Momentum Definition and 1000 Threads

A) and b) should be useful for solving the initial question. If the truck is at rest initially, the magnitude of the momentum of the ball becomes ##|mv'|=|MV' - mv|##, but this may or may not be less than the magnitude ##mv##, depending on how large ##V'## is. ##V' = \frac{m(v+v')}{M}## in this...

The correct answer is: #P = \int \frac{dp^3}{(2\pi)^3}\frac{1}{2E_{\vec{p}} \big(a a^{\dagger} + a^{\dagger}a\big)# But I get terms which are proportional to ##aa## and ##a^{\dagger}a^{\dagger}## I hereunder display the procedure I followed: First: ##\phi = \int...

https://www.physicsforums.com/threa...f-a-translating-and-rotating-pancake.1005990/ So,I think I posted this in the wrong place. So, I will move it to here. Here, in post #6, it is stated that ##\int R dm = M R##. As far as I know, R change from time to time and it is not constant. Hence, isn't...

So I have a trolley of mass m that moves on a straight line. A sphere of mass m, is attached on the trolley with a light string of length a and it is left to oscillate. Just to give some idea of their positions: r_trolley = xi r_sphere = (x-asinθ)i - acosθj (θ is the angle between the string...

I have read that the Schrodinger equation has no formal derivation we are simply applying the Hamiltonian operator on the wave function $$\hat H = i\hbar \frac{\partial}{\partial t} = \hat T + \hat V$$ here we substitute $$\hat T = \frac{\hat p^2}{2m}$$ where $$\hat p = -i \hbar...

I am currently reading David Morin book and found this statement : ##\,\,\,\,\,\,\,\,## "It is important to remember that you are free to choose your origin from the legal possibilities of fixed points or the CM" Is it really alright to choose the center of a...

.

In a head-on collision between the proton and electron, what is the squared 4-momentum transfer between the two particles. Starting with the difference in momentum of the electron with the 4-vectors before and after the event: $$(P-P')^2=P^2+P'^2-2P\cdot P'$$ The circumstances are such that the...

Now, deriving relativistic momentum isn't terribly difficult, but that's not the same as understanding it. I'm trying to figure out why conservation of momentum in special relativity requires the gamma factor. When I looked at conservation of momentum in elementary physics, we basically just...

I was thinking a little about how the absorption of angular momentum occurs from the point of view of QM. For example, suppose we have an atom A and an electron $e^-$. The electron $e^-$ is ejected from a source radially in direction of the center of the atom. Suppose that the atom has net...

Help me understand a concept I came across by accident. So there is an axis (red) that is rotating with two rods attached to it (45 degrees from axis and 90 degrees with respect to one another) now if the balls at first are located closest to the red axis , as the axis begins to rotate the balls...

##\vec{L} = \vec{P} \times\vec{r}## ##L = mvr sin \phi##, where P = mv Since ##\vec{r}## and ##\vec{v}## are always perpendicular, ##\phi## = 90. Then, ##L = mvr## At this point, I don't see how to get ##L = mvr = mr^2\omega##, using ##\omega = \dot{\phi}## I know that ##\omega =...

While physics is generally believed to be CPT symmetric, there are processes for which such symmetry is being questioned - especially the measurement. One of examples of (allegedly?) going out of QM unitary evolution is atom deexcitation - we can save its reversibility by remembering about...

I have read Classical Mechanics book by David Morin, and there are some parts that I do not understand from its derivation. Note : ## V## and ##v## is respectively the velocity of CM and a particle of the body relative to the fixed origin , while ##v'## is velocity of the particle relative to...

Hi all! These days I am brushing up my knowledge on EM Waves. I begin with the introductory level but I don't mind to engage in an advanced treatment of the topic. At the very basic level I had a high school book, the mentions straightway that if the wave carries with it an energy U, it posses...

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?

