Angular momentum Definition and 1000 Threads

Suppose a point mass B (m = 2 Kg) is rotating on a massless string (r = 2m) at v = 3m/s. Then KE = 9 J, p = 6 Kg m/s and L = p * r = 12 Nm (left in the sketch) Suppose B collides with A (m=2) the bob of a pendulum on a massless rod r = 1m. Is L conserved? It seems that there is no external...

Homework Statement Mass 2 collides with mass 1 as shown in the image, mass 1 is attached to the stick and it is initially stationary. Consider that the stick is massless and can rotate around the point O. The entire system is on a frictionless table. Which magnitudes are conserved in the system...

Homework Statement Consider the case of an atom with two unpaired electrons, both of which are in s-orbitals. Write the full basis of angular momentum eigenstates representing the coupled and uncoupled representations Homework Equations l=r×p lx=ypz-zpy ly=zpx-xpz lz=xpy-ypx l+=lx+ily...

Homework Statement I'm supposed to calculate all the states for a system with ##l=1## and ##s=1/2##. Let's say ##\vec{J} = \vec{L} + \vec{S}##. I want to find the Klebsch-Gordon coefficients. I know that said system has 2 towers, one with ##j=3/2## and the other with ##j=1/2##. I've...

Homework Statement At time t, particle with mass m has displacement ##\vec r (t)## relative to origin O. Write a formula for its angular momentum about O and discuss whether this depends on choice of origin. The second part is what I'm more unsure of. Homework EquationsThe Attempt at a...

Why do things which spin tend to keep spinning in the absence of external forces such as friction with the environment? In order for objects to keep spinning doesn't their periphery (relative to their centre of rotation - which would be their centre of mass, right? - ) have to be constantly...

Hi all I gather a normal black hole has maximum angular velocity at the point that the event horizon is moving at The speed of light. However what would be the maximum rotational velocity for a maximally charged black hole- for example one made purely of electrons? Thanks

The question is: A turtle is on a turntable. which is rotating on frictionless bearings at an angular velocity omega. The turtle walks towards the outside of the turntable (away from the center). Which of the following is true about the system's angular velocity omega and its angular momentum...

Homework Statement Two atoms of equal mass m, that move with the same speed but opposite direction, interact when they're in some region R of space, as in fig.1. After the interaction, one of the atoms moves with velocity ## \vec{V1} ## as in fig.2. a) Are the linear and angular momentum of...

When you add two angular momentum states together, you get states which have exchange symmetry i.e. the highest total angular momentum states (L = l1 + l2) will be symmetric under the interchange of the two particles, (L = l1 + l2 - 1) would be anti-symmetric...and the symmetry under exchange...

Homework Statement Consider a particle with orbital momentum ##l=1## and spin ##s = 1/2## to be in the state described by $$\Psi = \frac{1}{\sqrt{5}}| 1,1\rangle|\downarrow\rangle+\frac{2}{\sqrt{5}}|1,0\rangle|\uparrow\rangle$$ If the total angular momentum is measured what would be the...

I have a very basic questions about units for angular momentum. The measure is in kg m^2/s Angular velocity is in radians/s and therefore radians do not appear in the units. Here is my question, can we leave this in degees/s? Sure its not used but is it wrong? If we are dealing with...

Homework Statement Prove $$ j^{\mu} = j_ {EXTERIOR}^{\mu} + j_ {INTERIOR}^{\mu}$$. Writing $$j_ {EXTERIOR}^{\mu}$$ in terms of the energy-momentum tensor. Prove $$j_ {EXTERIOR}^{\mu}$$ is related to the Orbital Momentum and $$j_ {INTERIOR}^{\mu}$$ to the spin.Sorry, for the lane shifts...

Suppose a rod of 1m length and 10 kg mass is lying on a frictionless surface or in vacuum. Suppose now a point particle of mass 1 Kg hits one tip of the rod at speed 22 m/s in an elastic collision: If the CoM is fixed on a frictionless fulcrum, it is easy to predict that the particle will...

Hi, In the principles of quantum mechanics by P.A.M Dirac it says on page 149, For dealing with an angular momentum whose magnitude is 0.5(h_bar), it is convenient to put m=0.5(h_bar)a how is this if (m.m)^0.5= (3/4)^0.5*(h_bar)? Thanks

I was reading on gyroscopes, and everything seemed to make sense: the spin angular momentum along the axis of the gyroscope changes due to the torque by gravity, causing precession. However, I can't understand why we are measuring angular momentum (the spin of the gyroscope) from the center of...

