Maximum Angular velocity possible

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Discussion Overview

The discussion revolves around the maximum angular velocity that can be attained by a rigid body, exploring theoretical limits, practical constraints, and implications in both classical and relativistic physics. Participants consider various factors influencing angular velocity, including material properties and mass distribution.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants propose that the maximum angular velocity could be expressed as c/r, where c is the speed of light and r is the maximum perpendicular distance from points on the body to the rotation axis.
  • Others argue that in practice, a rigid body would fail at much lower angular velocities due to material limitations, suggesting that calculations would require knowledge of mass distribution and tensile stress.
  • A participant mentions that Iranian engineers are aware of the angular speed at which a rigid body explodes, implying practical knowledge in this area.
  • There is a discussion about the absence of a fixed limit for angular velocity, contrasting it with the speed of light limit for translational motion.
  • One participant raises a hypothetical scenario regarding the rotation of a photon about a fixed axis, questioning how fast it would rotate.
  • Another participant notes the conceptual issues with rigid bodies in Newtonian mechanics when considering relativistic effects, stating that a perfectly rigid body would imply an infinite speed of sound, which does not exist in reality.
  • Some participants express skepticism about the existence of a fixed limit for angular velocity, questioning the reasoning behind such a limit.

Areas of Agreement / Disagreement

Participants express differing views on the existence of a maximum angular velocity and the implications of rigid body mechanics in both classical and relativistic contexts. The discussion remains unresolved with multiple competing perspectives presented.

Contextual Notes

Participants acknowledge the limitations of the rigid body model, particularly at high rotation speeds, and the dependence on material properties and mass distribution for practical calculations.

khil_phys
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What it the maximum angular velocity that can possibly be attained by a rigid body?
 
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I'm tempted to say c/r in which c is the speed of light and r is the maximum perpendicular distance from points on the body to the rotation axis. In practice the body will fly apart at a far lower angular velocity. To calculate it you'd need to know the body's mass distribution and the ultimate tensile stress of its material. To get some idea of the order of magnitude you could consider the easy case of a thin rod rotated about an axis through one of its ends and perpendicular to the rod. I make it about 300 rad per second for a steel rod 1 metre long.
 
Iranian engineers know the angular speed at which a rigid body explodes.
 
Philip Wood said:
I'm tempted to say c/r in which c is the speed of light and r is the maximum perpendicular distance from points on the body to the rotation axis. In practice the body will fly apart at a far lower angular velocity.

This means that the value depends on the rotational inertia of the body. Why is it that there is no fixed limit for the angular velocity for any body, like there is c for translational motion?

This sounds incredulous, but if I have a photon that can rotate about a fixed given axis, how fast would it rotate?
 
These are deep waters...
 
khil_phys said:
Why is it that there is no fixed limit for the angular velocity for any body, like there is c for translational motion?
First off, why should there be?

That said, there is a problem with a rigid body in Newtonian mechanics in relativistic physics. A perfectly rigid body necessarily has an infinite speed of sound. The resolution is simple: There is no such thing as a perfectly rigid body in reality. It is a useful abstraction that is approximately valid at low rotation speeds, where "low" means the velocity at every point on the body relative to the center of mass is much, much smaller than speed of light.


This sounds incredulous, but if I have a photon that can rotate about a fixed given axis, how fast would it rotate?
Elementary particles are point masses.
 
D H said:
First off, why should there be?

On the flip side, why should there not be?
 

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