Ok, let’s say I build a disc of radius r, mount it onto a shaft, attach the shaft through some gears to an engine.
Now, we run the engine and find that a point on the outer rim of the disc is moving at 0.5 the speed of light.
Great! Now we shut it all down and attach a disc of radius 2r instead.
When we run the engine again, won’t a point on the outer rim be traveling at the speed of light? If I attached a ball bearing to the disc at points r and 2r, and then released them during the spin, wouldn’t they be flying through space at the speed of light, and half that, respectively?
What if I made a disc that was 3r?
Ignoring physical concerns, such as the disc wobbling or breaking apart, why won’t this work?
As the edge of the disc approaches c, the mass of that circular slice begins to increase. The closer you get the edge to c, the more the mass increases. As it approches c, the mass becomes all-but infinite and the energy required to continue to accelerate the disc also becomes all-but infinite.
So no matter how big your motor, you run out of horsepower before the edge gets to c, much less 1.5 c.
when he said not a giant disk, he was referring to Zweistein’s question which said that the rotation of the galaxy could be simplified to a giant disk…Flash-57 was just saying that it is an imperfect disk
He has not contradicted himself. In his first post, he talked about a hypothetical giant machine. Then Zweinstein suggested that a galaxy was a similar giant disc. Flash replied that the stars aren’t fixed to the disc of the galaxy, so a galaxy isn’t the same as his machine. There’s no contradiction there.
As LSLGuy implied, whatever the size of the disc, its edge could only approach c but never actually attain such a velocity.
To nitpick, it is not strictly the mass which increases but the multiplier usually denoted g. Interpreting this as “a change in mass” is a little misleading, but the effect is the same: Any force, no matter how enormous, provides a gradually smaller acceleration as c approaches, such that actually reaching c requires an infinite force.
As for the shape of the disc, I believe Lorentz contraction “bends the spokes” of the disc somewhat,
In Newtonian mechanics it’s okay to use perfectly rigid objects to illustrate points, in relativty it isn’t okay as a wave through a perfectly rigid body would be instantaneous, a major violation of causality.
I don’t think you can get a spinning disc to accelerate to c. The edge of the disc could theoretically attain that speed but the center of the disc would then be travelling at a slower rate. So the disc as a whole would be travelling slightly under the speed of light.
well that’s what Flash-57 was saying i belive,that the edge would be moving at the speed of light, so that the ball bearings placed on the edge and shot off would hurtle through space at the speed of light
Don’t forget that as something approaches the speed of light, relativity also dictates that its length will decrease. I don’t know what effect this would have on the edge of the disc (especially if we take it to be perfectly rigid), but it would probably have some dire consequence to the question as well - I’ll let someone more well-versed in relativity figure that out/correct anything I’ve gotten wrong.