I have access to this decorative windmill. It’s been in place for decades, spins freely in the wind, and has made millions of revolutions in its lifetime. Its RPM’s are impressive even in relatively low wind.
What are your thoughts on how I should harness this energy?
Agreed. The “impressive RPM” mentioned in the OP won’t matter, because it’s about angular momentum, not specifically angular frequency. You would certainly be putting in more energy to build it than you’d conceivably get out. At best this would be a “fun learning experience in your garage” project.
I agree that RPM isn’t the primary quality to assess here, but I think angular momentum doesn’t really matter either. As a quantity, momentum describes a conserved capacity to store kinetic energy. As in, it could tell us how long the fan would stay in motion when the wind stops blowing. But that’s not the objective for a wind turbine, which is supposed to convert lift from the wind to do some work.
At bottom, none of these quantities are the useful metric for what makes a good wind turbine. And that’s expected, because we have few details about the fan itself: the blade pitch, stall speed, and fan diameter, to list a few parameters. The only firm detail we can see is the blade count from the picture.
N… No? The wind applies a torque to the wind turbine that gets converted into angular momentum. The angular momentum drives a generator that produces electricity. That’s literally the entire point of a wind turbine.
The obvious point I was making was that the electricity produced doesn’t rely just on ω but also the moment of inertia I.
I feel like I’m being gaslit right now. Like: “Linear momentum isn’t the useful metric in assessing how deadly a collision with this car would be. I feel like that’s expected because we have few details about the car itself.” ???
Edit: And if you mean torque (because P = torque * angular frequency), then torque is just the time derivative of L. My point being that even if frequency is high, L here is piddly.