Greater than the speed of light?

Physics-is-Phun · #1 02-02-2010, 09:34 AM

This is a homework problem I'm having difficulty with. It reads like this:

Quote:

Originally Posted by Modern Physics Textbook

Suppose we made a pair of shears in which the cutting blades were many orders of magnitude longer than the handle. Let us in fact make it so long that, when we move the handles at angular velocity w, a point on the tip of the blade has a tangential velocity v = wr that is greater than c. Does this contradict special relativity? Justify your answer.

I think it has to do with while the tip of the blades is moving angularly at a speed greater than the speed of light, its "forward" speed in its path is not necessarily greater than c... but that leads me to only think if we made the blades long enough, wouldn't it travel faster than c anyway?

Guidance is appreciated... and also, it's been awhile since I've been on the site and I don't remember how to make the equations/variables all fancy-looking. Can someone provide a link to how to do this, or give me a quick crash-refresher-course? Many thanks!

YellowPeril · #2 02-08-2010, 12:19 PM

Obviously not, something that has been around for so long cannot be wrong. The most convenient answer to your question is simply that any particle traveling at the speed of light has infinite energy and as you know it is impossible to create infinite energy but wait.....

Lets say I build a rocketship, that can accelarate at 10m/s/s (convenient because then I can maintain artificial gravity) I bring along enough fuel to accelarate my rocket ship for a year and yes, it will be traveling at the speed of light (simply apply v=u+at). Since all the laws of physics are the same for every inertial frame of reference, I will reach the speed of light in a year. (Maybe a bit longer if I have to skirt around the odd obstacle or two). Now after a year in my space craft I reach the speed of light, but all of a sudden, this is a prefered inertial frame of reference. This appears to be a form of circular reference.

Pmb · #3 02-14-2010, 08:04 AM

Quote:

Originally Posted by Physics-is-Phun

This is a homework problem I'm having difficulty with. It reads like this:

I think it has to do with while the tip of the blades is moving angularly at a speed greater than the speed of light, its "forward" speed in its path is not necessarily greater than c... but that leads me to only think if we made the blades long enough, wouldn't it travel faster than c anyway?

Guidance is appreciated... and also, it's been awhile since I've been on the site and I don't remember how to make the equations/variables all fancy-looking. Can someone provide a link to how to do this, or give me a quick crash-refresher-course? Many thanks!

Yes. That is a contradiction since no object (e.g. the tip) can move at or faster than the speed of light. The tip has mass so it can't move at v>c or v=c. This problem treats the scissors as if it were a rigid body and in relativity there are no rigid bodies. However if you had two straight rods which were at an angle with each other and passed by each other in a scissor like fashion then the point of interection could move at v>c. But that is an imaginary point with no mass associated with it so it wouldn't be a contradiction.