Derivation Definition and 1000 Threads

In the special theory of relativity, it seems impossible to derive the lorentz transformation without assuming that the lorentz factor is independent of the sign of the relative velocity. For some reason, I can't get my head around why this assumption is so easily made, as if it's trivial. Can...

Consider that the particle is moving in circular with tangential velocity v, and (0,0)is its origin. I wonder why dr/dt is equal to tangential velocity instead of radial velocity (since dr/dt means how much change in radial distance in a really short duration of time)

Consider the situation where an observer at rest on the ground measures the frequency of a siren which is moving away from the observer at speed ##v_{Ex}##. Let ##v_w## be the speed of the sound wave. Let ##\lambda_0##, ##f_0##, ##\lambda_D##, and ##f_D## be the wavelengths and frequencies...

Hi, I'm following an introduction course to chemistry and I am reviewing the chapter on Chemical kinetics. It's shown that the reaction speed for a certain component of a general chemical equation such as aA +bB <-> cC + dD , might be expressed as v = k[A]m[ B]m. I was wondering where it does...

Another question about the use of the micro-canonical ensemble in deriving distributions. On the Wikipedia-page the authors mention that the total volume of the system has to be constant. See...

Sorry if there are other threads on this, but after a discussion with a friend on this (im in the mountains, so no books, and my googlefu isn't helping), I realize that my understanding of the variational principles arent exactly... great! So, maybe some one can help. Start with a functional...

The total energy of the particle is ##u^2 / 2 - k/R##. When ##u^2 \gg 2k/R##, we take the total energy to be ##u^2/2## only. By the conservation of energy, we have: $$ \frac{u^2}{2} = \frac{w^2}{2} - \frac{k}{p} $$ Take the angular momentum expression ##l = bu##, we can replace ##u## with...

Can somebody please derive for me an example of the Binding energy from the Semi Empirical mass formula? I am trying myself but always there is a difference between the database binding energy and my own result. I am calculating the BE of Niobium 93. For the mass formula I used the coefficients...

The covariant form for the Levi-Civita is defined as ##\varepsilon_{i,j,k}:=\sqrt{g}\epsilon_{i,j,k}##. I want to show from this definition that it's contravariant form is given by ##\varepsilon^{i,j,k}=\frac{1}{\sqrt{g}}\epsilon^{i,j,k}##.My attemptWhat I have tried is to express this tensor...

I am trying to understand the Helmholtz equation, where the Helmholtz equation can be considered as the time-independent form of the wave equation. It seems to me that the Helmholtz equation can be derived from the Fourier transform, such that it is part of a larger set of equations of varying...

Summary:: According to Yale’s University PHYS: 200: v*(dv/dt) = d(v^2/2)/dt Could someone explain how has he reached that conclusion? He claims to be some standard derivation rules, but I can’t find anything about it. As much as I can tell: (dv/dt)* v = v’ * v = a* v thanks! [Moderator's...

In the screenshots below there are the equations (11.49) and (11.53). I don't understand how did he derive equation (11.53) from Eq.(11.49)? From (11.49) I get: ##d\phi/dy= d\phi/du du/dy = (1/b^2-u^2+2Mu^3)^{-1/2}(1+2My)##. It seems he neglected the ##2Mu^3## since ##Mu\ll 1##, so ##y\approx...

In general, if R is the recovery channel of an error channel ε, with state ρ, then and according to these lecture slides, we get the final result highlighted in red for a bit flip error channel. I am simply asking how one reaches this final result. Thank you (a full-ish derivation can be found...

There are two parts to my question. The first is concerns the variation of the Reimann tensor. I am trying to show $$\delta...

I figure that either the Force F2 is applied in the opposite direction because of some kind of resistance, but I'm not sure. Thanks!

I've been noodling around with derivations of the relativistic energy and momentum, and I almost got it down to just a few lines. But not quite. I'm going to work in one spatial dimension, for simplicity (even though some derivations require a second spatial dimension) Let's assume that there...

My mentor wants the derivation of this formula. Me a computer undergrad, unable to figure it out, and my final project are on a halt due to this, any help from the community is greatly appreciated!

