# How fast can a particle rotate?

1. Oct 26, 2013

### emergentsystem

Without moving in any direction, what is the maximum speed at which a particle can rotate? Does it depend on its mass or size?

Is there a maximum speed of rotation analogous to or dependent on the speed of light? If so, are there any odd temporal effects from the perspective of the particle as it approaches that speed?

2. Oct 26, 2013

### Drakkith

Staff Emeritus
First, I think it's important to understand that fundamental particles are considered to be point-like, meaning they have no size. As such, I'm not sure if the term "rotation" can be applied to them. (Perhaps their wavefunction can be rotated?) Composite particles and larger objects are limited by the strength of their bonds versus the centrifugal force of the rotation. And no object can be rotated so fast that any part of it meets or exceeds the speed of light.

3. Oct 26, 2013

### emergentsystem

Is the "spin" property of particles related to rotation?

And is there a way to calculate the maximum rotation speed for composite particles?

4. Oct 26, 2013

### Drakkith

Staff Emeritus
Quantum spin? No. Quantum spin is a fundamental property of particles. It is "as if" the particle is spinning around on its axis, but it is not. If it were actually spinning, it would have to spin faster than the speed of light in order to generate the magnetic field of the measured stength.

I'm sure there is but I do not know how.

5. Oct 26, 2013

### CWatters

As I understand it the Quantum Spin of a composite particle is the sum of the spins of it's components. So for a proton (three quarks) the overall spin Quantum spin is 1/2.

I'm no expert but I though particles had fixed quantum spin. As Wikipedia says..

http://en.wikipedia.org/wiki/Spin_(physics)#Spin_quantum_number

Selected quotes..

In other words we haven't discovered particles with larger quantum spin than these values.

6. Oct 26, 2013

### emergentsystem

I see. So everything except fundamental particles can be rotated fast enough to break apart? Are there any exceptions to this?

I was actually more interested in maximum speed of physical rotation of particles, I should have been more clear. Thanks for your answer anyway.

Last edited: Oct 26, 2013
7. Oct 26, 2013

### CWatters

The man made record was broken in August this year...

http://www.bbc.co.uk/news/uk-scotland-edinburgh-east-fife-23861397

University of St Andrews scientists create 'fastest man-made spinning object'

Perhaps they did.

8. Oct 26, 2013

### 256bits

Your question is a contradiction is it not, or rather the terms 'without moving in any direction' and 'particle' can be loosely defined.

If you are asking about anything other than fundamental particles such as protons, neutrons and electrons, which has already been explained, do not have a size but have an intrinsic angular momentum given the term spin, then that type of spin can be explained with an anology of a macroscopic object rotating about an axis but only so far. One can also include a composite particle such as the nucleus of an atom as having a spin.

A macroscopic object spinning about an axis has an angular momentum and that can be explained classically with equations. The equations will give the tangential velocity of a point as a function of the radius and also the radial acceleration that a point will experience as a function of the radius.

Are you asking about a particle of dust, a water mist particle, a marble, a top, or an object such as the earth? You might want to ponder the idea of when does a particle become an object.

If you consider the earth, it does as a whole rotate on its axis in addition to revolving around the sun. But are not the constituant parts of the earth also revolving about an axis, with a velocity and change in direction. Would you consider yourself on the surface of the earth to be spinning about an axis or rotating about an axis? So even if the earth's rotation as a whole is described as 24 hours long, points on the earth's surface or anywhere along its radius actually revolve about the axis.

The revolution about an axis is what gives rise to the centripetal force ( or centrifugal force if one wishes to look at it that way ) and the subsequent angular velocities and radial accelerations of points along a radius. The strength of cohesion of the object is what will determine whether an object ( of any size down to small particles ) will stay together as one or not during 'spinning'.

The reason I wrote this up as such is because I was thinking of Cern, Fermi Lab where elementary particles are following a curved path at near light speed, and if following the curve is a rotation or a revolution about an axis or a circulation gave me something to think about.

9. Oct 26, 2013

### CWatters

Interesting. Lets do the numbers for the ring at Cern...

Circumference of 27km
Particles in it are going at the speed of light 3 * 10^8 m/s
Assume they rotate once per lap of the ring