# 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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### 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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### 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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### 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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### 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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