45(7). A cockroach, mass \' m \' , runscounterclockwise around the rim of a lazy

Question

45(7). A cockroach, mass ' m ' , runscounterclockwise around the rim of a lazy Susan ( a circulardish mounted on a vertical axis ) ofradius   ' R ' and rotational inertia ' I' with frictionless bearings. The cockroach's speed ( relative to the earth ) is ' v ' , whereasthe lazy Susan turns clockwise with angular speed ' w 0 ' .   The cockroach finds abread crumb on the rim and of course, stops.   ( a) What is the angular speed of the lazy Susan after the cockroachstops ?   ( b ) Is energy conserved ? 45(7). A cockroach, mass ' m ' , runscounterclockwise around the rim of a lazy Susan ( a circulardish mounted on a vertical axis ) ofradius   ' R ' and rotational inertia ' I' with frictionless bearings. The cockroach's speed ( relative to the earth ) is ' v ' , whereasthe lazy Susan turns clockwise with angular speed ' w 0 ' .   The cockroach finds abread crumb on the rim and of course, stops.   ( a) What is the angular speed of the lazy Susan after the cockroachstops ?   ( b ) Is energy conserved ?

Explanation / Answer

       (A) .Momentum isconserved. The lazy Susan is turning clockwise ( anegative rotational direction, that is ,  ' -' . ) So, we have :    I =L1 -  L2       ( I + m R 2 )( -1 )    =    ( I 0   -   mR  v )   ... ( mRv ; R theperpendicular distance to mv from r P sin 90 0)           - 1 =   ( I 0   - mRv ) / ( I   +   mR2)   . (B)   Is energy conserved ?                  Momentum isconserved but, the kinetic energy is not conserved.    The answer to (B)is        No.

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