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Questions tagged [rotation]

Circular motion about a central point or axis

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How can both angular displacement and angular distance share similar equations?

Equation for finding angular displacement is: $$ d\vec{\theta} = \vec{\omega} dt$$ In the case of rotational motion with constant acceleration, we can use the following equation for angular velocity: $...
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If we take a sufficiently large axle for a wheel then is it possible that the top of the wheel would have thrice the velocity of its axle?

I recently learnt that the top of a wheel has velocity twice that of its axle. In all such cases of why this is so the axle is always considered to be very small in comparison to the wheel. Thus, I ...
Madly_Maths's user avatar
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Generators of rotations: $[J_i, J_j] = \epsilon_{ijk} J_k$ and $(J_i)_{jk} = -\epsilon_{ijk}$. Is this a coincidence?

Thinking about $SO(3)$. Any rotation matrix $R$ can be written $$ R = e^{\theta \hat{n}\cdot J} $$ where $J$ is a vector the three skew-symmetric generators of rotation $J_x$, $J_y$, and $J_z$. In ...
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$Ad\circ\exp=\exp\circ ad$ and $e^{i(\theta/2)\hat{n}\cdot\sigma}\sigma e^{-i(\theta/2)\hat{n}\cdot\sigma}=e^{\theta\hat{n}\cdot J}\sigma$

This question is inspired by my recent question How to prove $e^{+i(\theta/2)(\hat{n}\cdot \sigma)}\sigma e^{-i(\theta/2)(\hat{n}\cdot \sigma)} = e^{\theta \hat{n}\cdot J}\sigma$? with answer https://...
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How to prove $e^{+i(\theta/2)(\hat{n}\cdot \sigma)}\sigma e^{-i(\theta/2)(\hat{n}\cdot \sigma)} = e^{\theta \hat{n}\cdot J}\sigma$?

Disclaimer: I'm sure this has been asked 100 times before, but I can't find the question asked or answered quite like this. If there are specific duplicates that could give me a simple satisfactory ...
Jagerber48's user avatar
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What is the advantage of using spherical tensor over cartesian tensor?

I am trying to train a machine-learning model to forecast the polarizability of atoms within a molecule. Typically, the tensor is characterised as a Cartesian rank-2 tensor, like this: $$\alpha= \...
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Can you ever obtain a pure rotation from composing Lorentz transformations?

An exercise asks one to show that given $v, u$ speeds much smaller than $c$ and oriented orthagonally, the composition of the lorentz boosts $B(\mathbf{v})B(\mathbf{u})B(\mathbf{-v})B(\mathbf{-u})$ is ...
Y G's user avatar
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Rotation and translation of a function of a 3D vector

I want to change the frame by doing translation and rotation. $$f(\vec{v})=\sum_{n,l,m}R_{nl}(v)Y_{lm}(\hat{v})f_{nlm}^v.$$ Let, $\mathcal{R}$ be the rotation matrix and $\mathcal{T}$ be the ...
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Rotation of spherical harmonics

I have a question about the rotation of spherical harmonics. In Wikipedia it is mentioned that if we make a rotation in 3D space: $R\vec{r}=\vec{r}'$,then the Spherical Harmonics can be written as a ...
Thanos Athanasopoulos's user avatar
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Forces in tangentially-accelerating circular motion

Let's say a car is moving along a semicircular path. It moves with constant speed for the first half. Then, it accelerates with constant tangential acceleration for the second half of the semicircle. ...
Aliki G.'s user avatar
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Do we really see the back of a cube when cube moves in relativistic speed?

I am learning Terrell-Penrose's effect and it is often argued that the effect allows an observer to see the back of a cube. Many references even explicitly show the "back sides" of the ...
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Relative motion between two points on a rotating disc

Consider two children A and B sitting on diametrically opposite points of a merry go round rotating about its centre. Suppose A and B are facing each other. As seen from A, B never seems to move and ...
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Why sun revolve around the sun ? Why cant it just rotate ? ( gravitas attraction force makes it revolve , how?) [closed]

Why the revolution ? How General relativity theory explains it
Rumana Izzath's user avatar
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Rotation of Pauli Vectors with $SU(2)$ reproduces the $SO(3)$ matrix. but do all $SU(2)$ matrices reproduces $SO(3)$?

