The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation

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89 views

Intuitive explanation of rotational inertia with respect to angular momentum

I understand that there are proofs (e.g. proof, another proof) of why the angular momentum about two points for an object is the same. However, could someone give an intuitive explanation of why this ...
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4answers
149 views

Spinning disk touches stationary disk [closed]

Suppose we have a solid disk of mass $M$ and radius $R$ that is spinning at an angular velocity of $\omega_0$ about an axis going out its cm. It is brought to touch a stationary disk of mass $m$ and ...
2
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2answers
77 views

Two particles have the same linear momentum but their angular momentum differ. Which's harder to stop?

Which one is harder to stop, a 2 kg particle moving in a circular path of radius 5 m , with angular velocity of 10 rad/s or a 2 kg particle moving in a circular path of radius 2 m with a angular ...
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0answers
27 views

Conservation of angular momentum in a system under torque

Let's say we have a particle $A$ like this which is located in the disk $c$. Consider that the particle itself is not moving, but in general it is constrained to the semicircle $d$, in that if it ...
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1answer
90 views

Decomposition of tensor product space into direct sum [closed]

Consider a tensor product space of two representations $j = \frac{3}{2}$ and $j = 1$. How to show $4 \otimes 3 = 6 \oplus 4 \oplus 2$?
3
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1answer
67 views

Second Kepler's law implies that constant velocity

I was trying deduce that if we suppose that the planet's orbits are circular and de Kepler's secong law is true: A line joining a planet and the Sun sweeps out equal areas during equal intervals of ...
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0answers
26 views

Assigning values of angular momentum transfer

How do the shapes of the experimentally measured differential scattering or transfer cross sections help in assigning reliable angular momentum transfer values?
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1answer
41 views

If a system is in a state $L^2 =2 \hbar^2$ and $L_x=0$ why can't $L_z$ be 0?

A particle is in a state where $L_x=0$ and $L^2 = 2\hbar^2$. This means $l=1$ and $m_x = 0$. I will call this state $Y^x_{lm} = Y^x_{10}$ I wanted to know what possible values $L_z$ could have in ...
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0answers
25 views

Coupling between angular momenta of particles conserve angular momentum of each particle?

Suppose there are two particles in angular momentum numbers $j_1$ and $j_2$ respectively. Suppose there is some interaction that couple together the particles' angular momenta. As there is no external ...
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2answers
115 views

Find the error: If $L_x$ and $L_y$ are zero, then $L_z$ is conserved

From Goldstein's Classical Mechanics (2nd ed.), problem 38 of chapter 9 basically says the following: It's been shown that the Poisson bracket of two constants of the motion is also a constant of ...
3
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1answer
54 views

Conservation of Angular Momentum in Einstein - de Haas effect

I am not really sure why the law of conservation of angular momentum should hold true in the Einstein - de Haas effect. Consider the following excerpt about the phenomenon (taken from Magnetism in ...
3
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1answer
183 views

Why is there no 1/3 spin? [duplicate]

Why do no particles have a 1/3 spin? Why are all particles' spin either a half-integer or integer? How would a particle with such a spin behave, as a fermion, boson, or neither?
3
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0answers
90 views

Angular momentum of the vacuum

I'm studying quantum field theory from "An introduction to Quantum field theory" by Peskin and Schroeder and from "A modern introduction to quantum field theory" by Maggiore. I've read from "An ...
3
votes
2answers
130 views

Conservation of angular momentum while sitting on a spinning chair

Today my friend was sitting on a spinning char. By moving his top part of the body left to right and his bottom part of the body the opposite he managed to spin. As I understand Conservation of ...
0
votes
1answer
44 views

Expressing angular velocity of solid body [closed]

The problem: We have a circular disk of radius $R$ and mass $M$ that is mounted on a rotation axis that is not the axis of symmetry of the disk. The moment of inertia with respect to the axis of ...
0
votes
1answer
25 views

If $z_G$ is a principal axis that goes through the center of mass, are every other axes $z$ parralel to $z_G$ also principal axes?

