Angular momentum Definition and 1000 Threads

Hi, I have the following problem: A homogeneous disc with M = 1.78 kg and R = 0.547 m is lying down at rest on a perfectly polished surface. The disc is kept in place by an axis O although it can turn freely around it. A particle with m = 0.311 kg and v = 103 m/s, normal to the disc's surface at...

I know that the force must be a central force and that under central forces, angular momentum is conserved. But I am unable to mathematically show if the angular and linear momentum are constants. Radial Momentum ##p=m\dot r = ma\dot \theta=ma\omega## Angular Momentum ##L=mr^2\dot\theta =...

We want to show that ##[\hat{ \vec H}, \hat{ \vec L}_T]=0##. I made a guess: we know that ##[\hat{ \vec H}, \hat{ \vec L}_T]=[\hat{ \vec H}, \hat{ \vec L}] + \frac 1 2 [\hat{ \vec H}, \vec \sigma]=0## must hold. I have already shown that $$[\hat{ \vec H}, -i \vec r \times \vec \nabla]= -...

I'm sure I've read somewhere that Jupiter has 99% of the solar system's angular momentum, which shouldn't be the case. However, I can't find a source for this, and any search online for the topic doesn't bring up any science sites. Did I mis-remember?

I am confused with the following two questions: 1. A particle moves under the influence of a central force directed toward a fixed origin ##O##. Explain why the particle's angular momentum about ##O## is constant. 2. Consider a planet orbiting the fixed sun. Take the plane of the planet's...

Wikipedia says that they are the equivalents of momentum and force in rotational motion but I don't understand why this comparison is possible. The torque's dimension is N*m it seems like energy. What is this energy? Why angular momentum is not mass times angular velocity?

Say we have a motor attached to the Earth with gear A, that drives identically sized gear B. Gear B spins on its own axis and but is also attached to ground. Torque between gears is equal. Technically each gear has equal but opposite AM right, but If I take Earth into account, how is Ang...

we neglect gravity and viscosity efects i really can't understand how does the author managed to get the equation in the image

I don’t understand how energy is conserved here. The energy of the atom when n=5 is -.544eV. The energy of the photon is 1.14eV. After release, the energy of the atom is -.544 - 1.14 = 1.68eV. Using this value, I get n = 2.67, not an integer, so n = 3 and the atom has energy = -1.51 eV. I...

I looked in the instructor solutions, which are given by: But I don't quite understand the solution, so I hope you can help me understand it. First. Why do we even know we are working with wavefunctions with the quantum numbers n,l,m? Don't we only get these quantum numbers if the particles...

Ok, I know there are a lot of strange things in our solar system. Can anyone explain why the small planets spin so slowly? and why does Jupiter spin so quickly? It seems like a ball of debris, getting smaller and smaller, would increase its speed like an ice-skater pulling their arms in...

Okay, i know that as a ball collides with a pivoting rod on an axis, the ball has angular momentum. Therefore after the collision, the ball is stopped or slowed, and the rod swings. The ball provides a force and torque to the rod. But if I isolate the ball, isn't the only thing acting on the...

Is it correct to say that that τ=0 since r has the same directacion as F?? and for \vec{L} que need to find \vec{p} So I thought solving this dif equation ## \int dp/dt =−kq/r^2 +β^4/r^5## Do you agree in the path I am going?

HI τ= r ˆr x - ##k / r ^ 2## ˆr= 0 right? since ˆr x ˆr is zero What about L?

I was first wondering wether we can solve this question by applying conservation or energy or not but after googling it I found that we can't apply conservation of energy since there will be some energy lost in this case. I don't know how this energy is getting lost. My second doubt was if we...

Summary:: Would energy method give us a different answer from conservation of angular momentum? Hello, I do not know how to type equations here. So, I typed my question in Word and attached it here. Please see photos. Note: This question is not a homework. I did not find it in textbooks or...

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In which coordinate system the components of angular momentum are quantized? Better to say, if we can select the coordinate system arbitrarily, how the components of angular momentum, say z-component, are always ##L_z=m\hbar##?

(just a illustrative picture)

Pretty much in a nutshell... fielded a question about how spin affects electron positron annihilation... ie do the spins have to be opposite in order to conserve angular momentum for two-photon annihilation to happen? Intuitively I figured that looks reasonable ... but decided to check, and...

I first tried to get the solution by conserving the rotational kinetic energy and got ##\omega'=\frac2{\sqrt5} \omega##. But, it was not the correct answer. Next I tried by conserving the angular momentum and got ##\omega'=\frac 45 \omega##, which is the correct answer. Why is the rotational...

In this article it discusses the generation of something called super chiral light and claims with metamaterials they can make it have very high angular momentum like l=100. What does that really mean? How does that relate in magnitude to the normally computed linear momentum of a photon p=h/λ...

Hello, I have this i am learning. I have been trying to find information online but have struggled to find anything which helps me. YouTube usually has good videos, but doesn't seem to on this. This is one topic i have never learned before. But keen to. I was hoping someone could help me...

IS my solution right? Comparing with the other solutions, the answer just exchange the signals, i don't know why, THats what ifound. And here is the three equations: {i use the point which occurs the collision} Lo = Lf >> 0 = Iw + M*Vcm(block) Eg = ct> mvo² = mvf² + MVcm² + Iw² I = ml²/3...

The Schwarzschild metric seems to model, for example, the earth’s gravity field above the earth’s surface pretty well, even though the Earth is not really a golf-ball sized black hole down at the center. Can the same be said for the Kerr metric? Does it model a rotating extended body’s gravity...

