Can a Circle Travel at the Speed of Light?

AI Thread Summary
A circle of radius R is analyzed as it travels in the x direction at the speed of light, with the center starting at -R. The derivative dr/dt, representing the intersection of the circle and a vertical line, is found to be c*cot(θ), which approaches infinity as θ approaches 0. The discussion emphasizes that no physical object can exceed the speed of light, clarifying that the scenario involves a geometric intersection rather than a physical object traveling faster than light. It is noted that while photons travel at the speed of light, nothing with mass can do so. The conversation ultimately reinforces the principles of relativity regarding speed limits.
Geranimo
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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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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.
 
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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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)
 
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