Relativistic mechanics:circle becoming ellipse.

In summary, the question asks for the calculation of the relativistic speed parameter β for a circle of radius 'b' in motion, resulting in an ellipse with semiminor axis 'a' and semimajor axis 'b' where a < b. The solution involves using the equation L = L0/γ and determining the value of β using the given information. The deduction provided appears to be correct, with the suggestion to use "becomes length contracted" instead of "shrinks." Further explanation or mathematical steps may be needed to support the solution.
  • #1
sudipmaity
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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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  • #2
Looks fine to me. I would say "becomes length contracted" rather than "shrinks" though.
 

Related to Relativistic mechanics:circle becoming ellipse.

1. What is the concept of relativistic mechanics?

Relativistic mechanics is a branch of physics that studies the behavior of objects moving at speeds close to the speed of light. It takes into account the principles of special relativity, which states that the laws of physics should be the same for all observers in uniform motion.

2. How does relativistic mechanics apply to a circle becoming an ellipse?

In relativistic mechanics, as an object approaches the speed of light, it experiences a phenomenon called time dilation, where time appears to slow down for the object. This means that the rate at which the object moves through space decreases, causing its circular motion to become an ellipse.

3. Can you explain the difference between classical mechanics and relativistic mechanics?

Classical mechanics is based on Newton's laws of motion and does not take into account the effects of high speeds and gravitational fields. Relativistic mechanics, on the other hand, incorporates the principles of special and general relativity to accurately describe the behavior of objects at high speeds or in strong gravitational fields.

4. What is the significance of the speed of light in relativistic mechanics?

The speed of light, denoted by the letter c, is a fundamental constant in relativistic mechanics. It is the maximum speed at which an object can travel and is a crucial factor in determining the behavior of objects at high speeds. According to special relativity, the speed of light is the same for all observers, regardless of their relative motion.

5. How is the concept of relativistic mechanics used in modern technology?

Relativistic mechanics is essential in modern technology, particularly in fields such as particle physics and astrophysics. It is used to explain the behavior of subatomic particles and the motion of objects in the universe, such as stars and galaxies. Relativistic mechanics also plays a crucial role in the development of technologies such as GPS, which relies on precise calculations of time dilation and the speed of light.

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