Momentum Definition and 1000 Threads

I am reading a proof of why \left[ \hat{L}_x, \hat{L}_y \right ] = i \hbar \hat{L}_z Given a wavefunction \psi, \hat{L}_x, \hat{L}_y \psi = \left( -i\hbar \right)^2 \left( y \frac{\partial}{\partial z} - z \frac {\partial}{\partial y} \right ) \left (z \frac{\partial \psi}{\partial x} -...

This is a problem for a fluid dynamics class I'm in. My current approach is to use a conservation of mass approach and say that the d/dt(momentum in the cart) = momentum into the cart. This leads to (u is speed of the cart, V is volume J is jet velocity, A is cross sectional area of the jet)...

Hello I need help to explain the affect of the cross product without the its current symbolism, but for angular momentum. I can explain angular momentum in terms of the cross product of 3D space formulated like this: |r| |v| * sin(angler.v) e-perp to r and v Eq.1 (I can explain this to...

In a closed system, I know the rider wouldn't be able to change the combined center of gravity of the system by moving his weight around. If he pushes the bike to lean to the right, he would go to the left by the amount that would keep the combined cog the same. But a bike with tires and a road...

Homework Statement The red box only Homework EquationsThe Attempt at a Solution I suppose we have to show L_3 (Π_1) | E,m> = λ (Π_1) | E,m> and H (Π_1) | E,m> = μ (Π_1) | E,m> And I guess there is something to do with the formula given? But they are in x_1 direction so what did they have...

Hi. I am revising my Mechanics: Dynamics by reading the Beer 10th edition textbook and Pytel 2nd edition In Pytel pg 358 art. 17.3 the angular momentum about the mass center of a rigid body in general motion is being calculated...

A spiral phase plate can change the orbital angular momentum of a beam of light. Should I think of the beam of light carrying the orbital angular momentum or the photons that make up the beam light? If the orbital angular momentum is carried by the individual photons what is being orbited, the...

Homework Statement [/B] Please check the attachments as to view the questions. Homework Equations Ek= 1/2 mv^2 EPSpring= 1/2 kx^2The Attempt at a Solution A) EPSpring= 1/2 kx^2 1/2 (100)(0.11) ^2 =0.605 JB) Is ok I understand it. C) EKO=EKFEPSpring(Initial) + EK(Initial) =...

Homework Statement A 39.00 kg rod of length 2.8 m is hanging vertically by one of its ends that is free to swing in a complete circle about a frictionless axle/pivot. The rod has uniform mass density. Suddenly it is struck horizontally by a 5 kg putty that sticks to the center of...

Hi. In a Mach-Zehnder interferometer, there are mirrors in both paths. When a photon gets reflected on a mirror, it transfers momentum. Also, mirrors are classical objects that are usually not assumed to exist in superposition states. Shouldn't it (at least in principle) be possible to measure...

Let's say you've got a boat filled with n frogs of mass m each. Let's also say that all the frogs jump simultaneously out of the boat in the same direction with velocity v, then the boat will get a velocity v1 in the opposite direction because of conservation of momentum. Now if we instead let...

Homework Statement The same horizontal force is applied separately to two objects initially at rest on a horizontal, frictionless surface. Object A has less mass than object B. In each case the force is applied for the same length of time. Which of the following statements is true after the...

If we define Si=(1/2)× (reduced Planck's const)×sigma Then what will be (sigma dot vect{A})multiplied by (Sigma dot vect{B}) Here (sigma)i is Pauli matrix. Next one is, what will we get from simplifying <Alpha|vect{S}|Alpha> where vect{S} is spin vector & |Apha>is equal to " exp[{i×(vect{S} dot...

Homework Statement Hi, Question attached: inserting ##\phi (x)= \int \frac{d^4k}{(2\pi)^2}\phi(x)e^{-i k_u x^u}## and similar for ##J(x) ## / ##J(k)## into the action and then integrating over ##k## gives: Solution attached: I AM STUCK on this part, completing the square ; so I see...

Homework Statement A police officer is attempting to reconstruct an accident in which a car traveling southward with a speed of 23 mph colided with another car of equal mass traveling eastward at an uknown speed. After the collision, the two cars coupled and slid at an angle of 60 degrees south...

Homework Statement its a nuclear physics problem : a deuterium atom with energy 4Mev collides with a boron atom B5/10 in an elastic collision producing an H1/1 and B5/11 ,the Q of the reaction = 9.23 Mev . find the E,E' , the energy of the boron and the hydrogen the unknowns : E,E', theta of...