I've tried this problem at least 10 times using the equations in my book and I keep getting the same answer. What am I doing wrong? Homework Statement A solid steel sphere of density 7.6 g/cm3 and mass 0.2 kg spin on an axis through its center with a period of 1.5 s. Given Vsphere =4/3π^3, what...

Homework Statement Why is it that the horse closest to the axis of rotation on a merry go round spins slower than the horse on the outer edges of the merry go round? I saw this video on youtube and got confused at the first merry go round example: According to conservation of mass, isn't v...

Lets say i have a rod (length = L) hinged at one end (A).It is initially at rest.Now if an impulse (J) acts on the other end (B),can i conserve the angular momentum about A(the hinge)? that is can i write: JL=Iw?(I=moment of inertia,w=angular velocity) this is what i saw in the book. My Doubt...

Homework Statement Calculate the commutator ##[\hat{L}_i, (\mathbf{rp})^2]## Homework Equations ##\hat{\vec{L}} = \sum\limits_{a=1}^N \vec{r}_a \times \hat{\vec{p}}## ##[r_i,p_k] = i\hbar\delta_{ik}## The Attempt at a Solution Okay so here is what I have so far: $$ \begin{eqnarray}...

Homework Statement Find out the angular momentum of particle as it reaches the highest point about the origin in projectile? m=1 kg angle(i)=60 degree(with horizontal) u=10 m/s g=10Homework Equations The Attempt at a Solution As angular momentum=##mrvsinB ## Here velocity at top=##ucos\theta...

I am reading "An Introduction to Mechanics" by Kleppner and Kolenkow (2014). On page 241 is the definition of the angular momentum: "Here is the formal definition of the angular momentum $$\vec{L}$$ of a particle that has momentum $$\vec{p}$$ and is at position $$\vec{r}$$ with respect to a...

I've been reading Kip Thorne's "Black Holes and Time Warps," and it mentioned something rather counter-intuitive; apparently, when material forms an accretion disk and falls into a spinning black hole, it increases the angular momentum of it. Now, let's take a gas cloud, and put a spinning...

Hello everyone! I'm going to uni in October and I'm brushing up on my mechanics before I go. I've just got to a bit that has confused me before and has confused me again now: When you have a rotating object, say it is rotating in front of you in a vertical plane and it is rotating...

Hi, I have a question related to the orbital angular momentum. In the referring to Arfken & Weber Mathematical Methods for physicists-6th edition page 267, "In the relativistic Dirac equation, orbital angular momentum is no longer conserved, but J=L+S is conserved," Here, I want to...

Suppose you have a bucket filled with superfluid Helium-4 and you spin it with a large angular velocity Ω, the bucket obviously has angular momentum. Spinning fast enough, the fluid develops irrotational vortex lines which carry quanta of angular momentum, while leaving the curl of the ∇xv 0...

Hi All, This is from a classical mechanics problem, and I already 'solved' the problem, but I'm interested in why a certain term is set to zero. I think I understand the concept but just want to clarify. The problem is a table with a hole in it and two masses on a string, one mass is...

In particle physics we know that total angular momentum is conserved and its equal to orbital angular momentum plus spin angular momentum Can you give an example for me this total angular momentum conservation with explain specificly tell orbital angular momentum and spin angular momentum.

How to prove when electron spin is perpendicular to linear momentum, orbital angular momentum can't be 0. And when they are paralleled, orbital angular momentum is 0. Thanks.

hey all! I have just finished processing the data of an n-body simulation (RAMSES code was used to do the simulation and AMIGA halo finder found our halos) ,so I have chosen a specific halo and it contains a massive galaxy (and of course satellite galaxies around it) and the code was run from...

Hi, I'm relatively new to QM so just a basic explanation of my problem would be amazing! I'm doing some internet research on superfluidity over my summer holiday, and was looking specifically at 3He, and the way it forms Cooper pairs. Having read a classical analogy to why the relative angular...

In vector form, L=Iω. I am trying to show that for a point particle, this reduces to L=rxp, but am getting an extra factor of r2 : For the case of a point particle, I=Mr2. Also, ω=rxv. Plugging these into L=Iω gives: L=Mr2(rxv) = r2(rxp). Thus this reduces to a point particle...

