Angular momemtum Definition and 117 Threads

Homework Statement Consider a 2-particle system where the two particles have angular momentum operators ##\vec{L}_1## and ##\vec{L}_2## respectively. The Hamiltonian is given by $$H = \mu\vec{B}\cdot (\vec{L}_1+\vec{L}_2)+\gamma \vec{L}_1\cdot \vec{L}_2.$$ Determine explicitly the eigenvalues...

Homework Statement Consider two pairs of operators Xα, Pα, with α=1,2, that satisfy the commutation relationships [Xα,Pβ]=ihδαβ,[Xα,Xβ]=0,[Pα,Pβ]=0. These are two copies of the canonical algebra of the phase space. a) Define the operators $$a_\alpha =...

Hello. I'm currently entering into a Physics II class at the start of my third semester at UCONN (my first semester was introductory modern physics - kinetic theory, hard-sphere atoms, electricity and magnetism, scattering, special relativity, Bohr model, etc), and finished Physics I off with...

Hello, in classical physics orbital angular momentum is defined as the cross product of the position vector 'r' and the momentum 'p'. A friend told me that all moving objects must have orbital angular momentum (even if it is moving along a straight line). That statement confuses me a lot...

Homework Statement Considering the atom made of an electron and a positron. The spin-orbit Hamiltonian is: $$H=\frac{e^2}{4\nu^2c^2r^34\pi\epsilon_0}\vec{L}\cdot\vec{S}$$ with ##\vec{L}## the relative angular momentum, with ##\vec{S}## the total spin and ##\mu## the reduced mass. Finding the...

1. At the instant of the figure, a 6.70 kg particle P has a position vector of magnitude 4.30 m and angle θ1 = 43.0° and a velocity vector of magnitude 3.40 m/s and angle θ2 = 32.0°. Force , of magnitude 7.40 N and angle θ3 = 32.0° acts on P. All three vectors lie in the xy plane. About the...

I explained this thinking to a meteorologist once and she couldn't give me an answer. Any physicists want to give it a shot? I find the typical explanation of tornadoes perplexing (that's a polite way of saying I don't believe it). The explanations I've seen claim that tornadoes start out...

Homework Statement Hi I'm having trouble with a question that's asking me to calculate the precession rate for a spinning top. The trouble that I'm having is that I don't understand how the angular momentum points along the axis of the spinning top (picture attached). When I use the formula...

On Griffiths's book page 166 first paragraph he said " It's not merely that you don't know all three components of L; there simply aren't three components—a particle just cannot have a determinate angular momentum vector, any more than it can simultaneously have a determinate position and...

Homework Statement The spherical harmonic, Ym,l(θ,φ) is given by: Y2,3(θ,φ) = √((105/32π))*sin2θcosθe2iφ 1) Use the ladder operator, L+ = +ħeiφ(∂/∂θ+icotθ∂/∂φ) to evaluate L+Y2,3(θ,φ) 2) Use the result in 1) to calculate Y3,3(θ,φ) Homework Equations L+Ym,l(θ,φ)=Am,lYm+1,l(θ,φ)...

Homework Statement The problem relates to the subject of torque and angular momentum: A man of mass ## M ## stands on a railroad car that is rounding an unbanked turn of radius R at speed v. His center of mass is height ## L ## above the car, and his feet are distance ## d ## apart. The man is...

In my EM class, this vector identity for the angular momentum operator (without the ##i##) was stated without proof. Is there anywhere I can look to to actually find a good example/proof on how this works? This is in spherical coordinates, and I can't seem to find this vector identity anywhere...

Homework Statement A comet orbits the sun. It's position in polar coordinates is given by, $$r(\phi)=\frac{1.8r_0}{1+0.8\cos{\phi}},$$ where ##r_0## is the position at closest approach. Its velocity at this point is given by ##v_0##. Use the concept of angular momentum to find the following...

Hi all! I'm currently working on a graphics/physics engine. The following Wikipedia page was extremely helpful in making rectilinear collisions look natural: https://en.wikipedia.org/wiki/Elastic_collision#Two-dimensional Specifically, the very general vector form of the equation on the bottom...

Homework Statement A rod of mass M y length L can spin freely around a fixed point P, as shown in the picture. A bullet of mass m is shot perpendicular to the rod, and after impact, it is embedded into it. After impact the system realizes small oscillations, and that immediately after impact...

