Questions tagged [rotation]
Circular motion about a central point or axis
647
questions
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2answers
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Emergence of rotational symmetry on 2D square lattice
On page 74 of David Tong's Statistical Field Theory lecture notes, it is said that $(\partial_1\phi)^2 + (\partial_2\phi)^2 $ respects both $D_8$ (that includes discrete four-dimensional rotation ...
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0answers
29 views
How many illusionary axes of rotation can coexist?
Consider the answer to this question:
How many different axes of rotation can coexist?
Any rigid body, at any time, can only be rotating about one instantaneous axis of rotation.
Now, that ...
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1answer
42 views
The Lorentz Transformation of the electric field of a moving charge
If I have a moving charge observed in frame $S$, may a Lorentz boost from $S$ in a direction not parallel to the charge's velocity in $S$ result in an electric field that has a different magnitude of ...
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0answers
11 views
Libration vs. rotation for mass on rotating disc
Hello I have a question about the difference between rotation and libration. In some textbook it is stated that for libration
\begin{equation}
q (t+\tau) = q(t) \\
p (t + \tau) = p(t)
\end{equation}
...
0
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0answers
16 views
Velocity composition effect of moving line charges acting on a moving charge - By what velocity (boost) is the E-field unchanged along the boost?
Claim 1) An infinitely long line current can be modeled as the linear superposition of two infinitely long line charges.
Claim 2) An infinitely long line current can exert forces on charges with ...
0
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0answers
19 views
Finding the total rotation about an arbitrary axis
I have a rigid body which is fixed in a x,y,z system and is free to rotate. The z vector is parallel to gravity. x and y are arbitrary and perpendicular to z.
The moving coordinate system is x',y',z' ...
0
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2answers
34 views
Are the tides scale independent?
What I mean is the following. Imagine two smooth massive spherical bodies ($M_1\neq{M_2}$), with equal and homogeneous mass densities. Both masses have a layer of water on them for which holds ($R_1$ ...
1
vote
1answer
37 views
Electromagnetic field of a point charge seen from a rotating reference frame
Let us consider a point charge sitting in the origin of our coordinate system. If we change to a rotating system, will the field of the point charge still look the same? Intuitively I would say yes, ...
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0answers
25 views
Transformation of dielctric constant tensor
I have a dielectric tensor
$$K = \begin{pmatrix}
2000 & 0 & 0 \\ 0 & 2000 & 0 \\ 0 & 0 & 50
\end{pmatrix};$$
which I want to transform to a new coordinate system given by ...
1
vote
1answer
27 views
Rotating coordinate frame connection of coordinates and mass
Hello I am still confused about rotating coordinate frames and want to ask a question about it.
Is it correct that strictly speaking the mass must be connected with the axis of rotation in the ...
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5answers
535 views
Acceleration in circular motion
Can motion of a particle be circular if the radial acceleration is zero, but the tangential acceleration is not $0$?
1
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1answer
73 views
Change of reference frame for a wavefunction: same modulus but different currents?
Suppose that, at a certain $t=0$, one has a wavefunction
$$
\psi=\psi(x,y)
$$
defined on a plane and well normalized to $1$. Coordinates (x,y) refer to the frame $xOy$.
How does the wavefunction ...
0
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0answers
20 views
Vorticity - Rankine vortex: how can we say that $\frac{\partial u_\phi}{\partial z} = 0$
\subsection{a}
A Vortex formed in a bathtub, tornado or in other real world scenarios, exhibit nearly a solid body rotation in the core while far away from the center the flow is irrotational. This ...
1
vote
2answers
97 views
Griffith's Electrodynamics problem 1.9 (rotation through (1,1,1))
I was compiling some solutions to Griffith's E&M, and I can't get my solution to square with the others I have found online. The question asks:
1.9 Find the transformation matrix R that ...
0
votes
1answer
23 views
Conservation of Angular momentum or Work = 0 , which is valid?
In the figure, the block on the smooth table is set into motion in a circular orbit of radius "r" around the Center hole. The hanging mass is identical to the mass on the table and remains in ...
