Change Definition and 1000 Threads

It's said that the below equation is invariant under a substitution of ##-\theta## for ##\theta## , ##\frac{d^{2} u}{d \theta^{2}}+u=-\frac{m}{l^{2}} \frac{d}{d u} V\left(\frac{1}{u}\right)## I can't understand this how this is so. It's supposed to be obvious but I can't see it. Please help...

I know that if the transformation was canonical, the form of Hamilton's equation would remain invariant. If the generating function for the transformation was time independent, then the Hamiltonian would be invariant and we could directly replace q and p with the transformation equations to get...

I have a question about changing variables in the context of thermodynamics, but I suppose this would extend to any set of variables that have defined and nonzero partial derivatives on a given set of points. First I should define the variables. ##T## is temperature, ##U## is internal energy...

I am looking to approximately calculate the temperature change of a sample that was exposed to a laser pulse. Experimentally, we know the optical absorption, reflection, and transmission, as well as the source parameters for our laser system. I realize that I will have to make approximations...

Not trolling here, just have genuine confusion over CO2 levels comparied to what we believe CO2 levels have been historically and their effect on climate change. I recently saw some Facebook group infographic posts which claimed that CO2 concentration in the atmosphere is the lowest it has ever...

can't understand

Changing the temperature of a metal changes the resistivity. But It also changes the size of a sample under test. Does the change in size have an additional effect on the resistance or is that already factored in ?

Magnetic fields coupling question. I had to make a small tool holder for my drill press, it hangs on side of press using N52 cylinder magnets. The holder is 4" long x 3/4 x 3/4" AL bar. With a spacing of 3", two 1/2" holes are bored to accept the 1/2 x 1/2 N52's, which will be epoxied in. I...

Bit of a long shot but can anyone remember a TV program where the presenter measured the weight of something at ground level and compared it to the weight at the top of a tall building, possibly the Empire State building? Sorry I can't recall more details. Think it was at least 10 years ago...

By using the given relationship that S=a/T --(1) along with the equation ∫ (delta Q rev)/T=∫dS -- (2) I found out that my answer for the value of Q is mc*ln (T2/T1)*a upon equating (1) & (2). But the solution is instead given as Q=a*ln*(T1/T2). I would be grateful if someone would point out...

Hello guys on PF, thanks for your attention. I am an undergraduated student from "Peking University", which is a top 2 university in China (There are two best university in China, the other one is Tsinghua University), that is a good university. But my major is not a popular major, which is...

If ##(u,v)## are null coordinates and ##S(u,v)## a two-surface of constant ##u## and ##v## then the Bondi-Sachs mass ##M_{\mathrm{BS}}(u) = -\dfrac{1}{8\pi} \displaystyle{\lim_{v \rightarrow \infty}} \oint_{S(u,v)}(k-k_0) \sqrt{\sigma} d^2 \theta## satisfies (Poisson, 2007)\begin{align*}...

Good morning everyone! I am an aerospace engineering working on my thesis and i am trying to solve a little problem. In the picture you can see an "aeordynamic" body. The CFD analysis gives me the forces and the moments acting on this body. How can i calculate the momentum acting on the body...

To my understanding any quantum system can be describes as a linear combination of eigenstates or eigevectors of any hermetian operator, and that the eigen values represent the observable properties. But how does the system change with time? I suppose big systems with many particles change with...

Upon seeing the question in my assignment I knew in a isobaric process, work done by the gas is ##W=P\Delta V## so if volume is increased ##4## times the original considering the original volume as ##V## we can say after expansion the volume is ##4V##. Then ##W=P(4V-V)=3PV## and the ##Q## would...

If you were to fire a single atom from a fixed point into a chamber of perfect vacuum and measure where it collides with the opposite wall. Could Spontaneous symmetry breaking in the sub atomic particles cause momentum change in the atom, changing the part of the wall the atom interacted with?

