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

learn more… | top users | synonyms

0
votes
1answer
40 views

Angular momentum consevation and central force

A circular orbit of radius $a$ passing through the centre of a central force is given by the equation $r=2a\cos\theta$. Then using the orbit equation one can show that the force varies as $\vec ...
1
vote
0answers
17 views

Wigner-Eckart theorem and Van Vleck paramagnetism

Using the Wigner-Eckart theorem, we can express the matrix elements of Langevin's paramagnetic Hamiltonian $L_z + g_S S_z$ using only the quantum numbers of the total angular momentum, $J$ and $m_J$, ...
1
vote
1answer
42 views

How to explain gyroscopic precession in a more intuitional way?

When Studying the phenomenon of precession a classic example installation is this: a wheel spins around the Y axis, gravity applies and the upper part starts spinning around the Z axis. The textbook ...
0
votes
0answers
14 views

Angular acceleration of rigid body due to a torque

For the rotation of a rigid body about a fixed axis $z$ the following holds. $$ \vec{τ_z}= \frac{d \vec{L_z}} {dt} =I_z \vec{α} \tag{1}$$ Where $ \vec{τ_z}$ is the component parallel to the axis ...
2
votes
0answers
37 views

Identical Particle Wavefunctions

Consider the process $$\rho^0\rightarrow\pi^0+\pi^0$$ The $\rho^0$ has $J=1$ whilst the two pions have $S_{tot}=0$ and thus require $L_{tot}=1$ by conservation of angular momentum. Consequently this ...
2
votes
1answer
50 views

Contraction of a rotating system

Consider a system of two masses that rotates with constant angular velocity. When a force contracts the system the velocitie of the two masses increase. I understand this in terms of conservation of ...
0
votes
1answer
26 views

Uncoupled and coupled bases for electrons in hydrogen atom?

I'm given that for an electron in a hydrogen atom, $L=2$ and $S=1/2$ (quantum numbers associated with $L^2$ and $S^2$). I'm also given that for the uncoupled representation, the basis function is ...
0
votes
4answers
60 views

What is the moment of inertia really?

Is moment of inertia or second moment of inertia, simply the resistance of a body to rotate it over an axis? What is radius of gyration? What if the axis is via the center of mass or somewhere ...
7
votes
3answers
155 views

Coriolis force and conservation of angular momentum

I'm trying to understand the relations between the existance of Coriolis force and the conservation of angular momentum. I found this example on Morin, which confuses me. A carousel rotates ...
0
votes
2answers
43 views

Acceleration due to conservation of angular momentum in absence of a force

I don't understand why the conservation of angular momentum can imply an acceleration, in absence of a force. Consider for istance planetary motion. The angular momentum $\vec{L}$ of the planets is ...
-1
votes
1answer
27 views

why laser beams don't get reflected (or knocked away) when they intersect with each other?

laser beams are photons with the same frequency and the same direction, but according to the wave-particle duality, photons have mass. but if we shoot two masses and they intersect at some point ...
1
vote
3answers
48 views

Seeming paradox regarding conservation of angular momentum

Two equal mass astronauts in space are holding hands: one's right hand with the other's left hand and left with right. They are facing each other and are stationary. Astronaut A pulls with her right ...
0
votes
0answers
36 views

Calculating Clebsch-Gordan coefficients through Racah's formula

So Clebsch-Gordan coefficients are found in tables, but I need to calculate them using Racah's formula, which reads as following: $c_+ (J,M) f_{m_1}^{M+1}=c_+(j_1,m_1-1) f_{m_1-1}^M + c_+(j_2,M-m_1) ...
1
vote
1answer
74 views

How to manipulate higher spin systems (higher than spin 1/2) using a given operator?

I’ve been reading ¨Halzen, F., and A. D. Martin. Quarks and Leptons. New York: Wiley Text Books, January 1984. ISBN: 9780471887416¨, and I’d like some clarification of a concept, please: I’m ...
2
votes
1answer
31 views

Component of angular momentum perpendicular to the rotation axis in rigid body rotation

I have difficulties in understanding, in the rotation of a rigid body, the properties of the component of the angular momentum vector $ \vec {L} $ which is perpendicular to the fixed axis of rotation ...
0
votes
0answers
35 views

Rigid body rotation about fixed axis with angular velocity not constant in magnitude

I'm trying to understand the properties of angular momentum in the rotation of a rigid body around a fixed axis $z$, when the angular momentum $\vec{L}$ is not parallel to the angular velocity ...
0
votes
1answer
34 views

Why will kinetic energy decrease?

Specific situation : A ring of mass M and radius R is rotating about its axis with angular velocity w. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ...
1
vote
0answers
35 views

Torque on rotating rigid body and pivot point [duplicate]

Consider a rigid body performing a rotational motion around a vertical fixed axis $z$ with constant angular velocity $\vec{\Omega}$. The angular momentum vector $\vec{L}$ is not parallel to $z$ (and ...
1
vote
2answers
103 views

Forces that exert torque on a rigid body in rotation when angular momentum is not parallel to angular velocity

I'm confused about the rotation of a rigid body, when the angular momentum $\vec{L}$ is not parallel to the angular velocity $\vec{\omega}$. Consider a barbell with two equal masses that rotates ...
0
votes
1answer
33 views

Angular momentum, its conservation and Nebula theory

I am carrying out a research work and I am stuck at the first page where there is an introduction to the angular momentum and its relationship in the formation of the solar system. According to that ...
0
votes
1answer
64 views

Derivation of Squared Angular Momentum in Spherical Coordinates

While reading my textbook, I found the following: I tried to prove the above equation by doing the following. Knowing that : ...
1
vote
1answer
59 views

Mechanics of a falling cat [duplicate]

It is a general statement that cats tend to fall on their feet. How far is this is a valid statement? If I were to drop a cat from 50 meters height, feet up(hypothetically), would it still land on ...
1
vote
1answer
34 views

Quantum Mechanism Dipole Moment Magnetic Field Problem [closed]

I figured 1a out pretty easily. For 1b I am a bit stuck. So far i have that in the field: $$ \Delta z = v_0t + (1/2) a_zt $$ $$ F_z = ma_z $$ so $$ a_z = F_z/m $$ We know $$ ...
0
votes
0answers
43 views

How can the energy of a spinning black hole be converted into magnetic field?

I've read about the Blandford-Znajek process, and what I understood is that the black hole is treated as if it were a conducting sphere spinning rapidly with an accretion disk around it, and the ...
2
votes
1answer
126 views

A mass hanging under a table: a problem from Goldstein [closed]

I'm trying to solve Problem 1.19 from Goldstein's Chapter 1 (2nd edition), and am getting bogged down in trigonometry (?). Please help me figure out what I'm doing wrong! Two mass points of mass ...
1
vote
0answers
27 views

In a spinning spacecraft, the astronaut lets out of a mass attached to a string from a window, what happens to the mass? [closed]

The spacecraft is a cylinder spinning about its cylindrical axis. A mass attached to a long string is slowly let out from the side of the cylinder. Why does it start to perform simple harmonic motion? ...
2
votes
0answers
39 views

Is the spin of an electron based on its direction of angular momentum? [duplicate]

Is the spin of an electron based on its direction of angular momentum? Is it based on the right hand rule of angular momentum? Does Spin up means that the electron is spinning anti-clockwise and spin ...
0
votes
0answers
26 views

Cylinders rotating on a table

Please consult this video for context, its an interesting watch. https://www.youtube.com/watch?v=JuuYFt8bahE In this video Tadashi spins a tube on a table and it rotates around the tube axis and ...
2
votes
3answers
33 views

Force at axis of spinning wheel

This is a newbie question, but I don't quite understand the forces at work when an object is rotating. So I've read that i can use my right hand to determine the direction of the force at the axis ...
0
votes
0answers
27 views

Statement of vector model of angular momentum in Eisberg and Resnick

While serving as a teaching assistant for a sophomore-level Quantum Physics course, I came across the following paragraph in Eisberg and Resnick regarding orbital angular momentum (section 7-8, page ...
4
votes
0answers
61 views

Why are generators defined oppositely in Weinberg's vs. Maggiore's QFT books?

I've been confused about the sign conventions used in Weinberg's QFT book for a long time. Here's my question: The generators $J^{\mu\nu}$ are defined in this book as ...
12
votes
3answers
3k views

Could an asteroid land slowly on Earth's surface?

The concept in my mind is that an asteroid is on a vector similar to Earth's, but slightly slower (e.g., 50kmh slower). As Earth passes it, it enters the atmosphere at a sharp angle, and since Earth ...
3
votes
2answers
62 views

Why do tops move opposite to each other when colliding, not tangentially?

