# Questions tagged [rotation]

Circular motion about a central point or axis

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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 ...
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### Rotations about a unit vector which doesn't pass through the origin in 3 dimensions

I am trying to understand how rotating a vector about an aribitrary axis which does not pass through the origin of the coordinate system $(x,y,z)$. Let the $\vec{r_{1}}$ and $\vec{r_{2}}$ be two ...
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### Center of mass and velocity of rotating object [closed]

I tried to solve this problem with V = R$\omega$, using $\omega$ = 2$\pi$/T and R = R - 2r (where the point opposite of contact is). However, I am not getting the correct answers at all. I looked at ...
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### Author doesn't explain this equals sign in $R(\theta)\stackrel{?}{=} R(\frac{\theta}{N})^N$

I am struggling to convince myself that the following relation holds: $$R(\theta)\stackrel{?}{=} R\left(\frac{\theta}{N}\right)^N,$$ where: $R$ is an $SO(2)$ matrix $\theta$ is some finite angle. ...
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### Why are the generators of rotation in the 4-dimensional Euclidean space correspond to rotations in a plane?

In three-dimensions, the rotation generators are represented by $J_1$, $J_2$ and $J_3$ where $1,2,3$ respectively stands for the generator of rotation about $x,y,z$ axes respectively. In general, in ...
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### How can a black hole rotate if time dilation stops time at the event horizon?

How does a black hole rotate if time is dilated to infinity (e.g. stopped) at the event horizon? Note: this is relevant to this question, but different: How can a singularity in a black hole rotate ...
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### Power and work of tension force of a rotating body [closed]

Suppose that we have a body rotating on a massless string with a uniform velocity. What can we say about the work done by this tension. Moreover, what is the power related to this work. I do not have ...
For an electric dipole $p$ in a uniform field $E$ we write the work done by an external agent in rotating dipole as $\text{d}W = pE\sin\theta \, \text{d}\theta$. I'm having trouble understanding ...