Here is a simple way to get Euler's relation for those learning pre-calculus/calculus, so the trigonometric addition formula and the derivative of sine and cosine are easy. We will assume some basic knowledge of complex numbers and properties of Euler's number, e. Consider a small segment of...

Good afternoon all, In David Griffiths' "Intro to Quantum Mechanics", I'm looking through Example 3.2 on page 115 that shows how to get the eigenfunctions and eigenvalues of the momentum operator. I completely understand everything up until this part: ##\int_{-\infty}^{\infty} f_p'^*(x)...

I've having trouble understanding a derivation of the speed of sound waves, which is actually similar to another derivation I found a couple days ago. Let's suppose the sound is moving through water in a long cylindrical horizontal pipe. The premises of the derivation are 1.) For a given...

Good afternoon all, On page 51 of David Griffith's 'Introduction to Quantum Mechanics', 2nd ed., there's a discussion involving the alternate method to getting at the energy levels of the harmonic oscillator. I'm filling in all the steps between the equations on my own, and I have a question...

hi guys i have a question about the derivation of the density of states , after solving the Schrodinger equation in the 3d potential box and using the boundary conditions ... etc we came to the conclusion that the quantum state occupy a volume of ##\frac{\pi^{3}}{V_{T}}## in k space and to...

https://en.wikipedia.org/wiki/Elastic_collision μα+mβ=μx+my, μα^2+mβ^2=μx^2+my^2 I want x in relation of all variables except y, therefore I need to replace-eliminate y: μα+mβ=μx+my =>y=(μα+mβ-μx)/m μα^2+mβ^2=μx^2+my^2=>y=((μα^2+mβ^2-μx^2)/m)^0.5 and it is eliminated if I equate these two parts...

Hey there I'm currently taking a course on numerical methods for solving differential equations, and atm we are working with the discrete laplacian operator. In particular the 9-point stencil: However unlike the 5-point stencil, this one is getting to me. I have tried several things, in...

Important note: I only derived the differential equation, I did not solve it. What I think caused the mistake: - the tangent approximation (tan(theta+dtheta) ~ tan theta + d theta

I'm reading about the derivation of ampere force law formula, which is $$ F=k_A \iint \frac{i'ds' \times (ids \times \vec{r})}{\vec{r}^2}$$ where K_A is mu_0/4pi. In the article that I read, they have assumed such these paths: And according to ampere's conclusion that he had from observation...

Summary:: partial differential equation (PDE) to describe the potential distribution φ in the system Hey, I need some help with the following question: We have a stationary electrolyte, a magnetic field "B" and a Current density "j" (2D). Derive the partial differential equation (PDE) to...

Hi, I was recently being taught a control theory course and was going through a 'derivation' of the controllable canonical form. I have a question about a certain step in the process. Question: Why does the coefficient ## b_0 ## in front of the ## u(t) ## mean that the output ## y(t) = b_0 y_1...

I am trying to derive the tangential acceleration of a particle. We have tangential velocity, radius and angular velocity. $$v_{tangential}= \omega r$$ then by multiplication rule, $$\dot v_{tangential} = a_{tangential} = \dot \omega r + \omega \dot r$$ and $$a_{tangential} = \ddot \theta r +...

Attached is the problem and my work through the problem. I got the problem correct, but my teacher said this could be done quicker on a calculator. Any idea how it could be done quicker.

in class we derived the following relationship: $$\frac{1}{V}\frac{dV}{dt}= \nabla \cdot \vec{v}$$ This was derived though the analysis of linear deformation for a fluid-volume, where: $$dV = dV_x +dV_y + dV_z$$ I understood the derived relation as: 1/V * (derivative wrt time) = div (velocity)...

How do I simplify the expression...

This derivation is found in Kleppner's mechanics book. It shows how to find the acceleration in rotating coordinates by differentiating ##\vec v_{in}=\vec v_{rot}+\vec\Omega\times\vec r##; subscripts IN and ROT stand for inertial and rotation respectively. My question is what the term...

Hi guys, in the derivation of the Euler equation we apply Newton's 2nd law to a gas flowing through a streamline. To do so, we consider a "box" with sides ##dx## ##dy## and ##dz##: as such; Here, with reference to the image, I can't understand where does that '##+dp##' comes from, and hence...

