Can a Circle Travel at the Speed of Light?

In summary, the conversation discusses the problem of finding the velocity of a circle of radius R moving in the x direction with velocity c, and the position of its intersection with a vertical line at x = 0. The solution found is dr/dt = c*cot(θ), and it is questioned whether this violates the 2nd postulate of relativity. It is concluded that this does not violate the postulate, as nothing can travel at or faster than the speed of light. However, it is noted that this statement must be clarified to include objects with mass.
  • #1
Geranimo
19
2

Homework Statement


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A circle of radius R travels in the x direction with velocity c. The center of the circle is at -R at t = 0. a vertical line rests at x = 0. Find dr/dt, where r is the position of the intersection between the circle and the vertical line, and explain if this violates 2nd postulate of relativity.

Homework Equations


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I already found
dr/dt = c*cot(θ)

The Attempt at a Solution



The speed approaches infinity when θ → 0... I seriously don't know how to start / which part of relativity I have to use to solve this extreme speed... Any hint to start the problem? Thanks
 
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  • #2
Well in fact it may not do anything because nothing is traveling faster than c, it's just the collision of the 2 lines, and nothing is wrong with that.
 
  • #3
Geranimo said:
Well in fact it may not do anything because nothing is traveling faster than c, it's just the collision of the 2 lines, and nothing is wrong with that.
Right. No physical object is moving with that speed.
 
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  • #4
Geranimo said:
Well in fact it may not do anything because nothing is traveling faster than c ...
That is an inadequate statement. It should be that nothing can travel as fast or faster than c, not just faster than c. (I am, of course, considering things with mass. Photons do travel at c and perhaps that's what you meant)
 

FAQ: Can a Circle Travel at the Speed of Light?

What is the speed of light and how does it relate to a circle?

The speed of light is approximately 299,792,458 meters per second in a vacuum. This speed is constant and is the maximum speed at which energy, matter, and information can travel. A circle at the speed of light would be constantly moving at this speed, maintaining its circular shape.

Is it possible for an object to travel in a perfect circle at the speed of light?

No, it is not possible for an object to reach the speed of light, let alone maintain a circular motion at that speed. According to Einstein's theory of relativity, as an object approaches the speed of light, its mass increases infinitely and it would require an infinite amount of energy to reach that speed.

How does the speed of light affect time and space in a circular motion?

The speed of light is known to be a constant in the universe and is a critical factor in the relationship between time and space. In a circular motion at the speed of light, time would appear to slow down and space would appear to contract, according to the theory of relativity.

What other factors could affect a circle at the speed of light?

Aside from the limitations imposed by the theory of relativity, factors such as gravity and friction would also affect a circle at the speed of light. These forces would cause the object to deviate from a perfect circular motion and potentially slow it down.

How does a circle at the speed of light relate to the concept of time travel?

The concept of time travel is closely related to the idea of a circle at the speed of light. According to the theory of relativity, an object moving at the speed of light would experience time dilation, where time would appear to pass slower for the object than for an outside observer. This could potentially allow for time travel to the future, but the concept is still speculative and has not been proven.

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