Homework Statement Homework Equations conservation of momentum Thrust of rocket engine = -u (dm/dt) u is the velocity of the gas being expelledAlso found this from Wikipedia, not sure if it is relevant The Attempt at a Solution For these kinds of problems I assume you need to apply...

Homework Statement [/B] A thin uniform bar 2.00 m long and weighing 90.0 N is hanging from the ceiling by a frictionless pivot. It is suddenly struck 1.50 m below the pivot by a small 3.00 kg ball initially travellimg horizontally at 10.0 m/s. The ball rebounds and moves in oppossite direction...

Homework Statement Consider an electron in a state described by angular wavefunction $$\psi(\theta,\phi)=\sqrt{\frac{3}{4 \pi}}\sin \theta \cos \phi$$ Here θ and φ are the polar and azimuthal angles, respectively, in the spherical coordinate system. i. Calculate the probability that a...

1. The problem statement, all variables and given/known How long does a 1kg ball to reach the momentum of 75.5kgm/s if it free falls? Homework Equations Momentum= mass x velocity F = (m x change in velocity) / change in time The Attempt at a Solution I used the first formula to find the...

Homework Statement a. A skateboarder of mass 52kg is riding her 5.5kg skateboard at a speed of 4.3m/s. She jumps off her skateboard, sending the skateboard forward at a speed of 8.6m/s. what is the velocity of the skateboarder after she jumps off? b. What is the net force if it takes 1.25 for...

I intuitively understand macroscopic vibration, but trying to understand what it means for a particle to vibrate doesn't seem to make sense from the classical understanding I have of momentum and energy. First, are particles even said to vibrate or have vibrational energy? If so, how is momentum...

I read from a text that Rutherford found out that all the mass must be concentrated in the middle of the atom due to fast-moving alpa ( high momentum) is deflected back at 180 degrees. I am wondering if there is going to be no contact collision due to the the kinetic energy being converted...

Apart from the fact that it is, what is the physical significance of the fact that you can get the momentum distribution of a particle by taking the Fourier transform of its position distribution?

Hi all - apologies, I'm starting a new thread here for something buried at the end of another thread - but I think the topic of that thread had changed sufficiently to warrant a more succinct top-level post. Thanks very much to PeterDonis for his very useful answers in the previous thread...

Homework Statement A block of mass 100 grammes was stationary on the flat surface at ##x = 0##. At time ##t = 0## a horizontal force of 10 Newtons was applied on the block in the positive x direction during ##\Delta t = 3## seconds. Find at what x position the block will stop, if the...

I know that P=m*v but I saw that Momentum (p) =E/c how can we say this We need to have inertia to call the momentum of entity. Plzz solve this dilemma

Homework Statement Given the Schwarzschild metric generalisation for a mass M rotating with angular momentum J ##ds^2 = -(1-\frac{2 M}{r}) \; dt^2 +(1-\frac{2 M}{r})^{-1} \;(dr^2 +r^2 \;d\theta ^2 +r^2 \sin ^2 \theta \; d\phi ^2) -\frac{4J}{r} \sin ^2 \theta \; dt d\phi ## a) Write the...

I would like to check my understanding for this problem : A puck with mass ##3m## is stationary on a horizontal friction-less surface. It is being impacted in an elastic head-on collision by another puck with the mass ##2m## traveling with speed ##u## to the right. Find the speed and direction...

Homework Statement Two solid spheres one of mass 'm' and other of mass '2m' are comin towards each other(translationally) with a velocity v1 and v2.After collision the sphere of mass 2m comes to rest and the sphere of mass m does oblique projectile motion at an angle 30 with the vertical till...

In general relativity, does momentum conservation mean conservation of 4-momentum or 3-momentum

1. A moving rough cylinder of radius a, and mass m collides with an identical cylinder, on a smooth horizontal surface. Its centre of mass moves with linear velocity v0, and its angular velocity is ω0. What is the motion of the cylinders after the collision? I have be told that the answer to...

I have a set of k-points, e.g. k1,k2,k3,k4. and they are equivalent by symmetry. Now I have calculated the momentum matrix element <i|p|j> at k1 point ONLY, and then calculate the optical properties which, for example, depend on <i|p|j><j|p|i> I have to make a summation on four k-points...