I know that : If $y$ is a principal axis $\iff$ you can express the angular momentum with respect to a point $Y$ on that axis (if the solid is rotating around that axis of course) with the formula : $\...
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1answer
115 views

Conservation of angular momentum during rolling

A disk having initial angular velocity $\omega$ is gently placed on a rough horizontal surface. What is the angular velocity of rotation when pure rolling starts? I've tried applying conservation of ...
4
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2answers
136 views

Radial quantum number for infinite circular well

For completeness, I will sketch the solution of a particle in an infinite circular well first and then get to my question. I apologize in advance since the introduction is standard undergraduate ...
1
vote
1answer
53 views

Finding the proportionality constant of the Quantum Angular Momentum raising operator $T_{+}$ [closed]

This is a question about the mathematics of angular momentum operators in Quantum Mechanics- specifically a recursive relation from Robert Cahn's Semi-Simple Lie Algebras and their Representations ...
1
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1answer
115 views

Gyroscope precession

I have a system diagrammed and explained in the image below. Experimentally I believe the wheel will rotate around the pivot point where the cable is attached in a counter-clock motion if ...
1
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0answers
42 views

Deriving the equation for Angular Momentum? [duplicate]

The equation for angular momentum is L=mvr in which L is the angular momentum, m is the mass, v is the velocity, r is the radius. How does one derive this equation from the other laws of motion?
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1answer
49 views

With radian as a unit, should action and angular momentum have the different units?

If one accepts radian as a fundamental unit, does it make sense that action and angular momentum have units differing in radian to the power of one? The same question applies for energy and torque. ...
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2answers
79 views

Conservation of angular momentum in a collision

Suppose I have a stick hinged to a pivot and it is released from its horizontal position and just after it becomes completely vertical, it strikes a ball completely stationary as in the given figure ...
0
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1answer
60 views

Spectrum of Laplacian on one hemisphere

as is well-known, the spectrum of the Laplace operator on $S^2$, computed via $-\Delta f=\lambda f$, is positive and discrete. What happens to the spectrum if we just take one hemisphere into account?...
2
votes
2answers
45 views

The way planets rotate and revolve [duplicate]

Why is that the all planets move in the same plane?(correct me if I'm wrong) Why not some of them in anticlockwise direction and others in clockwise direction?
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vote
2answers
77 views

Angular momentum changes depending on orign

Consider the image below where we have two point masses $m_1$ and $m_2$ with different masses which are rotating around a fixed axis with angular velocity $\omega$. If the origin is placed on the axis ...
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0answers
74 views

Does a planet's orbital angular momentum affect its rotational angular momentum?

For example: If the moon was closer to the earth, assuming the orbital momentum was conserved and not worrying about earth's rotation, would the moon's rotation rate be effected?
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3answers
512 views

Classical proof of the gyromagnetic ratio $g=2$

I was reading Representing Electrons: A Biographical Approach to Theoretical Entities, by Theodore Arabatzis. At a certain point, where he is explaining the history of the magnetic moment of the ...
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1answer
89 views

Angular momentum of a rigid body about any points

Is angular momentum about all points same if the body is rigid and is rotating/translating/rolling with a constant velocity? Why? No external force is acting on the body.
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1answer
23 views

Changing angular momentum with no forces to do torque

Suppose a particle of mass $m$ moves in a straight line at velocity $v$ some distance away from an axis, as shown here at times t1 and t2 (where the axis of rotation is located at the origin of the ...
1
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1answer
65 views

Torque and Angular Momentum

An ice skater is spinning in a circle with an angular velocity, $\omega$, and rotational inertia $I$. Let's say that the skater then pulls his arms directly inwards at a constant rate over a time of $...
4
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0answers
50 views

What kind of torques cause an object to precess?

In studying precession, my textbook (Taylor's Classical Mechanics) makes the assumption that a top spinning about its symmetric axis, but tipped at an angle $\theta$, will precess nicely so long as ...
15
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4answers
2k views

What would happen if the Earth was in a polar orbit around the sun?

This is a question that has been bugging me for a while now, I was wondering about the effects on the Earth if it was in different orbital situations to what it is now, and one of those was what would ...
2
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1answer
106 views

How are these marbles being accelerated?

This question refers to an effect visible starting at around 5m45s in this video1. (The question will make little sense if one has not first watched the clip.) The observation At around 5m45s we ...
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0answers
24 views

How can I calculate the torque of draw force which affect on spinning ball flying in the air?

