If we were to reproduce a spinning ball holding water, we should have gravitation exceeding the centrifugal acceleration (300 times stronger normally).
The gravity (acceleration) holding the water should be: g = Gm1/R².
Since we will scale down the model, we will need to know the limit to where we can go.
We need to convert m1/R² to use density:
density = mass/volume -> mass = density * volume.
volume of a sphere = 4πr³/3
m1/R² = d1 * 4πR³/3R² = d1 * 4πR/3 where d1 is the earth’s density (5.51g/cm³)
On earth and the scale model, the gravity is g = Gm1/R² = 4πGRd1/3
We can see here that the gravity at “sea” level is proportional to the radius (other values are constants) hence g = kR where k = 4πGd1/3
The centrifugal acceleration is also proportional to the radius: α = ω²r
To not fling everything in space we need to have g ≥ α, or kR ≥ ω²R or k ≥ ω²
So the rotational speed limit doesn’t depend on the radius. This means that we can make a model small enough for experiments.
The limit for the rotational speed is 1.24 mrad/s which is 17 revolutions per day.