A Texas cockroach of mass 0.120 kg runs counterclockwise around the rim of a laz

Question

A Texas cockroach of mass 0.120 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has a radius 18.3 cm, rotational inertia 5.26 x 10-3 kg·m2, and frictionless bearings. The cockroach's speed (relative to the ground) is 2.73 m/s, and the lazy Susan turns clockwise with angular velocity 0 = 2.52 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) angular momentum of Susan and cockroach will not change.

Using angular momentum (Iw & mvr) conservation,

(5.26 x 10^-3 x 2.52 ) + ( 0.120 x 2.73 x 0.183 ) = ( (5.26 x 10^-3) + (0.120 x 0.183^2))w

w = 7.9 rad/s

b) initial ME= (5.26 x 10^-3 x 2.52^2 /2 ) + ( 0.120 x 2.73^2 /2 )

        = 0.464 J

final ME = ( (5.26 x 10^-3) + (0.120 x 0.183^2)) x 7.9^2 /2 = 0.29 J

so energy is not conserved.

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