Relativistic mechanics:circle becoming ellipse.

AI Thread Summary
The discussion focuses on calculating the relativistic speed parameter β for a circle in motion that appears as an ellipse with semiminor axis 'a' and semimajor axis 'b'. The key equation used is L = L0/γ, where the radius in the direction of motion contracts to 'a', leading to the relationship a = b/γ. The user derives the equation (a/b)² = 1 - (v/c)² and concludes that β = √[1 - (a/b)²]. There is a suggestion to use the term "length contracted" instead of "shrinks" for clarity. The overall approach and deductions presented are deemed sufficient for the problem.
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Homework Statement



Suppose a circle of radius 'b' is set in motion.Calculate the relativistic speed parameter β(=v/c) such that the circle is seen as an ellipse of semiminor axis 'a' and semimajor axis 'b' where a <b.3 marks.


Homework Equations



L=L0/γ

The Attempt at a Solution


Whichever direction the circle travels say x-axis the radius shrinks in that direction to 'a'.
So a=b/γ.
(a/b)2=1-(v/c)2
β=√[1-(a/b)2]
Is my deduction correct? Do I need to show more mathematics here or to say is my above workout enough?
 
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Looks fine to me. I would say "becomes length contracted" rather than "shrinks" though.
 

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