So we can write the $SU(2)$ matrices multiplication as this. $$\begin{bmatrix}\alpha&\beta\\-\beta^*&\alpha^*\end{bmatrix}\begin{bmatrix}z&x-iy\\x+iy&-z\end{bmatrix}\begin{bmatrix}\...
abx_pradB's user avatar
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Doran Geo Algebra for Physicists Exercise 2.9 [closed]

In the question says The Cayley-Klein parameters are a set of four real numbers $\alpha$, $\beta$, $\gamma$ and $\delta$ subject to the normalisation condition $\alpha^2+\beta^2+\gamma^2+\delta^2=1$ ...
Cro's user avatar
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When a wheel begins to roll on a flat surface, is it due to fulcrum generated at the contact point by friction?

[Edit: What I'm trying to understand is how any wheel rolls on a surface, instead of just spinning in place. I know that friction provides the force to make the wheel roll, but I'm unsure about the ...
cosmos's user avatar
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Doubt in pitch of screw gauge [closed]

I have just started learning about screw gauge and I came across this statement about pitch The pitch is the distance between two consecutive threads of a screw which is equal to the distance moved ...
Dhyaneshwar's user avatar
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"Symmetric" photon polarization rotation

The usual linear polarization matrix/operator for a photon or classical light transforming from some combination of $|H\rangle$ and $|V\rangle$ to another is: $$ \begin{pmatrix} \cos(\theta) & -\...
user401228's user avatar
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Direction of angular momentum

I came across this question in one of my tests: A bob of mass $m$ is attached to an inextensible string of length $l$ suspended from a vertical support. The bob rotates in a horizontal circle with an ...
Tanush Gupta's user avatar
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How to calculate the rotation speed of spinning top, which will be enough that it is not falling down or stays within certain angle to vertical axis [duplicate]

I found many articles with the calculation of the precession rotation speed of the spinning top like this or this. They give this equation for Precession rotation speed $\Omega$: $$\Omega=\frac{mgr}{I\...
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Wrong concept in rolling question

A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct? ...
Starlight's user avatar
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Rotational speed using conservation of angular momentum

I know that angular momentum is conserved, but I don't know how to calculate the new speed of an object after it shrinks. Say you have a spinning object, then it shrinks, then how do you calculate the ...
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Why can't rotations in general be associated with vectors?

In my textbook, there's a question: A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector? The rotation of a body can be ...
archthegreat's user avatar
6 votes
2 answers
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Radian unit mystery (damped oscillator)

I would be extremely grateful for any help that anyone could offer here. I am interested in solving the optical bloch equations for the excited state population Rabi oscillations with damping due to ...
HB123's user avatar
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A drum is rolling down a hill - is the force of friction with the surface a constant?

A drum is rolling down a hill without slipping. We ignore air drag. In order for the drum to not slip, there must be a (static, correct?) friction force exerted by the surface on the drum at the point ...
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Understanding the relationship between the angular velocity and angular acceleration vectors

In this question the people who answered helped me validate my understanding of the $\vec\omega$ vector, the angular velocity of a particle or a rigid object. I would now like to add the angular ...
Aviv Cohn's user avatar
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Why does more rotational inertia result in a smaller velocity down an incline?

In my physics class we are learning about how objects with greater rotational inertia result in less translational velocity when "rolling without slipping" down an incline. When explained, ...
physics.nathan's user avatar
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3 answers
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Rotation of disc on smooth surface

If we apply a force on the rim of a disc kept on a frictionless surface the disc rotates but can it be called rolling? Because what I know is that for rolling friction is necessary. Also can I ...
yyzr's user avatar
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Can the same rough surface provide frictional force on opposite directions for translation and rotation of a sphere under a tangential external force?

I came across a question which says: "A force $F$ acts tangentially at the highest point of a sphere of mass m kept on a rough horizontal plane. If the rolls without slipping , find the ...
Synthia's user avatar
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Unitary Representation of $\text{SO}(3)$ in Position Representation

Let $R\in\text{SO}(3)$ be an arbitrary rotation, and let $U_R$ be the unitary representation of $R$ on some Hilbert space $\mathcal H$. To me, the defining property of $U_R$ is how it conjugates the ...
William Deng's user avatar
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Angular Momentum Operators generates rotation transformations - Stern-Gerlach device explanation?

In a lecture we were taught how the angular momentum operator $\vec{L}$ acts as the generator of rotations in quantum mechanics, which are defined using the following equation: $R_u(\alpha)=\hat{1}-(i/...
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Coriolis Acceleration in Local Cartesian Coordinates

Generally, the coriolis acceleration is given as $-2\vec{\Omega}\times\vec{v}$ Just as $\vec{\Omega}$ or $\vec{v}$, the coriolis acceleration can be rewritten in local cartesian coordinates (edited): $...
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General relativity, Mach's principle and rotation

During the Gravity Probe B press conference, Kip Thorne gave the following statement: Suppose that the entire universe were rotating rigidly instead of being non-rotating [...]. How would we know? ...
WordP's user avatar
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Does the Wigner D-matrix suffer from gimbal lock?