1
vote
2answers
43 views
Rotating coordinate frame
Hello I have a question about rotating coordinate frames. Following the book of Brizard the Lagrangian is given by
\begin{equation}
L(\mathbf{r}, \mathbf{\dot{r}}) = \frac{m}{2} \vert \mathbf{\dot{r}} ...
0
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2answers
83 views
What is a rotation group and how do we get its unitary representation?
The rotation group is ${\rm SO(3)}$. It is the group of $3\times 3$ orthogonal matrices $\{g(\theta)\}$ with unit determinant. So these are already defined in terms of $3\times 3$ matrices. But we use ...
1
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2answers
43 views
Angular momentum as an operator on triple product space
General arguments about introduction of angular momentum to QM is that under a transformation of coordinates the x and y position operators mix (as it is usually written)
$$\hat{x}' = \cos(\theta) \...
0
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4answers
58 views
A rod rotating about a pivot
A long, uniform rod of length L and mass M is pivoted about a frictionless, horizontal pin through one end. The rod is nudged from rest in a vertical position as shown in figure. At the instant the ...
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0answers
25 views
Does acceleration of the rim mean just tangential or both tangential and centripetal acceleration?
On my physics homework, the problem specifies that the acceleration of the rim of a flywheel can't exceed 100g. Does this mean that the tangential acceleration only, or the sum of the tangential and ...
0
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2answers
31 views
Point of application of tangential velocity in rotational motion
The tangential velocity of a particle in a rigid body is given by: $\vec{v}=\vec{\omega}\times \vec{r}$. Since the cross product is perpendicular to both $\vec{\omega}$ and $\vec{r}$, the velocity $\...
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0answers
30 views
Single number to quantify difference between two local reference frames?
I'm working with some satellite data that defines the spacecraft reference frame from two star cameras and two different measurements of orientation configuration of the cameras, and I'm trying to ...
1
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0answers
24 views
How to properly align my relaxed molecule onto my gold electrode?
the question is described below since it can be considered a chemistry or physics question: How to translate from one plane to another? originally posted on mathematics SE
I am trying to get ...
2
votes
3answers
92 views
What is wrong with this reasoning?
Suppose a particle is rotating about a point at a distance $r$, then since $r$ is constant $\frac{\text dr}{\text dt}=0$ so the component of velocity along the position vector should be zero. ...
0
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1answer
35 views
Rotation of object at different positions
Why do object placed in a river rotates at different position when object is in center of flowing river it just moves forward but when it is on either side it rotates and moves forward what's the ...
1
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1answer
44 views
Earth rotation with atmosphere
Note: This might be a very dumb question
Considering Earth's rotation on its axis, I was thinking it made sense for the outer sides of the Earth to have a significantly higher tangential speed, ...
0
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0answers
17 views
Producing Yaw (Orientation)
I am working with a car and trailer model which has a GPS sensor attached and I am looking for ways to calculate it's yaw (orientation).
One way I am working on is two resolve both the car and ...
4
votes
3answers
143 views
Three spin states of a spin-1 particle
For a spin-1 particle at rest, it has three spin states(+1, -1, 0, along the z axis). If we rotate the z axis to -z direction, the spin +1 state will become the spin -1 state. Can we transfer the spin ...
8
votes
2answers
191 views
How to infer that the black hole in M87 is rotating clockwise?
The spokesperson mentioned that the rotation of M87 supermassive blackhole is rotating in the clockwise direction by looking at the bright and dim region of the image taken, is it the resolution of ...
0
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1answer
19 views
Wheel RPM measuring reference point [closed]
Attached is picture of a car wheel in 3D. Assume it is suspended and rotating in the air. If I put a nut + proximity sensor right on top of the nut within the red line to measure RPM, will the nut ...
2
votes
1answer
61 views
Definition of Vector
In a book on General Relativity that I am reading, it defines a vector as an object or array of numbers that transforms like a vector (under rotations). I understand that under rotation $\theta$, a ...
1
vote
0answers
15 views
How will a rotating, circular, and cylindrical body of a superfluid develop in outer space?
