A Texas cockroach of mass 0.17 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has radius 15 cm, rotational inertia 5.0 x 10^-3 kg ∙ m², and frictionless bearings. The cockroach's speed (relative to the ground) is 2.0 m/s, and the lazy Susan turns clockwise with angular velocity w₀ = 2.8 rad/s. The cockroach finds a bread crumb on the rim and, of course stops.

(a) What is the angular speed of the lazy Susan after the cockroach stops?

(b) Is mechanical energy conserved as it stops?