<p>A particle travelling in a circle of radius <span class="math-container">$R$</span> at velocity <span class="math-container">$v$</span> has an acceleration of <span class="math-container">$v^2/R$</span>. So either <span class="math-container">$R$</span> is very large, or a very strong force is acting to stop the particles at the surface of the object flying away. We see no very large objects (galactic clusters, for instance) rotating this quickly, so we need to look for strong forces.</p>

<p>One option is gravity. We know of sub-millisecond pulsars, which we believe are neutron stars with a radius of perhaps 10 km, rotating 1000+ times per second. This gives a surface velocity at the equator of about <span class="math-container">$60\,000 km/s$</span> which is <span class="math-container">$0.2c$</span>. So those meet your conditions.</p>

<p>Defining how fast the surface of a black hole is rotating is difficult on several levels, but black holes do have angular momentum, and there is a dimensionless number relating that to their mass (or equivalently radius) which can be loosely thought of as the fraction of light-speed at which the event horizon is moving. <a href="https://academic.oup.com/mnrasl/article/403/1/L74/1187293" rel="nofollow noreferrer">This paper</a> measures a value of about 0.44 for that parameter for the black hole in the centre of the milky way.</p>

<p>At the other extreme, <a href="https://physics.stackexchange.com/questions/20187/how-fast-do-electrons-travel-in-an-atomic-orbital">this stackexchange answer</a> suggests that the electrons in a hydrogen atom rotate about the nucleus at something a bit less than <span class="math-container">$0.01c$</span>. This scales up linearly with the charge on the nucleus, so the inner electrons in a lead or uranium atom are in some sense rotating at close to light-speed.</p>

<p>Finally, the particles in a large particle accelerator, rotate around the centre of the accelerator at velocities very close to that of light.</p>

CC BY-SA 4.0
2019-04-12T13:01:55.487Z
thank you @Steve Linton!
J. Doe
CC BY-SA 4.0
2019-04-12T18:44:02.887Z
"rotation" is about one's own center.  I'm not sure what you meant by "electrons rotating about the nucleus."    I  think it's easy to point out NLS things in the universe, but for a given *object* to be rotating without hurling itself apart is a different question.
Carl Witthoft
CC BY-SA 4.0
2021-06-29T18:05:54.777Z
Electrons bound to an atom are not moving as the Bhor model would suggest.  There is no orbital speed; it is actually called a "stationary state".  I don't think OK was talking about orbital motion, though, but the spin of an object on its own internal axis.
JDługosz
CC BY-SA 4.0
2019-04-12T10:54:52.920Z
2019-04-12T10:54:52.920Z
Steve Linton
<p>For example, <span class="math-container">$0.1c &lt; v &lt; c$</span>? Is this actually possible?</p>

<p>Background: is that true that the black hole in the center of the Milky Way rotates once per 20 minutes?</p>

CC BY-SA 4.0
2019-04-12T09:52:20.913Z
The unit of the angular velocity is $\frac{1}{s}$, and not $\frac{m}{s}$. Please fix it.
peterh
CC BY-SA 4.0
2019-04-12T10:40:31.987Z
I take it the velocity in question is at the "surface" of the object.
Steve Linton
CC BY-SA 4.0
2019-04-12T19:30:45.623Z
Can you provide your source for the 20 minutes?  Are you talking about things orbiting the BH at that period?  Periodic variations in brightness?  Spin measurements? What?
eshaya
<rotation><speed>
Are there known objects rotating at close-to-light speeds?
J. Doe
# Are there known objects rotating at close-to-light speeds?

(Asked by: username_0 on 2019-04-12)

For example, $0.1c < v < c$? Is this actually possible?

Background: is that true that the black hole in the center of the Milky Way rotates once per 20 minutes?

**Tags:** rotation, speed
> **Comments:**
> **username_1**: The unit of the angular velocity is $\frac{1}{s}$, and not $\frac{m}{s}$. Please fix it.  
> **username_2**: I take it the velocity in question is at the "surface" of the object.  
> **username_3**: Can you provide your source for the 20 minutes?  Are you talking about things orbiting the BH at that period?  Periodic variations in brightness?  Spin measurements? What?  

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## 1 answers

### Answer by username_2 on 2019-04-12. Score: 1

A particle travelling in a circle of radius $R$ at velocity $v$ has an acceleration of $v^2/R$. So either $R$ is very large, or a very strong force is acting to stop the particles at the surface of the object flying away. We see no very large objects (galactic clusters, for instance) rotating this quickly, so we need to look for strong forces.

One option is gravity. We know of sub-millisecond pulsars, which we believe are neutron stars with a radius of perhaps 10 km, rotating 1000+ times per second. This gives a surface velocity at the equator of about $60\,000 km/s$ which is $0.2c$. So those meet your conditions.

Defining how fast the surface of a black hole is rotating is difficult on several levels, but black holes do have angular momentum, and there is a dimensionless number relating that to their mass (or equivalently radius) which can be loosely thought of as the fraction of light-speed at which the event horizon is moving. [This paper](https://academic.oup.com/mnrasl/article/403/1/L74/1187293) measures a value of about 0.44 for that parameter for the black hole in the centre of the milky way.

At the other extreme, [this stackexchange answer](https://physics.stackexchange.com/questions/20187/how-fast-do-electrons-travel-in-an-atomic-orbital) suggests that the electrons in a hydrogen atom rotate about the nucleus at something a bit less than $0.01c$. This scales up linearly with the charge on the nucleus, so the inner electrons in a lead or uranium atom are in some sense rotating at close to light-speed.

Finally, the particles in a large particle accelerator, rotate around the centre of the accelerator at velocities very close to that of light.

> **Comments:**
> **username_0**: thank you @Steve Linton!  
> **username_4**: "rotation" is about one's own center.  I'm not sure what you meant by "electrons rotating about the nucleus."    I  think it's easy to point out NLS things in the universe, but for a given *object* to be rotating without hurling itself apart is a different question.  
> **username_5**: Electrons bound to an atom are not moving as the Bhor model would suggest.  There is no orbital speed; it is actually called a "stationary state".  I don't think OK was talking about orbital motion, though, but the spin of an object on its own internal axis.  

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