Homework Statement 'Consider an inertial frame in which a free particle travels past the origin O but does not go through it. Show by direct calculation that the particle's angular momentum about O is constant.' Homework Equations \frac{d\vec{l}}{dt}=∑\vec{\tau}...

Hi all, Just a quick theory based question regarding the Zeeman Effect. The effect of the applied magnetic field in the Zeeman effect separates the possible angular momentum states (each of which has a magnetic dipole associated with it) into different energy levels. However, if the...

Homework Statement On a level billiards table a cue ball, initially at rest at point O on the table, is struck so that it leaves the cue stick with a center-of-mass speed v0 and a "reverse" spin of angular speed w0. A kinetic friction force acts on the ball as it initially skids across the...

Homework Statement A student sits on a rotating stool holding two weights, each of mass 10 kg. When his arms are extended horizontally, the weights are 1 m from the axis of rotation and he rotates with an angular speed of 3 rad/s. The moment of inertia of the student plus the stool is 8 kg*m^2...

Definition/Summary Angular momentum carries over from classical mechanics into quantum mechanics, but quantum-mechanical angular momentum is restricted to discrete values. There are two main types: orbital or kinematic angular momentum, and spin or intrinsic angular momentum, carried by a...

Definition/Summary Angular momentum (or "moment of momentum") of a point particle is position "cross" momentum: \mathbf{L}\ =\ \mathbf{r}\times m\mathbf{v} Angular momentum of a rigid body about its centre of mass or centre of rotation equals moment of inertia tensor "times" angular...

Why the torque is called moment of force and angular momentum is called moment of linear momentum ? Please explain.

Sometimes the concept of angular momentum is presented using the idea of total angular momentum J. In those cases, its always said that we have \vec{J}=\vec L + \vec S . But I can't understand how that's possible. Because orbital angular momentum operators are differential operators and so are...

Homework Statement A merry-go-round rotates at an angular velocity of 0.2 rev/s with an 80 kg man standing at a point 2 m form the axis of rotation. what is the new angular velocity when the man walks to a point 1 m from the center? Assume the merry-go-round is a solid cylinder of mass 25 kg...

Homework Statement A particle is under a central potential. Initially its wave function is an eigenfunction ##\psi## such that ##\hat {\vec L ^2} \psi = 2 \hbar ^2## , ##\hat L_3 \psi =0##. Calculate the expectation value of ##\hat {\vec L}## for all times. Homework Equations...

Homework Statement Two children on opposite ends of a merry-go-round of radius 1.6 m throw baseballs at the same speed of 30 m/s but in opposite directions as shown. The mass of each baseball is 0.14 kg, and the moment of inertia of the merry-go-round and children combined is 180 kg-m^2. If...

So, I've been looking into orbital angular momentum and magnetic moments, (which, at least in normal space with a normal angular topology seems limited to integer values of spin). (My model so far has been a parabolic potential harmonic oscillator in 3d, and the sort of spinning modes you can...

Angular momentum L is defined by summation of mrxv about a certain point. For a rigid body that rotate about an axis that is not the axis of symmetry, in general the direction of L is keep on changing. Also we get different L if we take about different point. Iω is constant for constant ω and...

So, I'm trying to study phase shift in an unbalanced rotating system (where "phase shift" means the resulting response of orbital motion lags behind in time/position relative to the force that's causing it) I know that conservation of angular momentum applies ideally in a closed system...

If spherical harmonics are simultaneous eigenfunctions of \hat{L} and \hat{L}_{z}, then that means for a state at which l=1, and where you have three possible values of m (1, 0 , -1) that the value of L and L_{z} cannot really be determined simultaneously. Because the three fold degeneracy of...

If a person hangs still from a rope some distance above water and then the rope is cut off, is it possible for the person to start somersaulting in the air before hitting the water? When I try to imagine myself in this situation, I would think that "of course it is, one can just start moving in...

Homework Statement Find ##\langle L_z \rangle##. What is ##\langle L_Z \rangle## for one atom only? Homework Equations The Attempt at a Solution Using ##L_z = -i\hbar \frac{\partial }{\partial \phi}##, I get: \langle L_z\rangle = \frac{32}{3} \pi k^2 \hbar a_0^3 Not...

"Locally, the spin density S is an intrinsic (i.e. origin-independent) quantity, which is associated with the local ellipticity of the polarization of light. In turn, the orbital AM density L=r x P0 is a manifestly extrinsic (origin-dependent) and is produced by the corresponding canonical...