# Tag Info

### Confusion about the Wigner-Eckart theorem

The eigenstates of the total angular momentum are not eigenstates of the individual angular momenta. The eigenstates of the total angular momentum are superpositions of the eigenstates of the ...

### Confusion about the Wigner-Eckart theorem

In principle there exist tensor operators of arbitrary angular momentum/spin - if you consider that the angular momentum generators $L_i$ themselves are a vector operator, then e.g. $L_i$ in a spin-3/...

### Equation to tell if precession will happen?

The expression for rate of precession that you refer to is an approximation, the validity of that approximation is limited to cases where the spin rate is high enough such that any resulting ...
Accepted

1 vote

### Null conserved angular momentum

The angular momentum is defined relative to a chosen point. For it to be zero, the velocity vector of the center of mass of a non-rotating rigid object must be directed toward that point.
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### Why is isoclinic rotation preferred in spaces of $d \gt 3$ dimensions?

The Clifford Algebra for this might be that the bivector for double rotation ae12+be34 may be written as a sum of two commuting and orthogonal isoclinic rotations [(a+b)(e12+e34)+(a-b)(e12-e34)]/2.

### Precise definitions for higher spin operators

Giving a completely precise definition of everything would take a large amount of time, and would likely not be helpful. So instead here I will spell out the general picture, and any terms which are ...

### Precise definitions for higher spin operators

I am not really sure about the scope of this question and the type of answer OP is looking for but computing those higher spin matrices/representations successively is relatively straight forward: ...
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Accepted

### If a boy tries to walk on a circular disc , the disc rotates but the boy remains stationary. Why it violets the law of cons. of angular momentum?

Assuming the disk is on a friction-less axle at its center, when the boy starts to walk, he will exert a backward force on the disk, and it will exert a forward force on him. He will move and gain ...
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### The mathematics of different particle rotations

Consider a point in space, and the effect a rotation would have on that point. Because the point has no internal structure (in other words, it is characterized entirely by its spatial location), a ...
1 vote
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### Is change of angular momentum of two rotating disks colliding w.r.t. time $L(t) = \omega_0 I(1-e^{-t/C})$?

with $$\underbrace{I\,\frac{d\omega}{dt}}_{\dot L}=\tau\quad \Rightarrow\\ I\,\int_{\omega_i}^{\omega_f}\,d\omega=I\,(\omega_f-\omega_i)=\int \tau\,dt$$ where $\omega_f~$ is the final angular ...

### (Why) Is orbital angular momentum conserved for point masses?

For a particle of mass $m$ with velocity $\vec v$, with respect to a point $O$ the angular momentum is $$(1) \vec l = \vec r \times m\vec v$$ where $\vec r$ is the vector distance from $O$ to the ...
1 vote

### (Why) Is orbital angular momentum conserved for point masses?

Angular momentum(and torque) does not necessarily mean that there are rotations in place. you can define angular momentum for straight lines, however, that isn't very useful to solve any problem. If ...
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### Does an irregular rigid body can only rotate in three directions?

A general rigid body has 3 principal axis. Suppose $I_1<I_2<I_3$. If it rotates around $I_1$ or $I_3$ without external torques, the angular velocity doesn't change and is parallel to the angular ...
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### (Why) Is orbital angular momentum conserved for point masses?

Imagine you had a particle traveling at constant $\mathbf{v_0} = \dot{z_0}\mathbf{\hat{k}}$ upwards. At time $t = 0$, your particle is at $\mathbf{r} = z_0 \mathbf{\hat{k}}$ and you apply an ...
1 vote

### Does an irregular rigid body can only rotate in three directions?

You state "an irregular rigid body has only 3 axes such that $\vec{L}_{cm}$ and $\vec{\omega}$ are parallel." I presume you mean the principal axes? In terms of the Cartesian principal ...
1 vote

### Spin Orbit Coupling Hamiltonians

No, these are not always the same thing. Spin-orbit coupling in atoms Spin-orbit coupling can be derived by reduction of the Dirac equation to non-relativistic limit, as one of several relativistic ...

### Can conservation of angular momentum be proven?

While both answers already given by rob and Anna v are correct, let me add my answer, this answer will provide a proof. As it has been pointed out to you, angular momentum is well defined without any ...