Questions tagged [rotation]

Circular motion about a central point or axis

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Why is angular velocity a vector quantity? [duplicate]

Angular velocity is $$\omega= \frac{dƟ}{dt},$$ here $\theta$ and $t$ are scalar quantities. But $\omega$ is a vector quantity. Why is it such? So far I know the direction of $\omega$ is along the ...
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What are the limitations of using instantaneous axis of rotation? [closed]

I know when the body rotatates as well as translates IAR or ICR shouldn't be used but I am not able to understand why?
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Is sun revolving around certain mass in space with reference to some other galaxy?

Every planet and satellite revolves around their mother planet and about their own axis as we know. So they are compacted as a system. Then why not sun?
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What is the Earth truly rotating about/revolving around?

Earth rotates on its axis and revolves around the sun, the sun revolves around the galaxy, the galaxy is also moving. So Earth's net rotation as observed from a fixed inertial frame consists of all ...
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Artificial gravity on rotating spaceship?

One of the possible ways to simulate gravity in outer space is to have a rotating spaceship, so that the centrifugal force experienced provides a gravity-like force. My question is: shouldn't this ...
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Why wouldn't the part of the Earth facing the Sun a half year before be facing away from it now at noon?

The Earth takes 24 hours to spin around its own axis and 365 days to spin around the Sun. So in approximately half a year the Earth will have spun around its axis 182.5 times. Now take a look at the ...
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Rotation vs translation

What is so fundamentally different between a rotation and a translation that one can be represented with a single n-vector and the other one needs an n-n matrix?
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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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Does the sun rotate?

As implied from the question, does the sun rotate? If so, do other stars not including the sun also rotate? Would there be any consequences if the sun and other stars didn't rotate? Me and my friends ...
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Coupling between galaxy spin and central black hole spin

What is the relationship between the spin of a galaxy and the spin of its corresponding black hole? Associated questions: Do they always have the same axis of rotation? Do they always spin in the ...
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Pauli matrix rotations

When doing physics with two-level systems and introducing rotations, a term that appears quite often is the rotation of a Pauli matrix by another one: $$e^{- i \sigma_j \theta/2} \sigma_k e^{i \...
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How to remove gravity component from accelerometer $X$, $Y$ readings?

So I have an accelerometer which I am wanting to use in an IMU. When the device is tilted but stationary I want the x, y values to be 0, so effectively negate the effect of gravity along the x and y ...
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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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Force on different points on a body not passing through the centre of mass [duplicate]

I was studying about centre of mass and I found that if the line of action of force passes through centre of mass then it will execute pure translation. Moreover acceleration of centre of mass is net ...
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Dynamics of counter-rotating flywheels

I've wondered about this for ages. If we create a pair of flywheels that rotate in the opposite direction with the same angular momentum, but are co-located and have the same mass and inertial moment ...
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What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
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1answer
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Degrees of freedom in a diatomic molecule [duplicate]

We know that a monatomic compound can only have 3 degrees of freedom as we can consider it to be a point mass. However now that we consider a diatomic molecule, there are 3 degrees of freedom in ...
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Acceleration of body rolling down inclined plane

Acceleration of a body rolling down an inclined plane is given by: $$\frac{g\sin\theta}{1+\frac{k^2}{r^2}}$$ $g$=acceleration due to gravity $\theta$=angle of inclined plane $k$=radius of gyration ...
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Euler Rotations in Ordinary Space

I'm reading LittleJohn's notes on Rotations in Ordinary Space on Quantum Mechanics. Link: http://bohr.physics.berkeley.edu/classes/221/1011/notes/classrot.pdf. I'm trying the last question given in ...
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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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Which way do spiral galaxies rotate?

Is it known whether spiral galaxies typically (or exclusively?) rotate with the arms trailing or facing? Intuitively it feels weird to think of the arms as facing the direction of rotation, but that'...
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Would time dilation cause a planet to rotate?

For the sake of the argument lets use a black hole so the time dilation effects are greater and the planet in question is orbiting close enough to have significant TD effects but far enough to not ...
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How to calculate roll, yaw and pitch angles from 3D co-ordinates (Euler Angles)

I have digitized a video of a flying fly in a 3-dimensional space. At all instants I know the x, y, and z co-oridinates of the following points on the fly's body --- The points are my choice, and ...
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How do we prove the existence of the instantaneous axis of rotation?

Euler's theorem of rotation states that any rigid body motion with one point fixed is equivalent to a rotation about some axis passing through that fixed point. Now it is often said that Euler's ...
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How do experiments prove that fermion wavefunctions really pick up a minus sign when rotated by $2\pi$?