Let's consider a rotating (about its center, in the plane cutting the initial circular and cylindrical form into two halves), circular, and cylindrical body of a superfluid somewhere in outer space. ...
1
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5answers
77 views
Effect of earth's rotation in ballistics
For this purpose, let's consider earth's rotations constant. Do earth rotation momentum get transfered to any object (a missile for example) that get's lauched? If so, why do we have to consider earth ...
3
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1answer
74 views
Wigner-Eckart theorem: Are expectation values of all vector operators parallel?
The Wigner-Eckart theorem tells us that for any tensor operator, $\mathbf{T}^{(k)}$ that
\begin{align}
\langle jm|T^{(k)}_q|j'm'\rangle = \langle j'm'kq|jm\rangle \langle j||\mathbf{T}^{(k)}||j'\...
6
votes
3answers
139 views
Why do office chairs rotate when pushed/pulled out?
A common source of frustration when I'm at work is the fact that my rolling office chair's wheels rotate whenever I push it forward or backward from my desk, which can cause it to bump my computer ...
0
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0answers
17 views
What happens when an impulse is applied at right angles to one end of a rod (free to move on a frictionless surface)? [duplicate]
What will be the difference if we apply this impulse at the center of the rod? Will the translatory motion be same in both the cases?
0
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2answers
154 views
Infinitesimal Rotation under Orthogonal Similarity Transformation
I’m reading charpter 4.8 of Goldstein’s classical mechanics 3rd edition that deals with infinitesimal rotations, and the following is the part I got stuck:
(p.166~167) If $d\boldsymbol{\Omega}$ is ...
0
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1answer
90 views
Newton's third law for rotating systems [closed]
As often happens for the rotational world, the Newton's law can be restated in terms of angles, moment of inertia and torques replacing displacements, masses and forces (this is one source among ...
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0answers
19 views
Azimuthal Symmetry is on a certain axes that is not simply the $z$-axes
let's say in a problem, the azimuthal symmetry is along the axis $\frac{1}{\sqrt6}(-1, -1, 2)$. If I create two new basis angles and get solved the LaPlace's equation with that, what should I do to ...
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2answers
95 views
How the centripetal forces work on a point in a rigid body? [closed]
I know it was a question but when I asked last time I did not know the answer. It has been suggested that the question is not clear, it's badly written. Now I know the answer and I can introduce them ...
0
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0answers
19 views
Why sand in a water collects at center on rotating the water? [duplicate]
We commonly observe that on rotating dirty water, the dirt in water collects at the center. But why does it happens, and why does it not collect at edges due to centrifugal force. Does something ...
0
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0answers
25 views
How do the principles of weather vane design change for underwater applications?
I am doing some research into the use of weather vanes under water. This "water vane" would serve the same function as a weather vane does in air, just while submerged in water.
I understand that ...
0
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0answers
33 views
Forces on a Rotating Rigid Body
This question has been puzzling me for some days now and I thought I might ask you guys for some help.
Say that we have a rigid body (like a rod) that is in a vacuum in space. Furthermore, say that ...
2
votes
1answer
232 views
Difference between torque, moment and couple
I know the basics of them like
Torque is force multiplied by the distance (from the point where there is no rotation like centre of gravity).
Couple acts because of two equal and opposite forces ...
2
votes
1answer
110 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,...
2
votes
1answer
76 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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2answers
146 views
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 ...
0
votes
3answers
304 views
How to distinguish between angular frequency $\omega$ and frequency $f$
The relation between the "regular" frequency $f$ and the angular frequency $\omega$
($\omega = 2\pi f$) is clear to me. However, every time I see "rotations per second" I really get confused as to ...
0
votes
2answers
72 views
Gravitational potential energy of a rod, attached by its end to an axis
Situation: We suppose a rod is attached by its end to some pivot, and is allowed to fall from a horizontal position. As this occurs, the rod loses gravitational potential energy ($∆U_G$), say 10J, ...
0
votes
2answers
229 views
Torque, Angular Acceleration and Linear Acceleration
We know that we torque is applied, it cause an angular acceleration in the rotating body similar to what a force does to a body moving on a straight line.
But my question is, Does Torque affect the ...
