2. A Texas cockroach of mass 0.11 kg runs around the rim of a "Lazy Susan" (a circular tabletop that can rotate freely in the horizontal direction around its center). The rotating tabletop has radius 18 cm and rotational inertia 4.4 x 10 3 kg. m. Initially, the cockroach's speed (relative to the ground) is 1.1 m/s counterclockwise, while the Lazy Susan turns clockwise with angular speed wo = 2.7 rad/s. The cockroach finds a bread crumb on the rim and, of course, stops. (a) Calculate the angular momentum for each of the following, defining CCW rotation as positive: i. The cockroach: ii. The Lazy Susan: iii. The entire system (cockroach + Lazy Susan):(b) What is the angular velocity of the lazy Susan (including the CW or CCW direction) after the cockroach stops? Hint: what is the moment of inertial of the system? (c) Is mechanical energy conserved as it stops? ((1) The cockroach now walks to the center of the Lazy Susan. Once the cockroach reaches the center, What is the angular speed of the system? Hint: consider L, I, and to. Which is/are conserved, and which must change