Relativistic length contraction question

[Johnny5]

Suppose that I have a 'loop' with spokes, attached to a motor.

 

Let the ring be a regular N sided polygon.

 

Therefore N>3.

 

Might as well analyze the simplest case.

 

Let N=3.

 

So the polygon is an equilateral triangle.

 

There are three spokes, and they meet at the center of inertia of the triangular loop.

 

Let the perimeter of the equilateral triangle be one meter.

 

Therefore, the length of any side is 1/3 of a meter.

 

(incidentally you can tessalate a plane with equilateral triangles)

 

Ok so this object is going to start spinning.

 

Suppose that the Lorentz contraction formula is a true statement.

 

Here is my question.

 

What is the radius of the equilateral triangle, as a function of its rotational speed w ?

 

Thank you

 

PS: You can assume that the wire which this contraption is made out of has a uniform density r , when it isn't spinning.

 

Now, you cannot assume that the wire is a rigid body, because that contradicts the LCF, which this question has you assuming is true.

 

So you will have to deal with that some other way.

[Meir Achuz]

A rotating object cannot be treated in SR. It is a difficult (still unsolved) problem iin GR.

[Johnny5]

A rotating object cannot be treated in SR. It is a difficult (still unsolved) problem iin GR.

 

Thank you very much for this answer Meir...

 

Perhaps you can answer me this...

 

Would the circumference of the closed polygon be decreasing, as the rotational speed is increased?

 

GR or SR...

[J.C.MacSwell]

Thank you very much for this answer Meir...

 

Perhaps you can answer me this...

 

Would the circumference of the closed polygon be decreasing' date=' as the rotational speed is increased?

 

GR or SR...[/quote']

 

Circumference yes (radius no).

[Johnny5]

Circumference yes (radius no).

 

That makes no sense.

 

Here is the formula for the one, in terms of the other:

 

[math] C = 2 \pi R [/math]

 

If the circumference C increases, then the radius R increases, since the value of pi is constant in time.

 

If the circumference C decreases, then the radius R decreases, since the value of pi is constant in time.

 

The equation has to always be a true statement.

 

If either C,R varied, but the other didn't, a false statement would be true.

 

Regards

[J.C.MacSwell]

That makes no sense.

 

Here is the formula for the one' date=' in terms of the other:

 

[math'] C = 2 \pi R [/math]

 

If the circumference C increases, then the radius R increases, since the value of pi is constant in time.

 

If the circumference C decreases, then the radius R decreases, since the value of pi is constant in time.

 

The equation has to always be a true statement.

If either C,R varied, but the other didn't, a false statement would be true.

 

Regards

 

I think you are right if your assumptions are right.

 

However, I think you are not right, except when your "loop" is at rest (not spinning).

[ydoaPs]

i already made two threads on this. search "circle"

[Johnny5]

i already made two threads on this. search "circle"

 

Yes I see it here:

 

 

The equation of a circle where (h' date='k) is the center and r is the radius. The equation of the circumference has no bearing on if it is or isn't a circle.

When a circle spins, the circumference shortens and the radius stays the same. Is a circle, spinning near c, still a circle?

[/quote']

 

Did you ever get your answer? It didn't look like it.

[ydoaPs]

i don't remember. there was another one too, i think.

[Johnny5]

i don't remember. there was another one too, i think.

 

Do you remember the thread title of the other one?

[ydoaPs]

no