A translating and rotating ring of mass \( 1 \mathrm{~kg} \), angular speed of \( 500 \mathrm{rpm} \), and translational speed of \( 1 \mathrm{~m} / \mathrm{s} \) is placed on a horizontal surface. The coefficient of friction between the ring and the surface is 0.35 .

For an outside radius of \( 3 \mathrm{~cm} \), the time at which skidding stops and rolling begins is most nearly (A) \( 0.01 \mathrm{~s} \) (B) \( 0.1 \mathrm{~s} \) (C) \( 1 \mathrm{~s} \) (D) \( 10 \mathrm{~s} \)