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A cockroach of mass \( 0.20 \mathrm{~kg} \) runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has radius \( 18 \mathrm{~cm} \), rotational inertia \( 5.0 \times 10^{-3} \mathrm{~kg} \cdot \mathrm{m}^{2} \), and frictionless bearings. The cockroach's speed (relative to the ground) is \( 2.0 \mathrm{~m} / \mathrm{s} \), and the lazy Susan turns clockwise with angular speed \( \omega_{0}=2.8 \mathrm{rad} / \mathrm{s} \). The cockroach finds a bread crumb on the rim and, of course, stops. What is the angular speed of the lazy Susan after the cockroach stops?
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