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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 ...
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2 votes

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/...
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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 ...
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Angular Momentum of asymmetric physical pendulum (Rigid Body)

Even if the body is constrained to rotate about the $z$-axis only, this does not mean that the angular momentum $\vec{L}$ must point along the $z$-axis. Rather, we always have $\vec{L} = \mathbf{I} \...
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1 vote

Will a radioactive ball conserve its angular velocity?

In the frame of reference of a point on the surface, nearby radiation will be isotropic. But in an inertial frame of reference, the surface is moving. Photons in one direction will be blue shifted and ...
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Angular Momentum and Coefficient of Restitution

No the coefficient of restitution does not apply to with rotational velocity. In fact conservation of momentum will not apply either because the bodies are pinned and can transfer momentum to the ...
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Angular Momentum and Coefficient of Restitution

The problem is that angular momentum is not conserved in this scenario. In order to define angular momentum in a system, there needs to be an origin. If we put the origin at the center of the first ...
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Why is angular momentum equal to mass times radius times velocity?

Rotational distance from the center effects momentum because it effects the velocity. A mass rotating 100RPMs with radius x will have more energy if the radius is 2x because it changes the ...
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Why is angular momentum equal to mass times radius times velocity?

The linear momentum of a system is conserved in the absence of a net external force. The angular momentum of a rotating object is conserve in the absence of a net external torque. That is reflected ...
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1 vote

Why is angular momentum equal to mass times radius times velocity?

When momentum is mass times velocity, why is angular momentum mass times radius times velocity? High-school summary We are interested in both angular momentum and linear momentum because they are ...
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Null conserved angular momentum

First of all, the angular momentum is defined only with respect to a point. If we treat that point as the origin, and the position of the particle is $P(t)$, then angular momentum is $mP(t)\times P'(t)...
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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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Null conserved angular momentum

Yes, if the angular momentum of a particle is conserved and it is zero, the particle must move along a straight line. Indeed, by using the triple product identity, we have $$ {\bf r} \times ( {\bf r} \...
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3 votes

Is there a limit to how close faraway objects can get due to the conservation of angular momentum?

The mass factor in moment of inertia varies with velocity as $\gamma m$ where $\gamma$ is the tangent-velocity dependent Lorentz factor. Angular momentum can thus take any value zero to infinity for ...
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-1 votes

Is there a limit to how close faraway objects can get due to the conservation of angular momentum?

I know I asked the question but I think I have figured it out. Since you can not get above the speed of light then the only other variable that can change as you decrease the radius is the mass. When ...
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Relativistic angular momentum confusing definition

For Minkowski or Schwartzschild spacetimes, the quantity $$m\left(X^i\frac{dX^j}{d\tau} - X^j\frac{dX^i}{d\tau}\right)$$ is conserved for masses following geodesic trajectories. It results from the ...
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Precise definitions for higher spin operators

Thanks to all the contributions I think I finally solved the problem. It is similar to problems structuralist mathematicians often have when talking to physics. Stackexchange is full of questions ...
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Precise definitions for higher spin operators

In response to your followup questions (in a different order than you asked): (2) A general unitary matrix satisfies the condition $U^\dagger U = \mathbb{1}.$ Let $A$ be anti-Hermitian. Then $$(\...
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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.
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3 votes

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 ...
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10 votes

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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In relation to the correspondence principle, what happens when the orbital magnetic quantum number $m_\ell$ is very large?

In quantum mechanics angular momentum is quantized like this: $$L^2=\ell(\ell+1)\hbar^2$$ $$L_z=m_\ell\hbar$$ Semiclassically the angle $\theta$ between $\vec{L}$ and the $z$-axis is given by $$\cos\...
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Is angular momentum conservation Galilean invariant?

The answer is no. To begin with, a Galilean transformation in three dimensional Euclidean space(time) consists of space-time translation: $(t,\vec{x})\rightarrow(t+s,\vec{x}+\vec{a})$ spatial ...
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1 vote

Is angular momentum conservation Galilean invariant?

But this doesn't make sense to me because the rotational invariance of a system doesn't seem to change when I change to a new inertial reference frame. It can change. Torque depends on origin. As an ...
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1 vote

Angular Momentum Conservation and Conservation of Energy

The sphere is initially slipping. Only when its speed drops to $5u/7$ does it start rolling. The sphere's speed drops because it is moving on a rough surface. The friction between the slipping sphere ...
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A dilemma regarding torque when a body moves in circular motion

The example is similar to the olympic hammer throw. The athlete increases the tangential speed of the hammer by increasing the angular speed of his hands around his body. That is: the center of ...
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A dilemma regarding torque when a body moves in circular motion

Angular acceleration is the rate of change of the rate of angular velocity (relative to the point that the angle is measured from). If the string revolves with constant angular velocity it has no ...
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A dilemma regarding torque when a body moves in circular motion

"Now the mass 'm' accelerates in the circular path and thus there is an angular acceleration and thus tangential acceleration" The problem starts from above . The mass m accelerates as it's ...
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A dilemma regarding torque when a body moves in circular motion

Now the mass 'm' accelerates in the circular path and thus there is an angular acceleration and thus tangential acceleration. Your question is very unclear. Masses don’t just accelerate. There is a ...
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How do the inertia tensor varies when a rigid body rotates in space?

This has been answered below, but consider the rotation matrix $\mathrm{R}$ whose columns represent the local $\hat{x}$, $\hat{y}$ and $\hat{z}$ axis in the world coordinates. $$ \mathrm{R} = \begin{...
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4 votes
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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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2 votes
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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 ...
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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 ...
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(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 ...
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(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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2 votes
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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 ...
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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 ...
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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 ...
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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 ...
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Two final velocities for a mass launched from Earth

If the mass is launched directly away from the Earth, then its angular momentum is zero, since the displacement from the center of the earth $\mathbf{r}$ is parallel to the momentum of the mass $\...
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3 votes

Is It true that If the angular momentum is zero with respect to any point then the system is at rest?

I wrote this before I saw the other answers by Michael Seifert and John Alexiou had been posted so there is some overlap, but I'll post it anyway. The answer depends on what you mean by rest. Zero ...
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Is It true that If the angular momentum is zero with respect to any point then the system is at rest?

Angular momentum tells you where in space the axis of the momentum vector is. Consider a particle moving in a straight line. The magnitude of angular momentum $| \vec{L} |$ and the magnitude of ...
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Is It true that If the angular momentum is zero with respect to any point then the system is at rest?

Suppose we have two choices of origin point $\mathcal{O}$ and $\mathcal{O}'$, where $\vec{R}$ is the vector pointing from $\mathcal{O}$ to $\mathcal{O}'$. It is straightforward to show that the ...
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-1 votes

Is It true that If the angular momentum is zero with respect to any point then the system is at rest?

My earlier response was not correct, sorry. Here is my updated response. A system does not have to be at rest to have zero angular momentum with respect to any point. Here is a simple example; see ...
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4 votes

Can conservation of angular momentum be proven?

I am answering the title Can conservation of angular momentum be proven? Conservation laws are called laws because they are axiomatic, experiments and observations of the last centuries have given ...
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Can conservation of angular momentum be proven?

You write our linear velocity $v$ was constant according to our first claim where the “first claim” was The linear velocity is related to it by the equation $𝑣=𝑟𝜔$ But $v=r\omega$ is a scalar ...
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How does gravity make us rotate about the rotation axis of earth?

Friction between the body and earths surface provides a tangential force necessary to get a body rotating around earths axis in the first place.
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