Are there specific Euler angles and initial spherical vectors for which the D-matrix loses a degree of freedom, akin to gimbal lock in the conventional Euler rotation matrices? (Of course the ...
BenjaminDSmith's user avatar
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How can you understand curl of electric field illustratively?

Considering the curl of the electric field of an electric dipole, this will be zero in absence of magnetic effects which is clear to me. I watched a video by 3Blue1Brown (some time ago) who explained ...
Rasmus Andersen's user avatar
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Representation of groups

Can someone please explain to me the last sentence (in bold) from the following excerpt? It's from a set of lecture notes on classical fields and GR (Ch.2 Groups and representations, p.16). I went ...
Floyd's user avatar
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Is angular velocity and angular acceleration independent of translating frame

[CONSIDERING ALL BODY RIGID] So think of a body which is rotating if I see it from a rotating frame,let's say with same angular velocity then the body will appear rest to the frame , so will have zero ...
Guess's user avatar
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Proof that a scalar field invariant under rotations only depends on norm

Let $f: \mathbb{R}^3 \rightarrow \mathbb{R}$ be a real valued scalar field and $\mathbf{r}\in\mathbb{R}^3$ a vector with $r = \sqrt{\mathbf{r}\cdot\mathbf{r} }$ its norm. Let's say that $f$ is ...
Pere Rosselló's user avatar
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Calculating $C$ in $I_{CM} = CMR^2$

I am a bit new here, so please excuse any errors I might make. I am a student in an AP Physics C: Mechanics course and I am conducting an experiment where I am experimentally calculating the C values ...
Wizzrobe's user avatar
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Air resistance due to Helium vs Air

I was reading this technical note by NASA on windage power loss in alternators. In the paper, the power loss due to fluid shear between two concentric cylinders (a rotor and a stator) is derived. The ...
E400Jack's user avatar
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How to rotate a 3D matrix around a line by a certain degree? [closed]

Physics Ch 67.1 Advanced E&M: Review Vectors (15 of 55) Coordinate Transformation in 3-D: Ex. 2 I was watching the following video where the goal was to find the Coordinate Transformation matrix ...
lodo's user avatar
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Normal reaction exerted by a rolling object

If we take a disc of mass M and radius R and assume that the disc is performing Combined rotational and translational motion on a frictionless flat surface. then if we take a point at the top of the ...
Srivas's user avatar
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Does dimensional consistency imply the same units?

Can two units having the same dimensions always be used interchangeably? For example $s^{-1}$ and $\frac{rad}{s}$ have the same physical dimension, does that mean we can measure frequency $\nu$ with ...
Jack's user avatar
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When a force less than maximum static friction is applied on a round body, will the body roll? Also does static friction depend on area of contact?

I think the body should not move since maximum static friction is greater than the applied force but my book says that it will roll. Also I have read that static friction is independent of the area of ...
Anonymous's user avatar
5 votes
5 answers
348 views

Why does $\delta \vec{r} = \delta \vec{ \theta} \times \vec{r}$?

Hello fellow physicists, I was trying to understand some behavior on rotating objects, specifically about the formula $\vec{v} = \vec{\omega} \times \vec{r}$. The Book (Marion, J. B. (1965). Classical ...
Carrot Carron't's user avatar
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Where does this expression for infinitesimal rotations come from?

In Chapter 2, page 11 of Preskill's quantum computing notes, he mentions without explaining that a counterclockwise inifinitesimal rotation by $d\theta$ about the axis $\hat{n}$ is given by $$R(d\...
Eulerian's user avatar
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Balancing a flat rotating disk on edge

I am building a POV (persistence of vision) display, with LEDs on the edge of two different radius semicircles of a spinning disk. While the structure has been designed to have its center of gravity ...
Ag Primatic's user avatar
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How to prove that, if $A$ and $B$ are vectors, then their cross product is still a vector? [closed]

in my course of special relativity we are introducing tensors: however, before doing that, my professor sort of re-defined vectors saying that in a 3D euclidean space, $A$ can be called a vector if, ...
Fede's user avatar
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3 answers
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Normal Force Components For Circular Motion

Hey, I was working on a problem for physics and couldn't wrap my head around it at all. I was looking at this diagram that I found online 2 but it doesn't make sense to me on what the x component of ...
Garish19's user avatar
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Is there a known formula of the speed distribution of distinct layers in the frame-dragging region of a BH?

I am asking this question only because I want to figure out does space move in this case similarly to a fluid like water or oil are or even more better as speeds o planets around a star.. or this ...
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