First, for reply to the question of -Stradivarius257,
The expression of small parts of ring ejecting is not:
CaseA:
outer: dw1-rw2
inner: dw1+rw2
CaseB:
outer: dw1+rw2
inner: dw1-rw2
If d=r and w1=w2, with the case A, the external object has a velocity at 0. For the inner, the velocity is...