Questions tagged [rotation]

Circular motion about a central point or axis

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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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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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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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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} ...
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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' ...
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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 ($R_1$ ...
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1answer
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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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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 ...
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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 ...
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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 $0$?
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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 ...
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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 ...
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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 ...
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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}} ...
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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 ...
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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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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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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 ...
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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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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 ...
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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 ...
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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. ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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'\...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
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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,...
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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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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 ...
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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 ...
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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, ...
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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 ...