A Texas cockroach of mass 0.121 kg runs counterclockwise around the rim of a laz

Question

A Texas cockroach of mass 0.121 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has a radius 14.3 cm, rotational inertia 5.00 x 10-3 kg·m2, and frictionless bearings. The cockroach's speed (relative to the ground) is 1.57 m/s, and the lazy Susan turns clockwise with angular velocity ?0 = 3.57 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?

Explanation / Answer

a) The cockroach angular momentum is -m*v*r; the turntable angular momentum is I*0 The total initial angular momentum is

I*0 - m*v*r = 5*10^-3*3.57 - 0.121*1.57*0.143 = -0.00931

When the cockroach stops, the total moment of inertia of the system is

I + m*r² = 5*10^-3 + 0.121*0.143² = 0.007474

The final is then -0.00931 / 0.007474 = -1.25 rad/s

b) Yes

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