Creative science vlogger and author Steve Mould demonstrated why any ball (except a hollow one) will go into a spiral rather than falling off a spinning turntable, specifically at a ratio of 7:2. This is known as the “Turntable Paradox”
A ball on a spinning turntable won’t fly off as you might expect. In fact the ball will have it’s own little orbit that is exactly 2/7th the angular speed of the table.
Mould explains that all this has to do with the ball’s mass, its radius, and the moment of inertia.
Well… if you do the proper mathematical analysis, eventually an equation drops out for the orbital period of the ball…The orbital period of the ball is equal to the orbital period of the turntable, multiplied by …the mass of the ball multiplied by the radius of the ball squared divided by the moment of inertia of the ball plus one. The moment of inertia of something is just like, how hard is it to get the thing spinning.