Hi, I have just joined the forum. Thank you all for being a part of such places so that people like me can get answers to the questions on their minds! --------------------------- I have been trying to understand how a quadcopter yaws. Referring to the figure below which is bird's eye view of...

Since the equations are, actually, the question, i will post the image with relevant equations here: it seems strange, I'm almost sure that I didn't make a mistake in the differentiation, but differentiating 9.8b I found 9.7a with both positive terms

Angular momentum can be exchanged between objects in a closed system, but total angular momentum before and after an exchange remains constant (is conserved). There is a proof about this conservation?

is my solution correct?

"A smooth horizontal disc rotates with a constant angular velocity ω about a stationary vertical axis passing through its centre, the point O. At a moment t=0 a disc is set in motion from that point with velocity v0. Find the angular momentum M(t) of the disc relative to the point O in the...

given z(0) = 0 as well as ˙z(0)=0 How would one find the angular momentum along the x-axis in terms of t. Currently, I have formulated the following: $${\ddot{z} = \frac{g}{1+(\frac{4R}{s})^2}}$$

Hi With the 2-body problem relating to planetary orbits i have encountered the following ; the gravitational force on the reduced mass acts towards the large mass(Sun) and since it is a central force it exerts no torque about the fixed centre(Sun) so angular momentum is conserved. Conservation...

Well I am pretty sure that the kinetic energy stays the same because in this case the velocity vector and energy make a ninety degree angle so no work is done, but I am lost about angular momentum. It could decrease maybe if the torque is clockwise while the ship is going in a counterclockwise...

A cylinder of radius R spins with angular velocity w_0 . When the cylinder is gently laid on a plane, it skids for a short time and eventually rolls without slipping. What is the final angular velocity, w_f? The solution follows from angular momentum conservation. $$L_i = I \omega_0 = L_f =...

I got the correct answer for the first part but I'm not sure why the answer for (b) is the same for (a). Wouldn't the rings falling off mean that I_f = \frac{1}{12}M_L L^2 only where I_F, M_L, L are the final moment of inertia, mass of the rod and length of the rod as opposed to I_f =...

One part of König's theorem states that ##\vec{L} = \vec{L}_{\text{COM}} + \vec{L}^{'}##. The term ##\vec{L}^{'}## simply refers to the angular momentum wrt. the centre of mass. This is just a point, and doesn't have an axis implicitly associated with it (we have infinitely many choices!). The...

Hi ; I have a few question regarding the conservation of linear and angular momentum. Would appreciate any help. 1 - When no external forces act are both linear and angular momentum conserved in all 3 directions separately or just the total linear/angular momentum conserved ? 2 - if I approach...

I am reading Tong's lecture notes and I found an example in which there are several aspects I do not understand. This example is aimed at: - Understanding what is the analogy in field theory to the fact that, in classical mechanics, rotational invariance gives rise to conservation of angular...

In quantum mechanics one sees what J^2 can offer but why do we even consider looking at the eigenstates and eigenvalues of J^2 and a component of J, say J_z? Why don't we just use J?

Hello! I am reading some papers and I often noticed that it is mentioned that a strong magnetic field is able to decouple certain angular momenta from each other. For example in this paper: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.100.023003 they present a Hamiltonian (second column...

Consider the following experiment from the point-of-view of classical mechanics and classical electromagnetism: An originally free electron then passes through a magnetic field that is oriented so that it causes the electron to turn to, say, the right. During the “turning” of the electron (a...

Tell me if I'm right: A) Angular momentum is conserved because there are no external torques. Linear momentum isn't conserved because gravity is acting on the spacecraft . Mechanical energy isn't conserved because it has to change between different orbits. B) Parabolic orbit...

When I solved the problem using the conservation of angular momentum, I have got the correct result (ω = 0.006 rad/s). However, when I tried to find the answer using the conservation of energy the result was incorrect and I do not understand why.

This is a very special case. In my 50 years studying physics I have never seen any discussion of photons having orbital angular momentum. Any angular momentum for photons in orbit around a black hole must be a GR question. I have not specialized in GR but I don’t recall any discussion of it. I...

Lets do it for the left (the right will be similar): ##r_{left}=[(L-a\sin\theta)\sin\phi,(L+a\cos\theta)\cos\phi]## so ##v_{left}=[-a\dot{\theta}\cos\theta\sin\phi+(L-a\sin\theta)\dot{\phi}\cos\phi,-a\dot{\theta}\sin\theta\cos\phi-(L+a\cos\theta)\dot{\phi}\sin\phi]##. Is this right?

The balls used in the game of lawn bowls are biased so that they travel in a curved path of decreasing radius. When a bowl in motion collides at a glancing angle with another bowl at rest, it -appears- to increase its velocity. Due to conservation of linear momentum the post-collision velocity...

I can solve the two particle system easily enough: Using ##j_1 = 1## and ##j_2 = 1##, the possible total angular momentum values are ##j = 2, 1, 0##. With ## m = -j , -j+1, ..., j ##, ##j = 2: m = 2, 1, 0, -1, -2 ## (5 states) ##j = 1: m = 1, 0, -1## (3 states) ## j = 0: m = 0 ## (1 state) I...

In studying gyroscopic progression, the angular momentum vector is added to the torque vector. As intuitively these two vectors seem to be qualitatively quite different, how do we know that both vectors are in the same vector field and that they can be manipulated using the rules of vector...

Homework Statement:: Ball of mass mb and velocity vb hits rod of length L , Rod pivots about the center. What is the angular momentum aafter impact? Homework Equations:: I = 1/12 (mR^2) I = mR^2 See the attached figure. I understand the concept of linear and angular momentum separately but I...