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 4.9 ✕ 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 speed ω0 = 3.9 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?
L_i = L_f
L=Iw = mvr
The Attempt at a Solution
L_i = 4.9 ✕ 10^−3 * 3.9 + .17*2.0*.15
L_f = (4.9 ✕ 10^−3)w_f
But when I solve the equations putting L_i = L_f, the w_f I get is wrong. please help!