I'm trying to understand how many rotations/spins I need to put a given length around a core.
My specific problem is: I have a 30m long strip 1mm thick that I will roll around a rotation core that has a lever mechanism. At start the core OD is 50mm.
I don't have any idea how to calculate this.
(I am assuming that your $OD$ means the diameter of the rotation core. Perhaps this would be obvious to an engineer!)
The cross-sectional (or "side-on") area of the strip is $30$m$\times 1$mm$=30000$ mm$^2$. And the cross-sectional area of the core is $625\pi$ mm$^2$. If the completed roll has total radius $R$ mm, then its cross-sectional area is $\pi R^2$. But we know its cross-sectional area is $(30000+625\pi)$ mm$^2$. Therefore $$\pi R^2=30000+625\pi$$ $$R=\sqrt{30000/\pi+625}\approx 100.87$$
Subtracting the radius of the core, we get that the thickness of the wound strip is $R- 25\approx 75.87$ mm. Therefore there are $\approx 75.87$ windings.
In real life, this is of course unreasonably precise; expect about $76$ windings.