Theoretically, after a rotation of $2\pi$, a fermion wavefunction picks up a minus sign, and it is after a rotation through $4\pi$ that it returns to its initial quantum state. Now, the wave-functions ...
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EM Fields in a Rotating Frame of Reference

I'm struggling on my approach to the problem of figuring out E and B fields in a non-relativistic way for a rotating frame of reference in the x-y plane around the z-axis. I am attempting to do this ...
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How many different axes of rotation can coexist?

I have questions about rotation. There is a sphere in space. I can apply a force to cause the sphere to rotate around a central axis. An infinite number of possible central axes can be drawn. ...
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1answer
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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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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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Does being suspended in air allow you to not be affected by Earth's rotation?

Let's assume that there was some mechanism by which we could remain suspended in air. By this I mean that our feet is not in contact with the ground. One possible way of doing this would be by means ...
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Two objects connected by a rigid rod, one of which follows a determined path

Consider an object that follows a determined path, with it's position given by $f(t)$, parameterized by time. Then consider a second object that is connected to the first by a rigid rod of length $l$, ...
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What is the formula for the composition of two axis-angle rotation vectors?

Most people only know about representing rotations as matrices, quaternions, or Euler angles. But there's one other way to represent rotations, known as the axis-angle representation. This is where ...
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1answer
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Non-commutative property of rotation

Addition of angles are non-commutative in three dimensions. Hence some other angular vector quantities like angular velocity, momentum become non-commutative. What is the physical significance of this ...
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Irreducible form of Spherical tensor operators

In the section on spherical tensors in Sakurai, he introduces the idea of going from Cartesian tensors to irreducible spherical tensors. He states the following: A spherical harmonic can be written ...
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Can spin be related to a shift in angle?

If $\hat{T}(\Delta x) = e^{-\frac{i}{\hbar}\hat{p}\Delta x}$ is the spatial translation operator, then there exists a function $f$ from $\mathbb{R}$ to the ket space $V$ such that $\hat{T}(\Delta x) f(...
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Resultant center of rotation due to multiple moments

Say, there are multiple moments (M1, M2, M3) acting on a body (of irregular shape) at points P1, P2, P3 respectively. The body is free to rotate about any point. Now, which resultant center (the ...
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If the Earth didn't rotate, how would a Foucault pendulum work?

How does the Foucault pendulum work exactly, and would it work at all, if the Earth didn't rotate?
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1answer
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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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Does the Earth rotate vertically too?

We know that the earth has seen several Ice Ages. And we know the Earth's magnetic poles seem to flip once in a while. Could all of this be explained by a once every 250 Million Years or so the ...
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1answer
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What exactly is the definition of motion and its relation to Mach's conjecture?

The notion of "movement" seems to be well understood in physics. In fact, I don't recall any physics text-book defining motion. Special relativity theory says that there is no absolute frame of ...
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Rotation in the x-t plane

I am currently studying special relativity using tensors. My lecture notes (which happen to be publicly accessible, see top of page 99) say that the standard configuration can be viewed as a rotation ...
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Free rotation of a rigid body

So I am currently reading Fowles and Cassidy and there is something I'm confused about in the section about geometric description of free rotation of a rigid body. I will present the stuff first that ...
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Rotation, cats landing on their feet, and conservation of angular momentum [duplicate]

Let θ be the orientation (angle) of a body (such as a cat), and let ω be its angular velocity. It is well-known that θ can change even when the body is not rotating, using the conservation of angular ...
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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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0answers
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Rotation in an 'empty' universe [duplicate]

Possible Duplicate: Is rotational motion relative to space? Assume a universe with the same physics as ours, but containing only one rotating (charge-free) body - let's say the size of the Earth. ...
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1answer
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If, for a body rolling on an incline, the friction coefficient isn't enough to allow pure rolling will it still roll?

More specifically that it won't be pure rolling (obviously) but would it still have some rotational motion along with its translational motion? (if yes how would we write their mechanical equations). ...
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Two-rotation coordinate transformation

I've designed an electronic device that uses a 3-axis accelerometer to measure the acceleration of an automobile. I'm only interested in accelerations in the plane of the road surface, so I want to ...
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1answer
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What are the units of the creation and annihilation operators?

The creation and annihilation operators - also known as ladder operators are; $ \hat{a}^\dagger$ and $\hat{a}$ respectively. Using the equation $\hat{H} = \hbarω\left(\hat{a}^\dagger \hat{a} + \...
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1answer
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Explaining the restorative force in a bifilar pendulum

Ok so I am an A2 physics student, and for one of my pieces of coursework I conducted a practical investigation, my topic being the factors affecting the period and swing of a bifilar pendulum. The ...
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1answer
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Earth is rotating [duplicate]

Possible Duplicate: Why does the atmosphere rotate along with the earth? If i take off from land on a helicopter straight above the earth surface to a certain height and stay there for few mins/...