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Questions tagged [rotation]

Circular motion about a central point or axis

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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'\...
6
votes
3answers
82 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 ...
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0answers
16 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?
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2answers
137 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 ...
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1answer
50 views

Newton's third law for rotating systems [on hold]

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
10 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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4answers
55 views

How the centripetal forces work on a point in a rigid body?

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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0answers
18 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 ...
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0answers
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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 ...
0
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0answers
54 views

Force on the shifted axis of rotation of a body

Suppose you have a CD-like shape, so a homogeneous cylinder of thickness $d$, mass $M$, radius $R_1$ with a hole around the center of radius $R_2\ll R_1$. Then we know that the moment of inertia for ...
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0answers
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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 ...
2
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1answer
48 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 ...
3
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1answer
91 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
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1answer
69 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
81 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
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3answers
93 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 ...
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2answers
46 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, ...
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2answers
66 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 ...
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0answers
25 views

Lense-Thirring effect: Revolution, precession, rotation … inside rotating shell?

This is a very basic and vague question (I don't know general relativity, nor much physics, but am interested in this question for idiosyncratic reasons). Consider a rotating spherical shell of mass ...
2
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3answers
77 views

Maxwell's Equations in a Rotating Frame of Reference: How to transform E and B Fields?

I know there is allready a question on the topic, here, however the answer to this question deals with GRT, and I want to keep the level of the question basic (however enough to deal with thing like "...
1
vote
1answer
162 views

The physics of a cornering wheel and its centripetal force

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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0answers
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Windowless space station: rotation vs. gravity ring vs. frame dragging?

Imagine a windowless hollow cylinder, with an observer sitting inside on the curved wall. Something is pulling the observer against that wall. The observer can also walk easily along the inner ...
0
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2answers
52 views

Is the acceleration of a rotating body always it's centripetal component? [closed]

For constant circular motion where a rotating mass accelerates angularly. Would the linear acceleration of the rotating mass always be equal to its centripetal acceleration e.g. The earth's ...
0
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1answer
33 views

How can I find the power given only the torque?

I have a system where I am trying to find the power generated by a DC electric generator. However, I am not very familiar with generators, so I am having difficulty determining the rotational velocity....
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1answer
37 views

Why should the friction between two disks be zero when there velocity is same? [duplicate]

In this video here, Walter Lewin mentions two discs of different radius $r_1$ and $r_2$, of the same density, where the first disk is initially rotating, while the second is at rest. In the videos ...
0
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1answer
34 views

Should there be a significant differential in wind velocity indoors vs outdoors in relation to Earth's rotating atmosphere?

What is the behavior of a rotating Earth's atmosphere indoors? Should there be any differences experienced between the atmosphere spinning in lockstep with the Earth outdoors vs. closed-off indoors? ...
0
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1answer
40 views

If a ball were to roll through a loop, would the normal force change when compared to a frictionless block?

I am currently working through the following problem: Reaching part c), we are required to repeat the former parts using a spherical mass instead of a frictionless cube. I have no problems with the ...
2
votes
2answers
53 views

Rotation of a Bicycle Wheel

Circular motion at a constant velocity requires a net force toward the center of rotation. If I stand a bicycle on its seat, wheels upwards and spin the wheels with my hands, they start rotating. ...
3
votes
1answer
87 views

How to obtain $Y$ rotation with only $X$ and $Z$ rotation gates on the Bloch sphere?

Let's say you have a system with which you can perform arbitrary rotations around the $X$ and $Z$ axis. How would you then be able to use these rotations to obtain an arbitrary rotation around the $Y$ ...
0
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2answers
144 views

Rolling objects released from rest: time down the ramp [closed]

Since we are given the values of I for each object, I was able to calculate the KE's of each: the solid spheres had KE of $1/5mv^2$; the hollow sphere had a KE of $1/5 mv^2$, and the hoop had $1/2mv^2$...
3
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0answers
63 views

What does a basis rotation correspond to physically for linear position-momemtum?

