# Tag Info

• 23.3k

### A squared quantum operator is the same as using the same operator twice? So can't we find $L^2$ operator by using the $\mathbf L$ operator twice?

The squared operator $L^2$ is taken from a dot product: \begin{align} L^2 & = \mathbf L \cdot \mathbf L = L_x^2 + L_y^2 + L_z^2 . \end{align} Within that dot product, each product of operators (...
• 123k
Accepted

• 23k

### How can a pulsar slow down?

If the pulsar slows down, its angular momentum decreases. This implies that there's some angular momentum radiated away. Rotational energy decreases too, of course. There could be several ...
• 6,696
Accepted

### 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 ...
• 37.2k

### 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 ...
• 7,267
Accepted

### 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 ...

### 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 ...
• 1,028

### 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 ...
• 8,598

### How does gravity make us rotate about the rotation axis of earth?

Gravity always acts to the center of the Earth (if you assume the Earth as a sphere). The rotation (which has nothing to do with gravity) creates an additional centrifugal force acting outwards ...
• 1,529
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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 ...
• 50.9k
Accepted

### 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 ...

### 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/...
• 106k
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### Angular Momentum about a Point

If the angular momentum is calculated with respect to Q, both the position vector and the velocity vector must related to Q. So, the second expression is correct. If the momentum is calculated with ...
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 ...
• 2,014
1 vote
Accepted

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. $$\mathrm{R} = \begin{... • 2,601 1 vote ### Does an irregular rigid body can only rotate in three directions? You state "an irregular rigid body has only 3 axes such that  \vec{L}_{cm}  and  \vec{\omega}  are parallel." I presume you mean the principal axes? In terms of the Cartesian principal ... • 5,878 1 vote ### (Why) Is orbital angular momentum conserved for point masses? Angular momentum(and torque) does not necessarily mean that there are rotations in place. you can define angular momentum for straight lines, however, that isn't very useful to solve any problem. If ... • 354 1 vote ### Is It true that If the angular momentum is zero with respect to any point then the system is at rest? Angular momentum tells you where in space the axis of the momentum vector is. Consider a particle moving in a straight line. The magnitude of angular momentum | \vec{L} | and the magnitude of ... • 33k 1 vote Accepted ### Is change of angular momentum of two rotating disks colliding w.r.t. time L(t) = \omega_0 I(1-e^{-t/C})? with$$ \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 ...
• 8,389

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