In quantum mechanics, the velocity field which governs phase space, takes the form \begin{equation} \boldsymbol{\mathcal{w}}=\begin{pmatrix}\partial_tx\\\partial_tp\end{pmatrix} =\frac{1}{W}\begin{pmatrix}J_x\\J_p\end{pmatrix}...

Homework Statement So for those who aren't familiar with the Gauss Gun here is a video demonstrating its function: As you can see in the video, a steel ball is rolled towards a sequence of magnets and other steel balls and as the incoming ball strikes the magnet, the ball on the other end...

I am trying to understand Wen and Zee's article on topological quantum numbers of Hall fluid on curved space: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.69.953 They passingly mentiond the fact that a spinning particle with orbital angular momentum $s$ moving on a manifold with...

Homework Statement Let two particles of equal mass m collide. Particle 1 has initial velocity v, directed to the right, and particle 2 is initially stationary. A: If the collision is elastic, what are the final velocities v_1 and v_2 of particles 1 and 2? B: Now assume that the mass of...

Hello. The problem is this, what happens to angular momentum, tangential velocity and centripetal force when you change the center of rotation. For example, if we have rotating hinged arm, weight at the end, with certain angular momentum and tangential speed etc. which then gets stopped at...

I tried to get a relativistically correct expression of ##\int_0^t\frac{dp}{ds}dt## similar to the derivation of relativistic energy expression but I got a result which is not defined: $$\int_0^t\frac{dp}{ds}dt=\int_0^v\frac{d\left(\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}\right)}{v}$$...

##\frac{dp}{dt}## is given the name 'force' but ##\frac{dp}{ds}## has no name. I know 'force' is useful for calculations and predicting the future of the system. If 'convenience in calculations' is the reason why some quantities are given names, then I don't see why ##\frac{dp}{ds}## doesn't...

Homework Statement Homework Equations 0=viscous+gravitational+pressure I saw in the solutions that pressure=0 in this case, but why? I also knew that : accumulation= flow in - flow out+generation, why not use this one? The Attempt at a Solution (their solution) We are interested in...

Homework Statement The figure shows an overhead view of a 2.50-kg plastic rod of length 1.20 m on a table. One end of the rod is attached to the table, and the rod is free to pivot about this point without friction. A disk of mass 39.0 g slides toward the opposite end of the rod with an initial...

Two chunks of rock, each having a mass of 1.00 kg, collide in space. Just before the collision, an observer at rest in the reference frame of a nearby star determines that rock A is moving toward the star at 0.800 c and rock B is moving away from the star at 0.750 c . If the rocks stick...

Homework Statement Basically, I'm dealing with part d) in this document: https://s3.amazonaws.com/iedu-attachments-message/b663095a5021cb6aee55657de728a8d7_bfbe0ba9d2f10f8ac9ef9d049934c1da.jpg. I have found that the angular momentum only depends on spatial coordinate and it doesn't on time. Is...

Homework Statement Suppose that the momentum of a system is 8 kg m/s. What is the kinetic energy of the system if it has a mass of 10kg? If this system is brought to rest with a constant force in 5 seconds, what is the magnitude of this force? Homework Equations Momentum > p = (m)(v) Kinetic...

In classical field theory, translational (in space and time) symmetry leads the derivation of the energy-momentum tensor using Noether's theorem. From this it is possible to derive four conserved charges. The first turns out to be the Hamiltonian, and thus we have energy conservation. The...

Homework Statement So basically I have a train with two joined carriages which become separated (m1) Mass one =13563kg and (m2) Mass two =30394kg. the initial velocity of the joined carriages is 5.00m/s (u1). When the carriages separate I have the final velocity of (m2) which is 0.96m/s (v2)...

Hi. I have come across the following statement - the eigenvalue equation for J+ is given by J+ | j m > = ħ √{(j+1)-m(m+1)} | j , m+1> My question is this - how can this be an eigenvalue equaton as the ket | j, m> has changed to | j , m+1> ? Surely the raising/lowering operators don't have...

Please bare with me as I'm a beginner with this stuff, and am just learning lol But I was wondering if I did the right math to figure out the momentum of the Space Shuttle. Linear Momentum, in classical mechanics, is the product of the mass (the measure of an objects resistance to acceleration...

Why is it that introducing a hard cut-off ##p^{2}=\Lambda^{2}## breaks Lorentz invariance? Is it simply that it introduces an energy scale and energy is not a Lorentz invariant quantity? Sorry if this is a trivial question, but I just want to make sure I understand the reasoning as I've...