Hi, It's not a homework problem. I was just doing it and couldn't find a way to change the integral limit from "x" to "t". I should end up with kinetic energy formula, (1/2)mv^2. I've assumed that what I've done is correct. Thank you! Edit: "E" is work done.

Water is flowing in the pipe with velocity v0. Upon sudden closure of the valve at T, a pressure wave travels in the -ve x direction with speed c. The task is to find ##\alpha##, where ##\Delta P = \rho_0 c (\Delta v) \alpha##. The 1st step is to set up an equation using conservation of mass...

Ay ay ay. Here's yet another worry to give you headaches.

Hey dear physics community :) I ask myself what exactly happens to forces between materia when the materia hits near lightspeed. I know, that for an objective bystander watching let's say elon in his rocket with 99,99999% the speed of light, that the time goes slower, the mass of the rocket...

hi guys I am trying to implement the a second order differential equation tat contains a time dependent term, the equation looks something like r'' = -\mu/r^3+(g/g^3-m/m^3) the idea is that i want to calculate 'r' the position vector of a point, that is dependent on vectors g and m, I tired to...

Solution attempt : Option : I am sure that my work is wrong. But, I must add solution attempt in PF that's why I just added that. How can I solve the problem?

qn3: why is statement 2 the only answer? isn't speed one of the factors in velocity too? then shouldn't statement 1 be true too?

Bio-impedance technique is used to monitor various organ related qualities. Shift in metabolism will also show up as a shift in impedance. My question is if by exposing a target volume with ionizing radiation and thereby release electrons and at the same time measure the impedance (which will...

ΔQ=mC(T3-T1) But, will this C be Cp or Cv. Both pressure and volume changes. So, neither of them can be. Feeling so confused

So consider a subject system, a galaxy, with stars in it. This galaxy is passed by another object, the perturber. When the interaction is fast, we call this interaction a high-speed encounter. Now we consider that the interaction is really fast. This means that during the interaction, the...

What is the difference between percent change and percent difference? When would you use one over the other? Thanks.

Hi, This is as part of a larger probability change of variables question, but it was this part that was giving me problems. Question: If we have ## 0 < x_1 < \infty ## and ## 0 < x_2 < \infty ## and the transformations: ## y_1 = x_1 - x_2 ## and ## y_2 = x_1 + x_2 ##, find inequalities for...

I can get the citation code from Inspire.net for papers. However, can I change the Bibliography settings in some way such that there are hyperlinks to the paper? I don't want to embed it manually for every reference. For instance. Now, I use the citation code @article{Hawking:2000kj...

We have two different integrals, the first one being ∫∫erdrdθ where -1≤r≤1 and 0≤θ≤π which equals approximately 7 and ∫∫erdrdθ where 0≤r≤1 and 0≤θ≤2π which equals approximately 11. Why do these integrals have different values and do not go against the change of variables theorem? I'm having...

Your guys really helped me out with my last bulb problem so I thought I'd try again. There's a bulb over a staircase that is - a recessed floodlight - about 18 feet above the stairs directly beneath it (it's over the bottom of the stairs, and the staircase is exposed to the next floor) About...

*My bad if this question is a tad ree ree. I've just completed my first year of college and am still inexperienced. I just study physics for fun.* My intuition says the momentum of the water vapor is still conserved during the phase shift, as this question most probably relates to the...

Like the thread on Earthquakes possibly contributing to the collapse of civilizations in the last Bronze Age, I heard that a famine impacted Egypt, and possibly the Aegean region and perhaps into Eastern Europe and parts of North Africa during the period 2200 - 2000 BCE (aka Early Helladic III...

Don't understand from where should I start?

To find ##\delta## for the 1st order, all I need to do is to square the diameter of the 2nd ring and subtract it to the square of the diameter of the first ring. $$\delta_{1st \; order} = {d^2}_{2nd \; ring} - {d^2}_{1st \; ring}$$ To find ##\Delta##, I can use the below equation...

