Questions tagged [rotation]

Circular motion about a central point or axis

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374 views

Doppler shift and speed of rotating objects in space

I understand the concept of how we can use the doppler effect to know if an object is spinning, in the sense that the part of the object spinning towards us will exhibit a blueshift, and the part ...
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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 ...
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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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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,...
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Why can a Lorentz transformation be interpreted as a rotation in 4D?

This is basically the result of Michelson-Morley experiment: $$ (x^0)^2 - \sum_{\mu=1}^3 (x^\mu)^2 \stackrel{!}= (\bar x^0)^2 - \sum_{\mu=1}^3 (\bar x^\mu)^2 $$ Why can this be interpreted as a ...
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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 $45°$ ...
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1answer
83 views

Parametrizing $SU(2)$ with Hermitian matrices

There is something that is not clear to me Here is what I know: Pauli matrices are $\sigma_1 = \begin{pmatrix}0 & 1 \\ 1 & 0\end{pmatrix}$, $\sigma_2 = \begin{pmatrix}0 & -i \\ i & 0\...
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1answer
42 views

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 ...
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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 ...
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Does a tire need to slip to generate force?

Recently, I have been doing some research on racing and tire modelling. While I was doing this, I encountered many curves like those shown below. (source: insideracingtechnology.com) While I ...
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1answer
130 views

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 ...
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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 ...
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571 views

Acceleration in circular motion

Can motion of a particle be circular if the radial acceleration is zero, but the tangential acceleration is not $0$?
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How will two equal discs, rotating with equal but opposite angular velocities and put on top of each other affect the spacetime “surrounding” them?

In this article the Ehrenhaft paradox is described. You can read in it that, according to Einstein's General Relativity (to which this paradox contributed), the spacetime around a rotating disc is non-...
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1answer
112 views

Calculate the distance from the axis beyond which the particles have slid off a rotating disk

A collection of small particles is distributed on the top surface of a disc that is rotating at 91 revolutions per second, about an axis, which is vertical. Some of the particles slide off, and some ...
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A question about the tennis racket theorem with degenerate eigenvalues $I_1, I_2 , I_3$

If a rigid body has a symmetry such that two of the principal moments of inertia are equals, i.e. $$I_1=I_2> I_3 \qquad{\rm or}\qquad I_1>I_2=I_3.$$ Are the rotations around the principal axes ...
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1answer
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Possible Error in Marion and Thornton's Classical Dynamics of Particles and Systems

so I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3 The rotation matrix associated with 1.2a and ...
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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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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
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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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1answer
342 views

The dynamics of a cornering wheel

Can a rolling wheel create a side force without first rotating on a vertical axis? There is something wrong with the way we describe how a cornering vehicle wheel creates a cornering force. I think ...
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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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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 ($R_1$ ...
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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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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
28 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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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 ...
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1answer
76 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 ...
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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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A simple way of calculating Euler Angles from Rotation Matrix — help!

This is a follow up of this question : I have the rotation matrix $$ \left( \begin{matrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\\...
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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 ...
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0answers
271 views

Find the exact angle as a function of time for a rod that swings on a frictionless axle [closed]

This is a simple problem I thought of that I haven't been able to solve. Given a rod of uniform mass attached to a fixed axle, find the angle it makes with the horizontal if it is dropped from rest ...
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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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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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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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Does spin have anything to do with a rate of change?

The orbital angular momentum of a particle can be related to the revolution of that particle about some external axis. But in quantum mechanics, the spin angular momentum of a particle can't really ...
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1answer
299 views

Rotational motion activity for physics of sports class

I'm looking for a really solid rotational motion lab for a physics of sports class I'm teaching for younger students (HS Freshmen mainly). It should be something that the students can gather data ...
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1answer
134 views

When applying the equation of torque and equating it to $I\alpha$ which moment of inertia do we take?

I believe $T=I_{cm}\alpha$, where $I_{cm}$ is the moment of inertia about centre of mass and $\alpha$ is the angular acceleration. But do we take $I_{cm}$ even if the torque has been taken about a ...
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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}} ...
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How to calculate resisting torque due to moment of inertia

I'm trying to determine whether a motor is suitable for an experiment. I know the motor's torque and the moment of inertia of the disk it will be turning. I was able to find the angular acceleration. ...
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4answers
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Deriving the unitary operator $U(R)$ associated with a rotation $R$ using Wigner's theorem

A rotation $R(\hat{\textbf{n}},\phi)$ about an arbitrary axis $\hat{\textbf{n}}$ through an angle $\phi$ in the three-dimensional physical space is given by $$R(\hat{\textbf{n}},\phi)=e^{-i(\textbf{j}\...
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How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true?

Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about ...
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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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What is the cause of centripetal/centrifugal force?

What is the cause of centripetal/centrifugal force? When an object of mass $m$ is moved in a circular orbit, it experiences a centrifugal force radially away from the center. What is the cause of this ...
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1answer
227 views

Non Uniform Circular Motion and How External Force Affects The Motion

If there is a force angled inwards acting on the object in circular motion counterclockwise, and the force is split into 2 components, the tangential and the radial, how does each component force ...
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4answers
74 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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1answer
130 views

What periodic functions of the angle operator are Hermitian?

Let $\hat{\theta}$ be one of the position operators in cylindrical coordinates $(r,\theta,z)$. Then my question is, for what periodic functions $f$ (with period $2\pi$) is $f(\hat{\theta})$ a ...
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3answers
391 views

Why does the angular speed formula end up in radians per second?

So, in my homework I am given the radius and also the tangential speed $v$, the measurement for radius is meters; the measurement for $v$ is $m/s$. I don't understand how by after calculating the RPM ...