The physics
A body going round a circle needs a pull toward the centre. Its size is mω²r, or mv²/r.
F = m ω² r = m v² / r
Something real must give that pull: a string, a spring, or friction. A string snaps when the pull passes its strength. A spring stretches until kx is enough.
k x = m ω² (L0 + x) coin: m ω² r ≤ μ m g
Ride along with the table, and the block looks still. In that spinning frame, add the centrifugal force. It points out and balances the real pull.
A body that moves across the spinning table feels one more pseudo-force. It is the Coriolis force, at right angles to the motion.
Fcf = m ω² r Fcor = 2 m ω v
Any pull toward the centre can hold a circle. Set it equal to mv²/r at that radius.