Questions tagged [rotation]

Circular motion about a central point or axis

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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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253 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 ...
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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 ...
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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 ...
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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 "...
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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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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 ...
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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 ...
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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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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 ...
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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? ...
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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 ...
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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. ...
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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 $Y$ ...
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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 $1/2mv^2$...
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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 ...
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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 \\ ...
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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 ...
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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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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,...
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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 ...
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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 ...
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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, ...
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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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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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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-...
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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\...
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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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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 ...
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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 ...
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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 $2 \pi$, ...
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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 ...
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366 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 ...
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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 ...
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A hemisphere rotating on a flat surface ends up on the flat side. Why?

So I was playing with my kid and this wooden half Kiwi (radius about 20 to 25 mm) got my attention: What I noticed was, when I give it a spin on its pointy end and if a certain initial speed of ...
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Day/Year Length Of Larger, but same mass, Earth? [closed]

I’m wondering how the length of a day and year would change on Earth if it was twice as big, but the same mass (less density)? Also, would such a difference cause it to orbit closer or further from ...
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Comparison between Euler angles and Rodrigues rotation formula under small rotation hypothesis

Sorry for boring you during summer vacation, my friends. I am haunted by the comparison between Euler angles and Rodrigues rotation formula under the small rotation hypothesis. Maybe, they cannot be ...
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Rotating and Moving Water Container

I'm trying to solve the following problem, but I'm getting a different answer than the one in the book. I can't understand what I'm doing wrong. (The question is from Hibbeler's fluid dynamics) So ...
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Approximation of Euler angles with small rotation hypothesis

Sorry for boring you during summer vacation, my friends. I am haunted by the approximated expression of Euler angle rotation matrix found in this textbook. In the appendix, the author declares that ...
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$SO(3)$, orbital angular momentum, vector product

I have a big confusion with group theory terminology. I know that orbital angular momentum (OAM) is $\mathrm{SO}(3)$-symmetric in 3D-space. Let's define QM orbital angular momentum (OAM) ...
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Torque around the origin of a particle using moment of inertia (in 2D)

(You can skip this derivation and go down to my final question if you already are familiar with the results $(1)$ and $(2)'$ from this derivation) Suppose we are in the xy-plane: In two dimensions, ...
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Can I avoid spaghettification with a spin?

I am aware of spaghettification effect caused by entering a black hole, as well as fundamental physics of an object in space, so here is my theoretical construct: if I place an object in space where ...
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For what angles (and why) does the equation for finite rotation fail to work?

I am learning rotations and group theory/representations and my lecturer's note mentioned that: "The group is considered connected, but not simply connected [...] As a result, the formula for a ...
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Are rotation matrices faithful representations of the rotation group?

I would like to use rotation matrices as representations of the rotation group. I would like to know if these representations are faithful, i.e. isomorphic to the rotational group elements. I read ...