It made no sense to burn expensive coal to power an engine until you run into the problem of needing to drain coal mines, because you already have so much demand for coal that you have started to need to do that.
Also lack of calculus and newtons equations, almost all useful engineering equations depend on those so without them you can't make the necessary calculations for engines. Without engine calculations it takes way too much trial and error to get things to work well.
The industrial revolution happened pretty soon after those were discovered, I don't think that is a coincidence.
> they also would have been invented a 3. time if necessary
Not sure what you mean? Romans would have had great use of Newtonian physics, they made a ton of machines, but they didn't manage to invent the math/physics to do those calculations at the time. What do you suggest would replace this for making calculations for machines?
Well, they have been invented 2 times, roughly at the same time largely independent from each other. But it needed a general high level of math. The romans lacked many of the more sophisticated math tools I think.
No they weren't invented two times, Newtons physics equations were invented one time, then Leibniz reconstructed calculus after reading Newtons work on physics. Leibniz almost surely wouldn't have invented calculus without having read Newtons work on motion, so they aren't comparable.
The only thing that event proves is that inventing calculus if you have the the formulas of motion is easy, both Newton and Leibniz did that, but it was Newton who invented the formulas of motion that was required to invent calculus.
So I think Newtons equations of motions was a requirement for the industrial revolution, that is a key that unlocks the ability to understand machines on a whole new level.
Also Newtons motion equations are simply just
F = ma
They don't require a lot of mathematical pre work etc. But, nobody solved that properly for a really long time, and that is the basis for classical physics so basically every single thing we did during the industrial revolution. It was the key to modern engineering where we use math to calculate machine properties. I don't think it is just random chance that the industrial revolution happened just a few decades after classical physics was invented.
It is such a ridiculous coincidence otherwise, that the formulas and concepts that are the foundation to all of engineering was invented just before engineering took off for real.
Was it the case that nobody solve the problem, or was it solved many times but since there was no value in the solution at the time we don't remember those solutions? Or maybe it was the industrial revolution getting underway finally made it worth studying at all.
My physic courses have been a while, but I would argue with "F = ma" alone, you won't get far, when you want to build high pressure machines and model them before. You do need calculus for that. And quite a bit more I would think.
The industrial revolution happened pretty soon after those were discovered, I don't think that is a coincidence.