I am trying to create a momentum trap to calculate the velocity of a projectile when it hits the trap. It essentially consists of a plate if known mass at the bottom of a pendulum of known radius. When the projectile hits the plate, the degrees that the pendulum rotates are recorded. I believe...

<Moderator's note: Moved from a technical forum and thus no template.> I am trying to design and perform a physics lab. It needs to show the relationship between torque and angular momentum. I have gotten as far designing a 4" PVC coupling and have it on a ramp. I am not sure where to go from here.

Given a wave function $$\Psi(r,\theta,\phi)=f(r)\sin^2(\theta)(2\cos^2(\phi)-1-2i*\sin(\phi)\cos(\phi))$$ we are trying to find what a measurement of angular momentum of a particle in such wave function would yield. Attempts were made using the integral formula for the Expectation Value over a...

Homework Statement Given 3 spins, #1 and #3 are spin-1/2 and #2 is spin-1. The particles have spin operators ## \vec{S}_i, i=1,2,3 ##. The particles are fixed in space. Let ## \vec{S} = \vec{S}_1 + \vec{S}_2 + \vec{S}_3 ## be the total spin operator for the particles. (ii) Find the eigenvalues...

Homework Statement Three small, identical 0.70-kg pucks are attached to identical 0.50-m strings, tied together at a common center as shown in (Figure 1) . Pucks are whirled in circular motion at angular speed 3.0 s-1 What is the magnitude of the angular momentum of the system about the...

Homework Statement it is given in the image i uploaded Homework Equations L→=r→ × p→[/B] The Attempt at a Solution If the angular momentum of a particle is the cross product of the position vector of the particle from the axis and its linear momentum, how can the angular momentum of m1 and...

Homework Statement A bead of mass m slides in a frictionless hollow open-ended tube of length L which is held at an angle of β to the vertical and rotated by a motor at an angular velocity ω. The apparatus is in a vertical gravitational field. a) Find the bead's equations of motion b) Find...

So I've just started reading into how gyroscopes work and I've hit a wall. Previously I thought that the upwards angular momentum kept the spinning object up straight, but why does it do the same if it's spinning clockwise too even though the angular momentum would be pointing down? Does the...

Homework Statement Homework Equations Angular momentum = moment of inertia * angular velocity Change in angular momentum = impulsive moment v^2=u^2+2as The Attempt at a Solution First I used v^2=u^2+2as to find the velocity of the particle the moment the string goes taut. I got v=\sqrt{8ag}...

As a spinning mass is unwound, angular momentum is conserved, meaning ##Iω## remains constant. However, since rotational energy is proportional to the square of the angular velocity, how is it possible for energy to be conserved as well?

Homework Statement A horizontal plywood disk with mass 6.90 kg and diameter 1.14 m pivots on frictionless bearings about a vertical axis through its center. You attach a circular model-railroad track of negligible mass and average diameter 1.04 m to the disk. A 1.40 −kg , battery-driven model...

What I am interested in doing, is considering the angular momentum eigenstate for a spin ##1## system: ##|J=1, M=1\rangle = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}##, forming the coherent state ##|CS \rangle = \begin{bmatrix} 0.5 \\ -\frac{i}{\sqrt{2}} \\ -0.5...

This is the problem I'm trying to understand: Consider two particles with spin 1 without orbital angular momentum. If they are distinguishable, from the rule of addition of angular momentum applied to spin, we'll have states of total spin j=0,1,2. If we have, however, identical particles which...

Homework Statement A man of Mass M stands on a railroad car that is rounding an unbanked turn of radius R at speed v. His center of mass is height L above the car, and his feet are distance d apart. The man is facing the direction of motion. How much weight is on each of his feet. Homework...

I'm trying to understand the rotations of rigid diatomic molecules such as HCl. My understanding of the orbital angular momentum is that it is quantized with a total value equal to $$E=\frac{\hbar^2}{2I}J(J+1)$$ where I is the rotational moment of inertia and J is the quantum number. Also, J...

Homework Statement A sphere of radius R is rolling without slipping with a velocity v and collides inelastically with a step of height h < R. ¿What is the minimum velocity for which the sphere will be over the step? Homework Equations Total kinetic energy (maybe)...

Homework Statement Show that ##|l, m\rangle## for ##l=1## vanishes for the commutator ##[l_i^2, l_j^2]##. Homework Equations ##L^2 = l_1^2 + l_2^2 + l_3^2## and ##[l_i^2,L^2]=0## The Attempt at a Solution I managed to so far prove that ##[l_1^2, l_2^2] = [l_2^2, l_3^2] = [l_3^2, l_1^2]##. I...

