Velocity question

1. Dec 11, 2003

Wooh

Ok, lets say that we are in a giant vaccuum, but we have a crapload of space. A crapload. And we get a really powerful spinning machine and a tone of tubing. Really powerful, lots of tubing. Then we get the tubing and attach it to the machine, and lets say we attach the an amount of tubing equal to $$\displaystyle{\frac{c}{600}}$$. We then get the machine rotate at $$\displaystyle{\frac{600}{\pi}}$$ revolutions per second. At the outskirts of the machine, it would be rotating at 2 times the speed of light, according to classical physics. How would it really act? Would it form a spiral, as it got farther away and time dilated more? How would you figure out how fast the parts would really be moving?

Last edited: Dec 11, 2003
2. Dec 11, 2003

Janus

Staff Emeritus
Okay. First assuming that your tubing could withstand the stress, you could never get the machine up to 600/[pi] rps in the first place.

As you speed up the machine, the extreme end of the tubing will approach c, as it does so, the amount of energy it takes to accelerate it further increases, and approaches infinity. Thus no matter how powerful the machine, it will always fall short of getting the end of the tubing up to c. (Besides, if you keep upping the maximum power of the machine, eventually you will will reach the structual limt of the tubing and it will shear. )

In either case, the end never reaches c.

3. Dec 11, 2003

Wooh

Can you please explain why it takes an infinite amount of energy to get it up to C? If possible, an explanation for a newb :) Would you still have the problem if the rod where only half as long? If not, then why would the length of the rod matter at all if it is only being extended?

4. Dec 11, 2003

Janus

Staff Emeritus
Put quite simply, when you take the time dilation and length contractions into account, the kinetic energy formula is changed from
$$E=\frac{mv^2}{2}$$

to

$$E = mc^2\left( \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1 \right)$$

Yes, you still have the same problem if the tubing is shortened. You still can't get the end up to c.

5. Dec 11, 2003

Wooh

So would the end dilate while the bottom doesn't, thus forming a dilated spiral or something?