I am studying the Magnus effect on a flying ball i have calculate the magnus force but i trying calculate the angular acceleration, because the angular velocity of the ball is not constant. I have ...
0
votes
1answer
304 views

Angular momentum paradox with 2 identical gears

Consider two identical gears touching each other. The system is friction less. One has a handle that you use to apply a torque on the entire system. If you turn the handle, there will be a non-zero ...
0
votes
1answer
120 views

How many eigenstates for four (non-identical) spin 1/2 particles? [closed]

Question Consider a system of four non-identical spin 1/2 particles. Find the possible values for the total spin and state the number of eigenstates for each of these. Attempt So I coupled S1 and ...
1
vote
1answer
51 views

Operators and addition of angular momenta

Consider a two particle system with one particle having spin 1/2 and the other spin 1. One state of the system is $||\frac{3}{2},\frac{3}{2}\rangle\rangle$ where a double ket means this is in the ...
7
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3answers
574 views

Questions on the movie Gravity (2013)

To start off, I'm not a physicist but a programmer, and only had a few years of physics education in high school so I'm sorry if I'm asking a stupid question. I just finished watching the movie ...
1
vote
1answer
119 views

Dropping objects on a rotating disc: angular momentum?

I'm designing a very simplistic particle simulator. Particles are dropped on a spinning disc and then bounce back (although lose some momentum due to the friction of the disc). I'm working with an ...
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vote
4answers
209 views

How is angular momentum conserved

from a classical perspective, what is it about angular momentum fundamentally that means it has to be conserved? Surely if I have a rod about a fixed axis and a moving particle hits the end it will ...
0
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2answers
62 views

Momentum Equation VS Momentum of Momentum Equation

Newton's second law states that the linear momentum ($P$) rate is equal to the net force: $$F=\frac{d}{dt}P \tag{1} $$ On the other side, there is a same expression for angular momentum ($L$): $$M=\...
8
votes
6answers
351 views

How do point particles transfer angular momentum between each other?

I know that quantum physics says that one can't change the magnitude of spin of a point particle but that still leaves the question of how one changes the direction of spin. One possible way point ...
2
votes
1answer
74 views

Do particles also have intrinsic linear momentum (linear analogue of spin)?

We know from quantum mechanics that microscopic particles have spin, which is a kind of intrinsic angular momentum. The particle has angular momentum without physically rotating. In a similar way, do ...
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vote
1answer
63 views

Where to hit the pool ball such that it satisfies the given condition? [closed]

The question Where to hit the ball in such a way that after covering a certain distance it rolls back? You are given a pool ball and you have to find where to hit it such that it rolls back after ...
1
vote
2answers
106 views

Pauli Matrices & 2D Rotation Operators?

I was doing a strange calculation with my teacher the other day: find the eigenvalues and eigenvectors of the 2D rotation operator. Intuitively, there should be no solution to this problem in $\mathbb{...
0
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0answers
28 views

what is significance of direction of vector product(torque & angular momentum)?how can one use them practically? [duplicate]

since i came across vector product or cross product i have one doubt that is what direction of torque shows.the direction of product is along axis of rotation(+ve or -ve).is there is any practical use ...
1
vote
1answer
63 views

Is it right to write $\varepsilon_{ijk} \delta_{jl}=\varepsilon_{ilk}$? (indices notation)

Consider the $l$ component of vector position $\vec{r}$, $r_l$, and the $i$ component of angular momentum $\vec{L}$, $L_i$. We have that $$L_i=[r\times p]_{i}=\varepsilon_{ijk}r_jp_k$$ $\...
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0answers
26 views

What are physical observables that are connected to orbital angular momentum?

We considered a system that is confined to a curved surface. In the quantization process, we have obtained an additional orbital angular momentum that are from the surface geometrical deformation. Now ...
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0answers
73 views

Commutation between angular momentum and Hamiltonian

Consider the following Hamiltonian of a 3-dimensional system: $$H=\frac{p^2}{2m}+V(r)$$ If the components of the angular momentum, $L_i$, commute with $H$, then: $$[H,L_i]=0$$ This condition can ...