Consider an ideal fidget spinner, composed of a central disk (a bearing, usually) plus some N disks, all of them of radius L distributed regularly with their centres along a circle of radius R. In the simplest case all of them have the same mass, M, and are able to turn freely without...

Hello everyone, I have a problem while calculate dynamic for gyroscope system on bicycle. I use Lagrange's equation for modelling precession effect, with generalized coordinate is a angular, the applied generalized force will be a torque. The model of gyroscope system like picture below: I've...

There are two types of angular momentum: orbital and spin. If we define their operators as pseudo-vectors \vec{L} and \vec{S}, then we can also define the total angular momentum operator \vec{J} = \vec{L}+\vec{S}. Standard commutation relations will show that we can have simultaneous well...

1. Homework Statement Determine the total magnitude of angular momentum Ho of the particle about point O. The velocity of the particle is 5.5 m/s.Homework Equations Ho= r x mv The Attempt at a Solution The answer is 43.04. My question is, isn't the graph wrong? If you take the magnitude of the...

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} -...

Homework Statement A uniform rigid scale is held horizontally with one of its end at the edge of the table and the other supported by hand. Some coins of negligible mass are kept on the meter scale. As the hand supporting the scale is removed, the scale starts rotating about its edge on the...

Take a disc that can rotate with respect to the rotation axis. For simplicity, let's assume that its mass is homogeneously distributed along the rotation axis, and gravity and frictional forces do not act on the disk. In the first case, the disc does not rotate. All elements of the disk have...

https://link.springer.com/chapter/10.1007/978-3-540-39664-2_1 http://iopscience.iop.org/article/10.1088/0031-8949/1988/T22/016/pdf In these two experiments done back in the 80's, electrons were trapped inside a penning trap for long periods of time. They were measuring the ratio of the magnetic...

I'm trying to solve this problem, however I'm unsure if my reasoning is correct - I do agree with the answer, but something seems wrong to me in my reasoning. 1. Homework Statement A rod is on a frictionless surface, and is defined by the length L and mass M. It is hit on one end by a piece...

Homework Statement (This is a problem I myself created, so it may sound a bit trivial/stupid.) A particle of mass m in the xy plane has velocity v and a radius vector r with respect to some origin. After some time Δt, the same particle has velocity v and a radius vector r' with respect to the...

Homework Statement [/B] There is a solar panel array of 3 panels connected to a spacecraft . The panels in the array are connected linearly (in a row: panel1 + panel2 + panel3 + spacecraft ) with hinges. They are all 0.2 meters by 0.3 meters and connected along the 0.3 meter side using 2...

As far as I understand it, a nebula initially tends to have a small amount of rotation (on average) and then as it collapses under its own gravity this rotation increases significantly due to conservation of angular momentum (assuming that there is no external torque,right?!). What I'm unsure...

Homework Statement [/B] I messed up the original thread in terms of information, so I made a new better one. Ok here goes: I have a problem where a right circular cylinder with diameter .115meter and a mass of .03kg is rotating at 300 rev per min. Now an Ant which weighs .01kg collides with...

The angular momentum is related to the rotation. And when a black hole has angular momentum, it is said that it is a "rotating black hole". But what does it mean? A black hole does not have a conventional surface, like a basketball. How should we interpret that angular momentum? I asked this...

I'm doing research on why some galaxies and other phenomenon like Saturn's rings are flat. There seems to be two answers. Here they are in shortened form: 1) When the galaxy is forming, there is some net angular momentum in some direction.Over time, all particles with an angular momentum...

[Note: Post moved to homework forum by mentor] So I stumbled upon a reviewer for my physics exam tomorrow and I was wondering how the equation was formulated. Your help is very much appreciated :) ! Normally I would consult my professor for this but it's Sunday in my country today so I can't...

Homework Statement Consider the rigid body in the picture, rotating about a fixed axis z not passing through a principal axis of inertia, with an angular velocity \Omega that can vary in magnitude but not in direction. Find the angular momentum vector and its component parallel to z axis (...

Homework Statement Homework Equations Find Angular Momentum. How to find velocity of a particle. The Attempt at a Solution If i differentiate with `dt` both sides, I'm getting velocity y-component=velocity x-component. Then i feel helpless:cry: