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Questions tagged [angular-momentum]

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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rotation dynamics angular momentum [on hold]

please solve this rotation mechanics question 19,20 and 21
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3answers
984 views

Simple Question About Conservation of Angular Momentum

Lately I encountered a question in my physic book very simple looking but I can't understand why what I am thinking is wrong because I didn't satisfied from the right answer showed in a video about it,...
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1answer
36 views

Moment of inertia and torque [on hold]

Why there is different moment of inertia with respect to point P about which a rigid body is moving around a circle with some velocity and spinning about its own axis compared to the one which is just ...
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0answers
16 views

Help with deriving angular momentum balance from position and momentum [on hold]

I have no idea how to derive this! I've looked all over the internet and throughout two textbooks, and all I can find is very specific proofs, but none showing what I need. Any ideas?
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1answer
28 views

Decay of spin-1 particle into two spin-0 particles

If we consider the decay of a spin-1 particle with spin projection $m_s=1$ into two (distinguishable) spin-0 particles, what are the possible values of the orbital angular momenta $l$ of the resultant ...
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0answers
31 views

Will a spinning rocket induce an additional angular rate while ejecting a satellite? [on hold]

A rocket spins with 30 degrees per second, and ejects a satellite into the space. From the experiment on the ground we know that the ejecter will give a satellite angular rate 5 degrees per second if ...
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1answer
25 views

Angular acceleration of a double compound pendulum [on hold]

How can I calculate the angular acceleration of a double compound pendulum? I'd like to know what the angular acceleration of each of the pendulum's center of mass will face at any point in time. PS -...
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0answers
33 views

Angular Velocity About Instantaneous Axis of Rotation [duplicate]

If you consider a cone of half angle φ rolling without slipping on a plane with angular velocity Ω as shown in the figure. What would be the angular velocity about the Instantaneous Axis of rotation? ...
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1answer
35 views

How do you sum up torques for a macroscopic object

Torque is measured about a point. But angular momentum for some object is measured around an axis. This doesn't make sense to me as in for example, a cylinder. If there are multiple tangent forces on ...
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25 views

Angular momentum for asymptotic states in black hole spacetime

Consider a massless KG field propagating in a gravitational collapse spacetime which produced a black hole. Neglect backscattering for a moment. In that case, when asymptotic quantization is ...
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1answer
45 views

Parity of Harmonic oscillator in 2 and 3 dimensions: the case of $l_z$

From doing exercises and trying to understand their solutions, i figured in two dimensions, not all values of $l_z$ can be taken by the particles (this is to conserve parity). For example, for n=0, ...
2
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1answer
17 views

Radial term in the spin-orbit coupling

The spin-orbit interaction for the hydrogen atom is of the form $\hat{H_1} = A\frac{1}{r^3}\pmb{\hat{L}}\cdot \pmb{\hat{S}}$ Now in my course, we treated this interaction by working in the basis of ...
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1answer
132 views

Nature of Spin in QFT

If the orbital angular momentum of an electron in an atomic orbital is associated with (generated by) an asymmetry in the orbital wave function, is it also the case that the intrinsic spin of a free ...
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1answer
39 views

Generator of 3D rotations in $\mathbb{C}^2 \otimes \mathbb{C}^2$

Let us consider a system of two spinors. The 3D rotation operator around the $\vec{n}$ axis in $\mathbb{C}^2$ is clearly $R(\theta) = \exp(i \frac{\theta}{2}\vec{n}\cdot\vec{\sigma})$. If I wish to ...
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0answers
25 views

Rpm of disc calculations [closed]

I shoot a bullet of velocity Vb and mass Mb towards a disc fixed on a car. The disc mass is Md and car mass is Mc. The bullet hits tangentially on the disc and gets stuck to it. The disc starts ...
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0answers
29 views

Relation between spin degrees of freedom and the dimensions of Hilbert space

I came across a question which reads "Suppose the spin degree of freedom of two particles (nonzero rest mass and nonzero spin) is described completely by a Hilbert space of dimension twenty one. ...
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0answers
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Why does the ball on a string produce results consistent with angular energy conservation? [closed]

This third party experiment confirms exactly that angular energy (rotational kinetic energy) is conserved and not angular momentum. The gentleman announces his only genuine result at 5:40. Thereafter ...
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1answer
63 views

Can we use the Pascal triangle as an aid to construct superpositions of wavefunctions corresponding to $n$ electron spins?

Suppose we have n electrons and want to construct the wavefunction corresponding to the spins of the electrons. Can we construct this wavefunction (in the $(s_1,s_2,s_3 ... s_n)$ representation, so ...
3
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1answer
87 views

Classical angular momentum components are numbers. Can they be generators of some symmetry group?

In Quantum Mechanics (QM), angular momentum turn out to be the generator of rotational symmetry. This is trivial to see because in QM, angular momenta are defined by the commutation relations $$[J_j,...
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2answers
51 views

Clebsch-Gordan coefficients for more than 2 particles

I need to couple arbitrary spins together and need Clebsch-Gordan coefficients for them. This should be just coupling the last two particles, then couple the next until the first particle is coupled. ...
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1answer
37 views

Time reversal of a QM Hamiltonian

I'm interested in the time reversal properties of a term in the non-relativistic QM Hamiltonian proportional (up to a true scalar) to $$ H \propto (\vec S_1 \times \vec S_2) \cdot \vec L $$ The ...
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2answers
74 views

Simple question on Angular Momentum

Need to know why $L^2$ and ONLY ONE of $L_x$, $L_y$, $L_z$ are constants of motion. Main problem arrives when $V = f(r, \theta, \phi)$ causing none of the $L_x$, $L_y$, $L_z$ to commute with ...
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0answers
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Rigorous Treatment of Quantum Tensor Operators

Recently, my classes have introduced me to the idea of spherical tensors and the Wigner-Eckart (WE) Theorem, but my previous classes on tensors had emphasis on things like covariance, contravariance, ...
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1answer
155 views
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Doubt on Sakurai's proof of Wigner-Eckart theorem

In Sakurai's and Napolitano's book "Modern quantum mechanics" there's a nice proof of the theorem. This can be found also almost identical on Wikipedia's Wigner–Eckart theorem - Proof. The thing that ...
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1answer
45 views

Angular Momentum, and its Conservation

I am confused as to how to reconcile the conservation laws of linear and angular momentum. Are they independent (and how can this be, if $L = r$ x $p$?) Does one supersede the other? In short: how are ...
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2answers
54 views

Transformation of energy [duplicate]

Consider a man rotating on a frictionless turntable , initially with his hands folded . When he opens his hands the moment of inertia increases and as the angular momentum is conserved the kinetic ...
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2answers
23 views

Why the cycles completed by standing wave completed by electron in a certain orbit is same as principle quantum number?

According to the bohr model and de-broglie hypothesis why the cycles completed by standing wave completed by electron in a certain orbit is same as principle quantum number? When we derive the ...
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1answer
63 views

Relation Between Cross Product and Infinitesimal Rotations, Generators, Etc [duplicate]

Looking into the infinitesimal view of rotations from Lie, I noticed that the vector cross product can be written in terms of the generators of the rotation group $SO(3)$. For example: $$\vec{\mathbf{...
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0answers
25 views

How does changing the moment of inertia of an object being swung by a human affect the kinetic energy?

If a human swings a baseball bat with moment of inertia $I$ at velocity $\omega$, as hard as he/she can the swing has a given kinetic energy. If you increase $I$, then the human will not be able to ...
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3answers
1k views

Mistake in “Quantum Mechanics” by Auletta, Fortunato and Parisi?

On page 200 of Auletta, Fortunato and Parisi's textbook on Quantum Mechanics they write: \begin{equation} \hat{\mathbf{l}}^2|l, m_l\rangle=l(l+1)|l, m_l\rangle \tag{6.31} \end{equation} ...
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1answer
45 views

Does $x$-component $\hat{L}_x$ of angular momentum commute with $\hat{x}$? [closed]

Question from lecture notes: What of the following operators does not commute with $\hat x$? A. $ \hat L_x $ B. $ \hat L_y $ C. $ \hat L_z $ D. None of the above. The answer ...
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2answers
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Angular Momentum in a Straight Line

Edit: This is not a duplicate question. The other question asked how angular momentum remained constant if the distance varied. This question asks why you can select any point and calculate angular ...
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4answers
62 views

Kinetic energy, angular momentum of a rotating body

We have a disk rotating about an arbitrary axis, and we can supposedly quantify the kinetic energy of such a disk by $K = \frac 12Iw^2$. Now, it is also true that, as the disk is rotating, each ...
2
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2answers
120 views

Spin of 3 particles

I am trying to decompose the isospins of a three particle state using Clebsch-Gordan coefficients such as: $|1,1\rangle \otimes |1/2,-1/2\rangle \otimes |1,0\rangle$ Decomposing the first two ...
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0answers
30 views

Commutator $\vec{L}$ with $\vec{X}\cdot\vec{P}$

Let $\vec{X}=(X_1,X_2,X_3)^T$ and $\vec{P}=(P_1,P_2,P_3)^T$. Define $\vec{L}=\vec{X}\times\vec{P}$. Then, I can calculate $\vec{L}=(X_2P_3-X_3P_2,\,X_3P_2-X_2P_3,\,X_1P_2-P_1X_2)^t$. For all ...
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1answer
33 views

Problem on measurement of spin of an electron

I came across a problem which reads: "An electron is initially found to have z-component of spin=+h/4π. Then a measurement of component of its spin along x-direction is carried out but the result is ...
3
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2answers
130 views

Why does the triplet state $\dfrac{1}{\sqrt{2}}(\uparrow\downarrow+\downarrow\uparrow)$ have spin 1 and not 0?

Don't the spins in the state $\dfrac{1}{\sqrt{2}}(\uparrow\downarrow+\downarrow\uparrow)$ cancel each other so that the total spin is 0 just like for the singlet state $\dfrac{1}{\sqrt{2}}(\uparrow\...
2
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1answer
39 views

Quantisation of $z$-angular momentum eigenvalues

Consider the eigenvalue equation for the $\hat{l}_z$ angular momentum operator: $$\hat{l}_zY_{lm_l}(\theta,\phi)=m\hbar Y_{lm_l}(\theta,\phi)$$ with separable solution $$Y_{lm_l}(\theta,\phi)=\Theta_{...
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0answers
18 views

$\langle r \rangle$ and orbital energy [duplicate]

Even though $\langle r_{2s} \rangle > \langle r_{2p} \rangle$ based on the following formula $$ \langle r_{n\ell} \rangle = \frac{{a}_{0}}{2}(3{n}^{2}-\ell(\ell+1)) $$ $2s$ has a lower orbital ...
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2answers
66 views

Angular Momentum vs Moment of Inertia

Pretty sure that this question has already been answered in this site, but I cannot find it. Anyway, here's the question: What is the difference between angular momentum and moment of inertia?
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1answer
46 views

How to correctly apply the $L^2$-operator to a wave function?

If I have a wave function that says $$\psi = \alpha Y_1^1 + \beta Y_1^0 + \gamma Y_1^{-1},$$ then it is clearly that this wave function is an eigenfunction of $\hat{L}^2$ with its $l$-value being $1$. ...
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0answers
18 views

Check if total angular momentum is well-defined for a particular photon wave function

I have an exotic state, which can be expressed in a way: $$\pmb{A}(\rho, \phi, z; t)= \hat{e}_{\pmb k, \sigma} A_0 e^{i (k_z z - m \phi +\omega t)}$$ where $A_0$ is a scalar amplitude of the EM-...
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1answer
60 views

Why does a tidal bulge result in a net torque on the Moon?

I understand that a tidal bulge is caused because the side of the earth facing the moon experiences a stronger gravitational force than the other. This results in the oceans on that side slightly ...
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0answers
19 views

Gyroscopes - Uniform precession - Externam forces

Suppose that you have a gyroscope with revolution symmetry around a perpendicular axis $\bf{e}$ such that the inertia tensor of this gyroscope can be written: $${\bf{Jc}} = {A\bf{I}} + (\Gamma - A)\...
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0answers
29 views

Collapse of quantum state after measurement of degenerated eigenvalue (From textbook Shankar) (Closed)

I want to ask an easy question from Problem 4.2.1, Quantum Mechanics(2nd) by Shankar. Let's say Operators, $L_{x}$, $L_{y}$, $L_{z}$ are $$L_{x}$ = $1/2^{1/2}$ $\begin{pmatrix} 0& 1 &0 \\ ...
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3answers
84 views

Quantization of electrons' angular momentum in atoms and molecules

It is known that the Schrödinger's equation of the electron's wave function in atoms can be solved analitically only when a single electron is present (the "hydrogenlike atom"). In that case, the ...
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3answers
138 views

Why does angular momentum being constant prove Kepler's first law?

So I was watching this video and this video on Kepler's first law in order to understand the proof of Kepler's first law. He started off by saying that for an ellipse, the distance from a focus point ...
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3answers
99 views

Is there an anticommutator relation for orbital angular momentum?

So I know that there are commutator relations for $L$ such as $[L_x,L_y] = i\hbar L_z$, but is there a relation for the anticommutator? For example, $L_xL_y + L_yL_x$?
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1answer
67 views

Must the total orbital angular momentum quantum number $L$ be less than the principal quantum number $n$? If so, why?

I am studying LS coupling and term symbols. In my textbook, there is an exercise: Why is it impossible for a $2\ ^{2}\text{D}_{3/2}$ state to exist? The answer says, the total orbital angular ...
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2answers
82 views

Mechanics: angular momentum of disk

I am studying mechanical engineering and I've got a problem with the angular momentum of objects that have a rotation which is rather complex to describe like the following: The shaft rotates around ...