So we all know that the form of the momentum operator is: iħd/dx. And for energy it is iħd/dt. But how do we derive these operators? The only derivations of the i have seen is where the schrødinger equation was used, but that makes the logic circular, because the Schrødinger-Equation is derived...

The goal I am trying to achieve is to determine the momentum (2D) in a quantum system from the wavefunction values and the eigenergies. How would I go about this in a general manner? Any pointers to resources would be helpfull.

I am trying to find the equations of motion of the angular momentum ##\boldsymbol L## for a system consisting of a particle of mass ##m## and magnetic moment ##\boldsymbol{\mu} \equiv \gamma \boldsymbol{L}## in a magnetic field ##\boldsymbol B##. The Hamiltonian of the system is therefore...

Consider a car slamming into an unyielding wall at 60 mph. Objects in the car will be slammed against the dashboard with a certain amount of force. Now, instead of slamming into a stationary wall, you slam into another car coming towards you at 60 mph. Relative speed, 120MPH. QUESTION: Will...

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...

Since it asks for the time evolution of the wavefunction in the momentum space, I write : ##\tilde{\Psi}(k,t) = < p|U(t,t_{0})|\Psi> = < U^\dagger(t,t_{0})p|\Psi>## Since ##U(t,t_{0})^\dagger = e^{\frac{i}{\hbar}\frac{\hat{p^2}t}{2m}}##, the above equation becomes ##\tilde{\Psi}(k,t) =...

I made a new version of the falling cat video, with narration. It explains how cats turn around while having zero net angular momentum during the fall:

I've a body having initial angular velocity at ## t=0 ## as shown. The axis shown are fixed in inertial space and initially match with the principal axis. I want to find the infinitesimal change at ##t+\Delta t## in the angular momentum along the ##z## axis. I've seen the following approach...

The given lagrangian doesn't seem to correspond to any of the basic systems (like simple/ coupled harmonic oscillators, etc). So I calculated the momentum ##p## which is the partial derivative of ##L## with respect to generalized velocity ##\dot{q}##. Doing so I obtain $$p =...

A disc initially has angular velocities as shown It's angular momentum along the y-axis initially is ##L_s## I tried to find its angular momentum and ended up with this:##L=I_{x} \omega_{x}+I_{y} w_{y}+I_{z} z_{z}##The z component of angular momentum is thus ##L_{z}=I_{z} \omega_{z}## However...

Ball X has mass 0.03kg. It falls vertically from rest from a window that is 30 m above the ground. Ball Y has mass 0.01kg. At the same time that Ball X starts to fall, Ball Y is projected vertically upwards from ground level directly towards Ball X. The initial speed of Ball Y is 20 m/s...

Answer is (a) I thought it would be (b) due to conservation of momentum - so final momentum of the hockey stick is equal to the initial momentum of the ball. I assume this isn't correct because there are other external forces acting (air resistance?) Is that sound?

A hockey ball of mass 0.2kg is hit so that its initial speed is 8 m/s. The ball travels in a horizontal straight line with acceleration given by a= - 0.5- kt where t is the time in seconds measured from when the ball was hit. After 2s the ball has traveled 41/3 m. It is then intercepted by a...

It's been a few years since I failed my physics degree but I still really want to reach an understanding of QM, and I'm currently going through a QM textbook. One thing I cannot understand no matter how much I think about it, is momentum uncertainty. In classical mechanics a specific kinetic...

My understanding is that virtual particles don't really exist. However, they somehow come into existence under certain circumstances. For example, in the Casimir Effect the virtual particles on the outside of the plate now have the capacity to transfer momentum and kinetic energy to the...

The marker wrote that the answer is 4 and it's because m and v double. I don't understand how m doubles??

I aready got the solution for this exercise. However, the solution used the referance frame from the car: What I'm trying to understand is the line: Because before reading the solution, I was trying to solve it using the lab frame. So this is my work so far: Using conservation of momentum and...