When two well-balanced tops collide, they tend to bounce directly away from each, in other words along the line connecting their centers. Intuitively I would expect the tops to move tangentially, not ...
1
vote
3answers
81 views

Conversion of angular momentum to linear momentum in free space

If two objects both with angular and linear velocity collide in free space, can the total linear velocity of the objects increase at the expense of a loss in angular momentum? In other words, imagine ...
1
vote
2answers
65 views

Is Keplers First Law a consequence of the conservation of angular momentum?

It would seem that once you have deduced that the angular momentum is conserved then you can deduce: $r^2\dot{\theta}=h$ is constant Combining this with the radial equation of motion then yeilds a ...
0
votes
0answers
60 views

Are Black Holes really spinning? [duplicate]

I've had this question: are black holes really spinning? Well if they are not spinning then why would the galaxy around them spin at all? They must spin! Or? Do they spin like a ball? What if they ...
3
votes
1answer
47 views

Frame dragging resulting in an orbital plane?

In astrophysics today we talked about spinning black holes, ring singularities, and frame dragging. Is this also (to some degree) the cause of the milky way being as flat as it is? Does the spin of ...
1
vote
1answer
46 views

What is the relationship between $W_1$ and $W_2$? [closed]

I have a model which schematic is in the linked picture. Blue $A$ and $B$ are rotational joints, black and red shapes are rigid elements. $I_1$ is moment of inertia of black and red elements combined ...
3
votes
3answers
137 views

Can humans control rotation of the Earth?

I'm a class 12th student and this thought just struck me from nowhere. Assume a situation where every human on this planet turns towards west. All of them start walking simultaneously in west ...
1
vote
1answer
55 views

Impulse and momentum on a system of three particles (equilateral triangle)

I found this exercise on a textbook which provided solely the description of what is happening and the answers with little explanation. The solution being provided, I am mostly interested in ...
1
vote
2answers
42 views

What is the reason for Earth's rotation and revolution?

Is it because of the gravitational effect of the other planets and the sun then why do the other planets rotate and revolve too? And well does the Sun rotate and revolve too?
5
votes
1answer
69 views

Does the Universe spin? [duplicate]

Maybe it's a stupid question, so I will delete it if it will receive too many down votes but.. I was wondering about the Universe, and the fact that We know it's expanding; We don't know if it has ...
0
votes
2answers
52 views

Does Angular Momentum change what I change Center Of Mass?

So recently I've noticed some discrepancies in my physics simulation, and these occur when I add/remove particles from a rigid body. Strange things like things flying to the sky constantly occur, and ...
0
votes
1answer
39 views

Matrix for Ladder Operators?

I found this website which shows how to derive the matrices for $L_{+}, L_{-}$ and while I understand the derivation of the equation for $<lm|L_{+}|lm'>$ and $<lm|L_{-}|lm'>$ I do not ...
1
vote
1answer
20 views

Angular momentum for elliptic path in 2D isotropic oscillator

Assume a 2D isotropic oscillator, i.e $$U = \frac{1}{2}m\omega^2(x^2+y^2),$$ and assume for simplicity that the oscillator performs elliptical motion, with major axis $A$ and semi-major axis $B$. My ...
0
votes
1answer
48 views

Sum and Different and angular momentum operators

Why is $\overrightarrow{L_{1}}+\overrightarrow{L_{2}}$ an angular momentum operator, but not $\overrightarrow{L_{1}}-\overrightarrow{L_{2}}$? What does this show about the applicability of the vector ...
2
votes
1answer
42 views

Why is the matter orbiting a black hole in the shape of a disk? [duplicate]

More generally, if a blackhole is a singularity...a point in space...why is matter only circling in a flat disk-like region. It would seem to me matter would circle it in a sphere surrounding the ...
0
votes
0answers
11 views

How do jj and ls coupling arise depending on the relative strength of the terms of a Hamiltonian?

Hamiltonian of two electrons orbiting nucleus in an atom is given by the equation: $$ H = \frac{p_1^2}{2m} + \frac{p_2^2}{2m} + V(r_1) + V(r_2) + \frac{e^2}{\left|\vec r_1 - \vec r_2\right|} + \xi ...
0
votes
0answers
21 views

Gravity changes at the equator due to Earth's spin [duplicate]

If an object weights 100 kilos at the equator how much would it weight if the earth spun twice as fast?
28
votes
6answers
6k views

How does a spinning object “know” that it is spinning?

I am constructing a thought experiment about a spinning object that is floating in intergalactic space. I assume that this object is about the size of a planet so that it will have enough gravity so ...