'Speed of light' thought experiment: I'm missing something

Factual Questions
1

Starting with something small:

I’m in a circular room 100 feet across. I’m standing at the center with a laser, shining it on the wall 50 feet (more or less) away.

I spin around 360° in one second. My hand-held laser has traveled maybe five or six feet, as it whirls around with me (I’m holding it some small distance from my body).

The spot on the wall would seem to have traveled 314 or so feet in that same second, as it moves across the wall.

Is that accurate? If so, then, how about this:

Let’s say, I’m in a big, big room circular (apparently the walls and floor are made of unobtainium).

It’s big: 372,000 miles across.

I’m at the center and also have a really good laser that I’m pointing at the wall. It’s so good that it makes a spot on the wall 186,000 miles away.

Ok, holding the laser, I turn around really quickly in this room, 360° in one second. At first glance, it would appear that the spot would then travel around the wall (over 1M miles) in less than one second. An illusion of moving faster than the speed of light. But I don’t think that’s what would happen, would it? Would the spot’s motion max out at the speed of light?

I’m thinking that if we were looking at it from far above, there would be about a 1 second delay (as the walls are 186K miles away) before the change in position of the laser was indicated on the wall. That is, the spot cannot change instantaneously with respect to the laser source, right?

But once it does start moving, how fast does it move? Would it actually travel around across the 1M mile perimeter in about one second? I know that nothing is actually “moving” past the speed of light, that the spot is not anything physical, only a reflection of light that still has to obey the laws of physics, but it seems as though there is some ‘gotcha ya’ that I’m missing?

2

That’s exactly what would happen, and it doesn’t violate any laws. Like you said, it’s just an illusion of movement. Nothing is actually moving along the wall.

In fact there are real-life examples of superluminal motion.

3

Cool! Thanks!

4

What about a rigid pole that is just long enough to reach the wall and is held in some vice-like machine in the middle of the room which suddenly swings around 360 degrees? Assuming the pole is made of unbreakable, unbendable unobtainium.

5

As a practical matter, if something is unbreakable, it must be bendable. Motion is transmitted through material as a compression wave – it happens at the speed of sound (of that material.) If I take a stick and wag it back and forth, the force of my wag has to travel along the length of the stick in a non-zero length of time.

If you have a really, really long stick, wagging it would result in a noticeable lag between the time you move your hand and the time the end of the stick moves, as the wave travels down to the end.

6

As the tip of the pole approaches the speed of light the rotating vice has to exert more and more force to accelerate it. Reaching the speed of light requires infinite force, so at some speed below that the rotating vice maxes out and the pole ceases to accelerate.

7

There is no such thing, and this thought experiment illustrates why not.

8

Agree, and just want to add to this that some people think it violates laws since the dot must carry information, and not even information is allowed to move >c. However, there is no actual information moving faster than light. No information is being transmitted from one spot illuminated by the dot to any other spot.

So in this scenario there is actually nothing moving at all except the photons in a straight line out from the tip of your laser.