special relativity - Rotate a long bar in space and get close to (or even beyond) the speed of light $c$

Imagine a bar

spinning like a helicopter propeller,

At $\omega$ rad/s because the extremes of the bar goes at speed

$$V = \omega * r$$

then we can reach near $c$ (speed of light) applying some finite amount of energy just doing

$$\omega = V / r$$

The bar should be long, low density, strong to minimize the amount of energy needed

For example a $2000\,\mathrm{m}$ bar

$$\omega = 300 000 \frac{\mathrm{rad}}{\mathrm{s}} = 2864789\,\mathrm{rpm}$$

(a dental drill can commonly rotate at $400000\,\mathrm{rpm}$)

$V$ (with dental drill) = 14% of speed of light.

Then I say this experiment can be really made and bar extremes could approach $c$.

What do you say?

EDIT:

Our planet is orbiting at sun and it's orbiting milky way, and who knows what else, then any Earth point have a speed of 500 km/s or more agains CMB.

I wonder if we are orbiting something at that speed then there would be detectable relativist effect in different direction of measurements, simply extending a long bar or any directional mass in different galactic directions we should measure mass change due to relativity, simply because $V = \omega * r$

What do you think?

Answer

Imagine a rock on a rope. As you rotate the rope faster and faster, you need to pull stronger and stronger to provide centripetal force that keeps the stone on the orbit. The increasing tension in the rope would eventually break the it. The very same thing would happen with bar (just replace the rock with the bar's center of mass). And naturally, all of this would happen at speeds far below the speed of light.

Even if you imagined that there exists a material that could sustain the tension at relativistic speeds you'd need to take into account that signal can't travel faster than at the speed of light. This means that the bar can't be rigid. It would bend and the far end would trail around. So it's hard to even talk about rotation at these speeds. One thing that is certain is that strange things would happen. But to describe this fully you'd need a relativistic model of solid matter.

People often propose arguments similar to yours to show Special Relativity fails. In reality what fails is our intuition about materials, which is completely classical.