# Questions tagged [rotation]

Circular motion about a central point or axis

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0answers
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### Which of the following is not conserved ( for the following options) [on hold]

A smooth tube of certain mass is rotated in gravity free space and released. The two balls shown in the figure move towards ends of the tube. For the whole system which of the following quantity is ...
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### Recent/More accurate rotation velocity measurement?

I've been researching for papers for hours and can't seem to find this. Where can I find the most accurate equatorial rotational velocity measurement for Mars?
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+100

### Ray Tracing and Rotations

I would like to be able to write the matrix operations to be able to define the first arm of the picture below. How can I do that? I have learned beam physics, have read Siegman's Lasers, if that ...
1answer
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### Are there physical quantities constitute of magnitude, direction and rotation along that direction?

There are scalar quantities(magnitude) and vector quantities(magnitude and direction), but are there fundamental quantities that also depends on how it's oriented/rotated along the direction(magnitude,...
0answers
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### Spacetime rotation matrix using mostly minus conventions

When trying to find the Lorentz transformation in matrix form in the $x^2+x^3$-direction, I tried simply mapping the Lorentz boost in the $x^2$-direction to the $x+x^3$-direction by rotating it $45°$ ...
1answer
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### Is there an easy way to tell whether this “Curlmeter” would rotate or not?

Let us say we have the following symmetrical apparatus: Four equal positive charges, all connected to a shaft that can rotate, the connecting rods are insulated, and so does the shaft. Now ...
1answer
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### A thin rod is standing on a smooth surface [closed]

A uniform thin rod of mass m and length l is standing on a horizontal surface. A slight disturbance causes the lower end of the rod to start falling. find the velocity of the centre of mass of the rod ...
1answer
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### Will an object dropped from a high building displace due to the Earth's rotation?

I read that in the 16th and 17th century, the question of whether the Earth rotates around its axis or all celestial bodies rotate around it was extensively debated. One of the anti-rotation arguments ...
2answers
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### Why does twisting make it easier to remove a lid with a seal?

I have a pot with a lid that has a rubber seal (not a screw cap). When taking the lid off, it is incredibly difficult to lift the lid by pulling straight up on it, but twisting the lid whilst pulling ...
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 ...
0answers
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### 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 ...
1answer
54 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 ...
0answers
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### 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} ...
0answers
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### 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 ...
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### 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' ...
2answers
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### 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 ($R_1$ ...
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, ...
0answers
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### 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 ...
1answer
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### 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 ...
6answers
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### Acceleration in circular motion

Can motion of a particle be circular if the radial acceleration is zero, but the tangential acceleration is not $0$?
1answer
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### 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 ...
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### 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 ...
2answers
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### 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 ...
1answer
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### 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 ...
2answers
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### 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}} ...
2answers
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### 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 ...
2answers
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### 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) \...
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### 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 ...
0answers
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### 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 ...
3answers
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### 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. ...
1answer
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### 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 ...
1answer
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### 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, ...
0answers
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### 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 ...
3answers
146 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 ...
2answers
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### 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 ...
1answer
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### 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 ...
1answer
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### 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 ...
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### 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. ...
5answers
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### 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 ...
1answer
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### 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'\...
3answers
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### 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 ...
0answers
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### 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?
2answers
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### 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 ...
1answer
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### 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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### 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 ...
2answers
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### 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 ...