Velocity Question - How Fast Does It Move?

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In summary, the conversation discusses the theoretical scenario of a powerful spinning machine attached to tubing in a vacuum, where the end of the tubing would approach the speed of light according to classical physics. However, it is explained that due to the infinite amount of energy required to accelerate an object to the speed of light, this scenario is not possible. The length of the tubing also does not affect this limitation. The conversation ends with a question about the possible effects of time dilation on the tubing.
  • #1
Wooh
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Ok, let's 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 let's say we attach the an amount of tubing equal to [tex]\displaystyle{\frac{c}{600}}[/tex]. We then get the machine rotate at [tex]\displaystyle{\frac{600}{\pi}}[/tex] 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?
 
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  • #2
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
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
Originally posted by 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?

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

to

[tex]E = mc^2\left( \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1 \right)[/tex]

Yes, you still have the same problem if the tubing is shortened. You still can't get the end up to c.
 
  • #5
So would the end dilate while the bottom doesn't, thus forming a dilated spiral or something?
 

1. What is velocity?

Velocity is a measure of how fast an object is moving in a specific direction. It is a vector quantity, meaning it has both magnitude (speed) and direction.

2. How is velocity different from speed?

While both velocity and speed are measures of an object's motion, velocity also includes the direction of movement. Speed is a scalar quantity, meaning it only has magnitude (no direction).

3. How is velocity calculated?

The formula for velocity is velocity = displacement/time, where displacement is the change in position and time is the duration of the movement. It is typically measured in units of distance per time (e.g. meters per second).

4. How does acceleration affect velocity?

Acceleration is the rate of change of velocity over time. If an object's velocity is changing, it is undergoing acceleration. Acceleration can either increase or decrease the velocity of an object, depending on whether it is positive (speeding up) or negative (slowing down).

5. Can an object have a constant velocity?

Yes, an object can have a constant velocity if it is moving at a steady speed in a straight line with no changes in direction. This means that its acceleration is 0, and it is not speeding up or slowing down.

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