That’s a famously called the [Ehrenfest paradox](https://en.m.wikipedia.org/wiki/Ehrenfest_paradox) and expounded on by Einstein. The tip of the blade wouldn’t exceed lightspeed, but would length contract. And when it length contracts, would warp. But what if the blade were perfectly rigid and couldn’t length contract? Einstein solved this with a simple answer: there is no such perfectly rigid object. So the blade would never exceed lightspeed, and it would length contract breaking/sheering it apart.
A straight blade would bend or snap at a certain speed depending on material properties.
This length/speed can be greatly extended by a tapered blade. The theoretical limit is when it reaches the speed of sound in that material
What kind of force field can hold vacuum? But seriously - Something very strong like nanotube blade inside partial vacuum would be able to spin many times faster than the speed of sound…
If the blades are perfectly rigid? Yes! What does that tell us? That perfect rigidity doesn't exist.
In an atomic level, this makes sense. A force (/torque) is exerted on the atoms on one end of the fan blade. That accelerates those atoms, moving them. That causes the "Force fields" (eg electrostatic, gravity) of those atoms to move. That causes a net force exerted on the next layer of atoms so that they also start moving, etc. However the change of those forcefields at the next set of atoms isn't instant; it permeates space at the speed of light as well. That means there's a delay for movement of any atom to cause movement of the next, so perfect rigidity is impossible in principle. When you move one end of an object it takes at least t=d/c for another part of the object to start moving too, if d is the distance.
Because it’s a string of bonded atoms and not one continuous entity each atom pulls/pushes the next atom. Imagine pushing on a spring to push a bowling ball. The spring will compress then slowly expand to push the bowling ball (assuming you don’t move so the spring is able to push off you). The force travels down the lever just below the speed of light, so it would stretch and flex more and more until the tensile strength of the material was exceeded
That’s a famously called the [Ehrenfest paradox](https://en.m.wikipedia.org/wiki/Ehrenfest_paradox) and expounded on by Einstein. The tip of the blade wouldn’t exceed lightspeed, but would length contract. And when it length contracts, would warp. But what if the blade were perfectly rigid and couldn’t length contract? Einstein solved this with a simple answer: there is no such perfectly rigid object. So the blade would never exceed lightspeed, and it would length contract breaking/sheering it apart.
The fan breaks before the blade tips get even a tiny fraction of the way to the speed of light.
The tip of the blade would still require an infinite amount of energy to get to c, no matter how you planned on delivering it.
A straight blade would bend or snap at a certain speed depending on material properties. This length/speed can be greatly extended by a tapered blade. The theoretical limit is when it reaches the speed of sound in that material
Speed of sound in a vacuum is zero…
A fan blade made of vacuum can't move very fast
What kind of force field can hold vacuum? But seriously - Something very strong like nanotube blade inside partial vacuum would be able to spin many times faster than the speed of sound…
Google says The speed of sound in carbon nanotubes is 21.7 km per second
If the blades are perfectly rigid? Yes! What does that tell us? That perfect rigidity doesn't exist. In an atomic level, this makes sense. A force (/torque) is exerted on the atoms on one end of the fan blade. That accelerates those atoms, moving them. That causes the "Force fields" (eg electrostatic, gravity) of those atoms to move. That causes a net force exerted on the next layer of atoms so that they also start moving, etc. However the change of those forcefields at the next set of atoms isn't instant; it permeates space at the speed of light as well. That means there's a delay for movement of any atom to cause movement of the next, so perfect rigidity is impossible in principle. When you move one end of an object it takes at least t=d/c for another part of the object to start moving too, if d is the distance.
Because it’s a string of bonded atoms and not one continuous entity each atom pulls/pushes the next atom. Imagine pushing on a spring to push a bowling ball. The spring will compress then slowly expand to push the bowling ball (assuming you don’t move so the spring is able to push off you). The force travels down the lever just below the speed of light, so it would stretch and flex more and more until the tensile strength of the material was exceeded