Been wondering about this one for a long time. I sent it to http://www.last-word.com, but got no reply.
What is the fastest that something can spin? I assume that with a very powerful motor, revs per second could approach a blinding speed. Now, if you were to attach a long (very long) rod to this spinning motor, would there be some point along the rod that would approach the speed of light? Would there be some point beyond that point where it would exceed the speed of light?
Along the same lines…would it be possible to create a “table” from a spinning blade (similar to a fan). If the blade(s) were flat, could the motor spin them fast enough to simulate a solid? IOW, the blade is “everywhere” at once…enough so that you could place an item on the “surface” of the “table”? What if the blade(s) were near frictionless? How many blades would be needed?
It’s difficult to calculate, because you have to make various “simplifying” assumptions about the material and its strength, and each assumption moves you farther from reality. Of course, no part of any physical object can spin or move faster than the spped of light in a vacuum. Regarding spinning, this requires continual acceleration to maintain the circular motion. As the velocity of the object increases, so does its mass, and therefore the force required to keep it moving in a circle increases. As any part of the rod approaches the speed of light, its mass heads towards infinity and the force required also goes to infinity.
Also note that no physical disturbance can propagate along a material body faster than the speed of sound in the body, which depends on the rigidity of the body. We can only imagine an infinitely rigid body; anything real is going to have a time lag between the application of the force and the manifestation of the force’s effects in all parts of the body. So rods that are spun real fast will bend.
I’ll grant you a “fan” made of frictionless material, with all the blades in exactly the same plane. Assume this fan is rotating around an axis perpendicular to the local gravitational field, so the plane of the blade’s motion is horizontal. Now set an object on this fan. No matter how fast the fan is spinning, there will be a non-zero time between the time when one blade leaves the object and the time when the next blade contacts the object. During that time, the object will fall a non-sero distance. Therefore the edge of the next blade of the fan will hit some portion of the object and throw it off the fan.
Perhaps if the edges of the blades are chamfered just the correct amount and at just the correct angle for the particular rotation speed you select, and the object is shaped appropriately, the vertical falling problem could be overcome. But I think that there would be a slight horizontal component of motion introduced by the repreated whacking of the object by the chamfered blades, and the object would “walk off” the fan.
Both questions are interesting. I will focus on the second, because the first is well out of my league.
If you can make the blades frictionless, one of the very large problems with this thought experiment goes away, but the other remains. Gravity acts as a constant accelleration. Absent an opposing normal force, the object you set on the “surface” will immediately begin to accelerate in the direction of the gravitational attraction. In this situation, it will move a small distance below the vertical plane of the blades, enough to be clipped and thrown from the surface. In order for the object to maintain the same vertical position, the blades would have to be a)very close to one another (approximating a solid surface) b) moving at an infinite number of revolutions per second.
However, if the gaps in the blades were small compared with the footprint surface area of the object being supported, and friction was still removed from the experiment, what you describe may be possible, but not as impressive as what you’re going for, right? I believe that the moment the gaps in the fan exceed 1/2 of the cross-axial dimension of the object being supported, the experiment becomes impossible. Once the object has a chance to tip due to gravity’s influence, all bets are off.
stoli
“There’s always a little dirt, or infinity, or something.” -Feynman
Finally! Thank you both for your responses!!
Very interesting…
JonF wrote:
Does this mean that when I’m holding a baseball, it has less mass than when I throw it? Does its mass relate to density? If it were thrown fast enough, would its gravitational force increase? Enough to form a black hole?
Excuse my ignorance. These questions have been floating around in my head since high school (10+ years ago). I haven’t learned a lot since then.
One of the famous results of relativity is that the mass of an object gets larger as its velocity increases.
Here’s the formula:
m(v) = mass of an object at velocity v
m(o) = mass of an object at rest
c = the speed of light
sq(x) = the square root of x
x^2 = x squared
m(v) = m(o)
____________
sq(1-(v^2/c^2))
If you work out this formula for v much lower than c, then the square root of one minus v^2/c^2 is very close to one, so the difference in masses is almost imperceptible. As v becomes closer and closer to c, the denominator becomes closer and closer to zero, and m(v) gets closer and closer to infinity.
This is why Einstein declared that nothing can move faster than the speed of light, because (as JonF pointed out):
For other questions of this sort, I heartily reccommend Instant Physics by Tom Rothman, Ph.D. Copyright 1995 Byron Preiss Visual Publications, Inc.
stoli
“There’s always a little dirt, or infinity, or something.” -Feynman
The baseball IS heavier when it is in motion. This is all special relativity, and would really give a severe headache to anyone who didn’t have a background in physics. About the black hole, I can’t think of any reason why not, but I’m not an expert on relativity. You would have to throw it so fast, though, that the ball would almost be moving at the speed of light anyway. Of course, this is only theoretically possible, unless you happen to know anyone who’s done it.
If the fan table was actually in an atmosphere, that would, of course, screw everything up. In an idealized version, the object would start to fall immediately, as the others have mentioned. It may perhaps be possible to design the fan and the atmosphere just right so that the effects cancel each other out. This would be further complicated by the fact that air resistance is based on speed, and each point along the fan blade is moving at a different speed.
“It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest.” - Adam Smith
