3
votes
1answer
38 views

In 2-dimensional and 3-dimensional universes, stellar systems and galaxies are flat and disky. But what about in 4-dimensional universes?

I just watched that interesting video: https://www.youtube.com/watch?v=tmNXKqeUtJM In 2 dimensions a cloud of particles rotating in a plane is flat by definition since it's in 2 dimensions. ...
2
votes
1answer
83 views

Rotation from Goldstein's Classical Mechanics

I apologize for the ambiguity in my title. It was rather difficult to figure out what is the most appropriate title for my questions. My questions come from chapter 4 and chapter 5 of Goldstein, ...
2
votes
2answers
58 views

Why do rotations of a multicomponent state function take this form?

I am reading Leslie Ballentine's Quantum Mechanics, section 7.2, which is all about the explicit form of the Angular Momentum operators. I understand how he gets the form for the single component ...
0
votes
1answer
57 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
1
vote
1answer
96 views

Center of rotation and trajectory of a rigid body in a plane with applied *fixed* forces

This is my first question so please excuse me if my format is a bit off. Given a 2D rigid body with forces applied to it in such a way that the angle the force vector makes with the surface of the ...
4
votes
1answer
300 views

Does total angular momentum of the Earth-Moon system include individual rotational angular momenta?

To calculate the angular momentum of a body we need to specify a point (or an axis?) from which to define the displacement vector $\vec{r}$, so that $\vec{L} = \vec{r} \times \vec{p}$. For a rigid ...
2
votes
1answer
136 views

Sign wrong in angular momentum (Quantum Mechanics)

For small angles $\theta$ the rotation along a particular axis $n$ is given by $R(n,\theta)(r)=Id+ \theta (n \times r)+ o(\epsilon)$. Now, the rotation operator in Quantum Mechanics is given by ...
0
votes
0answers
58 views

Rotation matrix for a coupled spin system

For an angular momentum basis with magnitude $F$ and magnetic numbers $m_F\in [-F,F]$, the unitary matrix that will perform the Euler rotations is the Wigner-D matrix of order $F$. I have applied the ...
4
votes
2answers
2k views

Which force makes a wheel roll down the hill? What causes friction?

A wheel rolling down a hill has two axis of rotation. One is where the center or mass is and the other is the point of contact with the surface which acts as a fulcrum. I was trying to understand ...
9
votes
2answers
790 views

Dynamics of counter-rotating flywheels

I've wondered about this for ages. If we create a pair of flywheels that rotate in the opposite direction with the same angular momentum, but are co-located and have the same mass and inertial moment ...
1
vote
2answers
1k views

Slowdown rate of rotating body due to friction force [closed]

This isn't a homework question, but it might as well be. The problem I have been pondering is: If a disc (or children's roundabout if you like), of radius r, mass m, is spun around it's center ...
1
vote
1answer
147 views

Commutation relation of $J^2$ and $R(\alpha,\beta,\gamma)$

If $R(\alpha,\beta,\gamma)$ is the Rotation operator and $\alpha,\beta,\gamma$ are Euler angles and $J$ is the total angular momentum then how to get to this: $$[J^2,R]~=~0?$$ This is stated in ...
4
votes
1answer
798 views

What is the spin rotation operator for spin > 1/2?

For spin $\frac{1}{2}$, the spin rotation operator $R_\alpha(\textbf{n})=\exp(-i\frac{\alpha}{2}\vec{\sigma}\cdot\textbf{n})$ has a simple form: ...
7
votes
3answers
479 views

Can one make a ball rotate around a vertical axis using only a combination of horizontal axis rotations?

This is a nice problem that I would like to share. Problem: In a public garden, there a statue consisting of a spherical stone and a stone cup. The ball is 1 meter in diameter and weighs at least a ...
4
votes
2answers
165 views

Would the arms of a rotating ice skater still move outwards if there was no other object in the universe?

If there is no other object in the universe apart from a rotating ice skater, then nothing can be used as a reference frame. Would it make any sense to say that the skater is rotating? If so, rotating ...
4
votes
1answer
710 views

Is all angular momentum quantized?

Angular momentum is definitely quantized in elementary particles and electrons in atoms. Molecules also have characteristic rotation spectra. Is it true that all angular momentum is quantized, ...