For polarization and angular momentum, rotating the basis corresponds to a very straightforward physical transformation, namely, the physical rotation of an experimental apparatus about an axis in ...
1
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1answer
68 views

Relation between Spin 1 representation and angular momentum and $SO(3)$

This is a naive question. It occurred to me while studying in detail the the Spin 1 angular momentum matrices. The generators of $SO(3)$ are $J_x= \begin{pmatrix} 0&0&0 \\ 0&0&-1 \\ ...
2
votes
2answers
117 views

Rolling Without Slipping and Rotational Energy

I'm a little confused. Translational energy and rotational energy add separately, according to my textbook, to give the total kinetic energy of a moving object. That means that for a disk ...
1
vote
1answer
154 views

Integrating over Euler Angles

I have a $6\times6$ matrix having its elements being functions of Euler's angles (ZXZ rotation scheme) representing a tensor physical property. To find the average of the tensor property, I need to ...
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2answers
63 views

Rigid bar on a pivot

Say we have a solid bar in space. It is on a pivot, the pivot being right at the bar's center of mass There is a massless rocket pushing on one end of it, making it spin, faster and faster. Suddenly,...
0
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1answer
74 views

A rotating solid bar in space [closed]

Say there is a solid bar in space. Imagine it vertically, with the top point labeled $A$, and the bottom point labeled $B$ (these aren't points on the bar, but points in space between which the bar ...
0
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2answers
63 views

What is the tangent vector representing rotation?

I am reading Mathematics for physics: A guided tour for graduate students by Michael Stone. On the page 379, the book says The surface of the unit sphere is a manifold...We may label its points ...
0
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1answer
72 views

Relation between rotation vector derivative and angular velocity when the rotation angle is constant

$\def\va{\vec{\alpha}} \def\vw{\vec{\omega}} \def\vn{\vec{n}}$Let $\va(t)$ be a rotation vector such that its direction is the rotational axis and its length $\alpha=|\va|$ is the angle describing the ...
2
votes
3answers
99 views

Multiple Centers of Mass [closed]

This may sound like a trivial question, but I am wondering: is it possible for there to be multiple centers of mass? And if it isn't, why? For example, take some arbitrary 3-Dimensional object, ...
0
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2answers
80 views

Dynamics of a sphere in a horizontal plane driven by a force

I'm studying the dynamics of a sphere in a horizontal plane driven by a force. The situation is the following: I have a stationary sphere of mass $m$ and radius $r$ in a pool table whose lining has ...
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2answers
98 views

If a particle is undergoing a uniform circular motion, then how is its angular momentum conserved about its centre in its plane? [closed]

I didn't understand why is there no torque of the gravitational force of the particle?
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3answers
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Rotor why not opaque?

Helicopter rotors spin at around 300RPM. Now for the naked eye they look like transparent, like if the rotors were not even there. https://www.quora.com/Why-do-we-see-individual-helicopter-rotor-...
1
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1answer
74 views

Velocity in rotating frame projected onto axis in inertial frame

I want to look at the projection of the velocity of a particle in the rotating frame onto an axis in the inertial frame as a function of time. For example, I am calculating \begin{equation} \frac{d\...
2
votes
1answer
86 views

Irrep corresponding to a rotation, what's the definition?

My character tables for point group $T$(Schönflies-notation but easily convertible into other point group notations) tell me that the rotation around the $z$-axis, $R_z$ (the $z$-direction ...
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3answers
88 views

Rotation around which axis [closed]

Imagine you have a rigid rod which is free to move and a force is applied at a point away from the center of mass of the rod. This would create torques at multiple points on the rod as the force ...
4
votes
1answer
85 views

Does rotation always slow down in general relativity?

Suppose I have a rotating object in empty space. Will it lose angular momentum due to interactions with spacetime? The most obvious case if if the object has a quadrupole moment. Then the quadrupole ...
1
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1answer
80 views

Rotation matrix with deficit angle

I need to find the rotation matrix for a space with a deficit angle. The question is as pictured The following is my answer to the question: If $\theta$ could vary between $0$ and $2 \pi$, ...
2
votes
2answers
203 views

Why doesn't Foucault's pendulum show Earth's spin at the equator but works at the North/South poles

If you where directly above the North/South pole and set up Foucault's pendulum, why does it show the Earth's spin even though the Earth isn't spinning there? This is also where it takes the shortest ...
0
votes
1answer
215 views

Minimal angle that will cause a cube to tip on an inclined plane

Let's say that I have a cube with side $a$ and a ramp such, that the coefficient of friction between the cube and the ramp is $\mu$. I want to determine the minimal angle of inclination of the ramp ...
6
votes
3answers
1k views

Why do things spin?

Let's say I have 2 boxes, one of mass M and one of mass 2M. They are separated by a distance of 1 meter. I drop them from the same height and see that due to the earth's gravity, they accelerate at ...