Length Contraction: Measuring Circumference of Moving Circle

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SUMMARY

The discussion confirms that length contraction does not occur in the direction perpendicular to motion, specifically when measuring the circumference of a moving circle. When observing a circle moving along a line, the radius parallel to the motion contracts, resulting in a smaller calculated circumference. Conversely, the radius perpendicular to the motion remains unchanged, leading to the conclusion that a moving circle should be treated as an ellipse for circumference calculations. This phenomenon also applies to spherical objects, which compress into an oblate spheroid along their axis of travel.

PREREQUISITES
  • Understanding of special relativity concepts
  • Familiarity with the geometry of ellipses
  • Knowledge of inertial frames of reference
  • Basic principles of circumference and area calculations
NEXT STEPS
  • Study the implications of Lorentz contraction on various geometric shapes
  • Explore the mathematical derivation of the circumference of an ellipse
  • Learn about the effects of relativistic speeds on physical objects
  • Investigate the properties of oblate spheroids in physics
USEFUL FOR

Physicists, students of relativity, mathematicians, and anyone interested in the geometric implications of motion in relativistic contexts.

unchained1978
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As I understand it, there is no length contraction in the direction perpendicular to the motion being described. So if I were to observe a circle moving along a line (not rostating) and I were to measure the radius in te direction parallel to the motion, I would observe a contracted radius, and therefore calculate a smaller circumference. But if I were to measure the radius in the direction perpendicular to motion, I would observe the inertial radius and therefore the inertial circumference. Does this mean that to calculate the circumference of a moving circle, I would need to treat it as an ellipse?
 
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Yes, that is correct.
 
A spherical object will compress along its axis of travel into a disclike shape (an oblate spheroid).
 

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