The physics
Friction is the only sideways force on the dish. Static friction gives the dish the acceleration it needs. But it has a limit: it can never be more than μmg.
no slip: a = A (if A ≤ μg) slip: a = μg
When the dish slips, it falls behind the cloth at A − μg. It is free once it has fallen behind by L. That takes t² = 2L / (A − μg).
distance on the cloth: s = μgL / (A − μg)
So a faster pull means less time and less movement. Inertia keeps the dish almost where it was.