I have seen E=pc used to derive E=MC2. I have seen E=MC2 used to derive E=pc. This is circuitous. Which came first and how is E=pc derived?

hi guys i was trying to understand the derivation of the child Langmuir law that govern the current flow between the two plates of vacuum tubes and saw this derivation online : and i am stuck at couple of points : when i saw the derivation it seem like a direct application of the Poisson's...

Summary:: I am trying to derive that the divergence of a magnetic field is 0. One of the moves is to take the curl out of an integral. Can someone prove that this is addressable Biot Savart's law is $$B(r)=\frac{\mu _0}{4\pi} \int \frac{I(r') \times (r-r')}{|r-r|^3}dl'=\frac{\mu _0}{4\pi}...

https://arxiv.org/abs/2010.15621 Superselection of the weak hypercharge and the algebra of the Standard Model Ivan Todorov [Submitted on 29 Oct 2020] I haven't had time to study this paper yet. But a few curiosities: It talks about Clifford algebras. But in fact it builds on work due to...

$$cos\theta = \frac {s}{1-s} = \frac{p-1}{p}$$ in this equation ##\theta## is the bond angle and ##s## and ##p## are the fractional s-character of the orbital and p-character of the orbital. This is equation is used rigorously in showing that the s-character of the axial orbitals in a ##sp^3d##...

to I am a bit clueless on how to get break the ##r X(r)## from inside the derivative.P.S. I tried to copy from Symbolab instead of pasting the picture, but it didn't let me.

this method of derivation is approximating the function using a polyhedron. concentrating on one of the surfaces(say the L'th surface which has an area ##\Delta S_l## and let ##(x_l,y_l,z_l)## be the coordinate of the point at which the face is tangent to the surface and let ##\hat n## be the...

Hi all, I am having some troubles deriving the truth table of the following: I don't understand how does one gets to the highlight parts. For example, 10 10, when the carry is low, shouldn't the output be 0 0 1? I fully understand how to add if it is a single bit, but now with 2 bits, it is a...

Homework Statement:: i saw this simple derivation of the uncertainty principle in my college introductory quantum book Relevant Equations:: Δp.Δx = h hi guys i saw this derivation of the uncertainty principle in my college quantum book , but the derivation seems very simple and sloppy , i...

The specific heat capacity at constant volume and the specific heat capacity at constant pressure are intensive properties defined for pure, simple compressible substances as partial derivatives of the functions u(T, v) and h(T, p), respectively, $$c_v=\left ( \frac{\partial u}{\partial T}...

f(x+2h) = f(x) + 2hf’(x) + .5(2h)^2f”(x) f(x+h) = f(x) + hf’(x) + .5h^2f”(x) f(x+2h) - f(x+h)? f(x+2h) - 2f(x+h)?

In the last step of the derivation of escape velocity, the two sides of the equation seem to have opposite signs. $$-1/2mv_0^2=-mgR_e^2\,\lim_{r\to\infty}(1/r-1/R_e)$$ $$-1/2mv_0^2=mgR_e^2 \frac{1}{R_e}$$ Since the mass and the square of the velocity are positive, the left side of the equation...

Hi there. I have the following function: $$f(x)=\ln|\sin(x)|$$ I've caculated the derivative to: $$f'(x)=\frac{\cos(x)}{\sin(x)}$$ And the domain of f(x) to: $$(2\pi n, \pi+2\pi n ) \cup (-\pi + 2\pi n, 2\pi n)$$ And the domain of f'(x) to: $$(\pi n, \pi+\pi n )$$ I want to determine for...

Hello friends. I have this question about how the Einstein field equations were derived, the assumptions behind them and the possible applications of them. What could their solutions be?Also, how are they used in cosmology and in the big bang theory?What about astrophysics? Thank you very much.

What I don't understand is why ##dS## is expanded in only the two differentials ##dV## and ##dT.## Why doesn't it look more like: $$dS = \left(\dfrac{\partial S}{\partial V}\right)_{T,P,U} \ dV + \left(\dfrac{\partial S}{\partial T}\right)_{V,P,U} \ dT + \left(\dfrac{\partial S}{\partial...