LLG equation in polar coordinates \frac{\partial...

I'm reading Leonard Susskind's The Theoretical Minimum Vol. 1. 1. The problem: I'm on the section in which he asks the readers to derive the Lagrangian for a particle on a rotating carousel in polar coordinates. 2. Relevant ideas: The same Lagrangian in Cartesian coordinates is given as...

Hi all, I'm trying to derive that t=δ(t'+vx'/c^2) Using x'=δ(x-vt) then substituting for x=δ(x'+vt') I should be able to isolate t and solve the problem but I am getting to the following point after simplification and can't figure out where to go next...? x'= δ[δ(x'+vt')-vt] (isolate...

Hi all. As you may be aware, there are a handful of modern derivations of the Papapetrou equations i.e. the equations of motion for a pole-dipole particle in curved space-times. These are usually along the lines of a Hamiltonian or Lagrangian derivation (c.f. Racine et al 2009 and Anandan et al...

Homework Statement may i know how to derive the the sha[pe of graph and get the point of min (2f , 4f) ? i really have no idea how to get the shape of the graph and the min point. The book give it without any explanation. Homework Equations The Attempt at a Solution

Homework Statement This is the graph of v against u . i am having problem of getting the shape of graph and getting the point (2f, 2f) . can anyone teach me how to derive it? Homework Equations The Attempt at a Solution sorry. i don't know how to use LATEX. it may be quite...

Greetings everyone in MHB. :) Well I've just created a thread to just verify if my answer is correct. On a simple problem that using implicit differentiation. A cylindrical tank of radius 10 ft is having drained with water at the rate of 200 f^3/ min. How fast is the height of water changed...

For a uniform, hollow cylinder, why is this derivation wrong? M = mass of whole solid cylinder m = mass of missing cylindrical piece R = radius of whole cylinder r = radius of missing cylindrical piece moment of inertia = moment of inertia of whole cylinder - moment of inertia of...

$$\vec{F}=q\vec{v}\times\vec{B}$$ $$\frac{d\vec{F}}{dq}=\vec{v}\times\vec{B}$$ $$\int\frac{d\vec{F}}{dq} \cdot ds=\int(\frac{d\vec{s}}{dt}\times\vec{B}) \cdot ds$$ from here, I went about it two different ways: 1.) Here I assumed everything was at right angles and got rid of all the vectors...

Homework Statement Greetings! I am reading section 2.8 of Jackson and trying to understand how completeness relation was derived. It starts with the orthonormality condition: ∫U_N ^*(ε) U(ε) dε =δ_{nm} We can represent a function as a sum of orthonormal functions if N is finite...

I want to know the derivation of solid angle. I have found on net. But the derivation is to long, is there any short method?

Take a look at the attachment, my question is obvious from the colored points. The attachment is from: "state-of-the-art formulas for helicity amplitude calculation and all that (version 2.4) PART Ia. Spherical-Vector Method for Helicity Amplitudes (FORMALISM) Ken-ichi Hikasa" I think...

Just a quick question. Let A and B be two points. Electrical work is defined as the amount of energy it takes to move an amount of charge Q through a potential difference VB-VA (for our purposes here, we will assume that the voltage values are measured with respect to an Earth ground) and is...

I got stuck in deriving the velocity of the particle from the acceleration equation. Here are the details of the problem. The acceleration of a particle with a relativistic momentum is \vec{a} = \frac{\vec{F}}{\gamma m} - \frac{\vec{v}}{\gamma m c^2}\left(\vec{F} \cdot \vec{v}\right)...

Homework Statement So this isn't a homework problem but I don't know where else I am supposed to post for general help. I am basically trying to understand the derivation for the equation of motion of a particle in a rotating frame. See attachment for derivation and which steps I am stuck on...

Hi. on page 95 , I am not sure how did he derive the second term on the RHS of equation (13.16). http://books.google.co.il/books?id=5OepxIG42B4C&printsec=frontcover&dq=srednicki+page+95&hl=en&sa=X&ei=XDLFU8bCIobV4QSnhYFA&ved=0CBsQ6AEwAA#v=onepage&q&f=false I mean if I plug back I should get...

I was wondering if someone could show me the derivation of Faraday's Law of induction from the more fundamental Lorentz Force.

Hey guys! New to physicsforums. I wanted to ask a more conceptual question regarding RC time Circuits. I spent some time trying to derive the equations, and I feel like I'm not setting up the problem correctly. Here's my attempt: Solutions according to profecssor: 1)...

Homework Statement ## \alpha \frac{d^2\theta}{dt^2}+\beta\frac{d\theta}{dt}+V'(\theta)=V(t) ## Inertial effects are negligible at frequencies of up to several hundred megahertz, so the first therm can be neglected. I'm not sure if that means that ## \beta\frac{d\theta}{dt}+V'(\theta)=V(t) ##...

I am currently reading "Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles" by Robert Eisberg and Robert Resnick (2nd edition). In Appendix C they derive the boltzman distribution and they seem to be saying something that seems to me to be patently false. If you have the book...