Good night. I have a doubt, what is the meaning of the coherent states superposition of momentum? In a many of places, sites I see an explanation for the equations but I never see the explanation between diffences of the superposition of position from momentum.

Hi everyone, In my physics class, we are doing the Hollywood Physics Project. It's a project where you analyze the physics from a scene in a movie and talk about if it's accurate or not. I chose the scene from the Avengers where Thor strikes Captain America's shield with his hammer. The...

Momentum operator is ##p=-i\frac{d}{dx}## and its adjoint is ##p^\dagger=i\frac{d}{dx}##. So, ##p^\dagger=-p##. How is the momentum Hermitian?

I solved it by two methods: ----------------------------------------------------- First, by conservation of linear momentum, using the vector velocities of each particle: In the imminence of the impact, the velocity of all the three particles are the same, \vec v_0 = - \sqrt{2gh} \hat j...

##m=.3 kg, v = 11 \frac {m}{s}, t = .25 s, \vec v_1 = mv\langle cos(-55), sin(-55) \rangle, \vec v_2 = mv\langle cos(25), sin(25) \rangle## $$m\vec v_1 - m\vec v_2 = \vec Ft = mv\langle cos(25)-cos(-55), sin(25)-sin(-55) \rangle$$ $$Ft = mv\sqrt{(cos(25)-cos(-55))^2 + (sin(25)-sin(-55))^2}$$ $$F...

Hi guys, a special relativity problem requested to choose the right graph representing relativistic momentum ##p## as a function of rel. kinetic energy ##K##, from these four: At first, I tried writing ##p## as a function of ##K##, in order to then analyze the function's graph and see if it...

Any spinning item, proton, electron, even planet, has angular momentum that creates force. How can an electron exist in a random orbital cloud around a spinning proton if it has an angular momentum and requires force to alter from any circular orbital plane (like a planet orbiting a star)?

I am not sure how does the integral was did here. More preciselly, How to go from the first line to the second line? Shouldn't it be $$\frac{4 \pi}{(2 \pi)^3} \int _{0} ^{\infty} p^2 e^{ip*r}/(2 E_p)$$ ? (x-y is purelly spatial)

This problem I already solved using another resource (just get the coordinate of the center of mass reach and from it, get to the larger mass. R = (3v02) / (4g)). But I'm having some trouble calculating using moment conservation. Here what I've done so far: $$ 3\vec v_0 = \vec v_1 +2\vec v_2 $$...

I have attempted to plug in grams, kiliograms, and even pounds but it was wrong.

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)...

Find the probability distributions of the orbital angular momentum variables ##L^{2}## and ##L_{z}## for the following orbital state functions: ##\Psi(x) = f(r) sin(\theta) cos(\theta)## ##\Psi(x) = f(r) cos^{2}(\theta)##I am aware that the prob. distribution of an observable is ##|<a_{n} |...

[Mentor Note -- Specialized question moved to the general technical forums] Homework Statement:: To show that ##J = Ma## for the charged Kerr metric [Wald Ch. 11 Pr. 6] Relevant Equations:: \begin{align*} \mathrm{d}s^2 = &- \left( \frac{\Delta - a^2 \sin^2{\theta}}{\Sigma}\right) \mathrm{d}t^2...

So I can find the initial momentum using p=h/wave = 4.98 x 10-23. Now my problem is that I don't know the final momentum of the photon nor electron, I just know the photon is scattered at an angle of 34 degrees. I know how to solve this problem if I was given the final wavelength of the light...

So the initial wavelength gives the total momentum, p=h/11.2p. Which is 59.161y. Then I tried to substract the momentum from the scattered light to get the momentum of the electron. 59.161y-h/13.6p, which ends up being 0.4872 as the final answer, but the answer is supposed to be 0.77?

I am very confused when textbooks say the direction of Angular velocity is perpendicular ot radius and theta for that matter direction is in perpendicular direction. I know this comes from cross product rule but what is the meaning of Angular velocity and Angular momentum directing in upward...