Hello, I'm looking for a textbook on climate change that is not afraid to use advanced physics and mathematics (thermal/statistical physics, differential equations, fluid dynamics, etc.). Too many textbooks on the topic shy away from the mathematics, preventing me from obtaining a deep...

I'm reading "Differential Equations with Applications and Historical Notes" by George F. Simmons and I am confused about something on pages 431-432 He has the second order ordinary differential equation $$\frac {d^2v} {d\phi^2} + \frac {\cos(\phi)} {\sin(\phi)} \frac {dv} {d\phi} + n(n+1)v = 0...

I know the integral of a P(V) eqn gives an eqn for work. I was wondering if taking the derivative of a P(V) eqn gives an eqn for change in pressure?

So what I did was find the change in Q per min. Mass melted per min * latent heat capacity = Q per min = 11.5 kg /min * 3.4*10^5 J/kg = 3910000 J/min Now the equilibrium temperature is 100 degrees Celsius or 373.15 degrees kelvin. If I do 3910000 J/min / 373.15 K I get 10478 J/(K*min). This...

The problem I am having is simple. I have a Gaussian spectrum initially. Like this, Process 1: S = m0/sqrt(2*pi*sigma^2) * exp(-(vel_axis - mu).^2/(2*sigma^2)); Here, mu is the mean velocity (frequency) and sigma is the standard deviation. vel_axis is the axis on which I am calculating this...

Hi, I was attempting the problem above and got stuck along the way. Problem: Suppose that ## Y_1 ## and ## Y_2 ## are random variables with joint pdf: f_{y_1, y_2} (y_1, y_2) = 8y_1 y_2 for ## 0 < y_1 < y_2 < 1 ## and 0 otherwise. Let ## U_1 = Y_1/Y_2 ##. Find the probability distribution ##...

If we know the change of angle is twice the incident angle, then the rate of rotation is 2*100 rpm = 200 rpm. Is there a better explanation of it?

Textbooks always give an explanation for why electrons move between energy levels in atoms with an explanation something like this: 'An electron can jump to a higher energy level if it absorb's energy which exactly matches the difference between final and initial energy level'. My question...

$\tiny{2.1.5.1}$ Change the second-order initial-value problem into a system of equations $x''+6x'-2x= 0\quad x(0)=1\quad x'(0)=1$ ok my first step was to do this $e^{rt}(r^2+6r-2)=0$ using quadratic formula we get $r=-3+\sqrt{11},\quad r=-3-\sqrt{11}$ just seeing if I going down the right road🕶

Hello, Let's consider a vector ##X## in 2D with its two components ##(x_1 , x_2)_A## expressed in the basis ##A##. A basis is a set of two independent (unit or not) vectors. Any vector in the 2D space can be expressed as a linear combination of the two basis vectors in the chosen basis. There...

Remind me please? In a three level system, with discrete energies E0,E1,E2: would light-shift (Stark shift), applied due to an external electric field, change the values of E1 and E2 by the same \Delta E? Or would \Delta E1 be different from \Delta E2?

How much does the equivalent width of a line change by the introduction of 5% scattered light? We know the equivalent width is defined as We know the equivalent width is defined as $$W = \int_{-\infty}^{\infty} \bigg(\frac{1-F_{\nu}}{F_c}\bigg) \, d\nu$$ where ##F_{\nu}## represents the flux in...

I use the GMail web interface, in Firefox, for all my email needs. 
 I frequently change the color of text that I quoted from the Sender in my GMail replies. 
 Example: 
 Hi, 
 You wrote, ". . . a;sdkfjasl;fkjasl;kfj . . . ," 
 and I just want to...

So I calculated the final and initial pressures using the given eqns, ended up with the final pressure of 96629 and initial pressure of 62639. Then I used the PV=nRT eqn to calculate the final and initial temperatures. T=P*V/(n*1.5*R). I got an initial temperature of 81.79 and a final...