Centrifugal Acceleration GR: Formula for .8c, 1m Radius

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SUMMARY

The discussion focuses on calculating the proper acceleration experienced by an accelerometer swung at a speed of 0.8c with a radius of 1 meter. The relevant formula derived from the principles of relativistic physics is a = -v² / (r(1 - v²)), where v is the velocity and r is the radius. This formula incorporates a relativistic factor, confirming its alignment with Newtonian centripetal acceleration principles. The reference to Born coordinates provides additional context for understanding the relativistic effects involved.

PREREQUISITES
  • Understanding of special relativity concepts
  • Familiarity with centripetal acceleration principles
  • Knowledge of angular velocity and its relationship to linear velocity
  • Basic mathematical skills for manipulating equations
NEXT STEPS
  • Study the derivation of the Born coordinates in relativistic physics
  • Explore the implications of relativistic effects on acceleration
  • Learn about the concept of proper acceleration in different reference frames
  • Investigate the behavior of accelerometers in relativistic contexts
USEFUL FOR

This discussion is beneficial for physicists, students of relativity, and engineers interested in the applications of relativistic mechanics and proper acceleration calculations.

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I swing an accelerometer around my head with a constant relative speed of v and a radius of r. I want the exact formula with highly relativistic effects, so v = .8 c and r = 1 meter, say. What proper acceleration will the accelerometer read?
 
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Take a look at the Wikipedia page on Born coordinates:

http://en.wikipedia.org/wiki/Born_coordinates

They give a formula for the proper acceleration of a "Langevin observer", which corresponds to the accelerometer being swung around your head. They give it in terms of the angular velocity [itex]\omega[/itex], but using the formula [itex]v = \omega r[/itex], it is easy to come up with a formula in terms of the velocity [itex]v[/itex]:

[tex]a = \frac{- v^2}{r \left( 1 - v^2 \right)}[/tex]

This makes sense; it's just the standard Newtonian formula for centripetal acceleration, with an extra relativistic factor of [itex]\gamma^2[/itex].
 
Thank you PeterDonis.
 

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