340 Angular MomentumAdditional Problems*P11.43First, we define the following symbols:IP=moment of inertia due to mass of people on the equatorIE=moment of inertia of the Earth alone (without people)ω=angular velocity of the Earth (due to rotation on its axis)T==2πrotational period of the Earth (length of the day)R=radius of the EarthThe initial angular momentum of the system (before people start running) isLIII IiPiEiPEi=+=+ωωbgWhen the Earth has angular speed , the tangential speed of a point on the equator is vRt=.Thus, when the people run eastward along the equator at speed vrelative to the surface of the Earth,their tangential speed is vvvRvpt=+= +and their angular speed is PpvRvR+.The angular momentum of the system after the people begin to run isIIvRIIIIvRfPpEPEP=+FHGIKJ+=++ωωω.Since no external torques have acted on the system, angular momentum is conserved LLfi=di,giving RPi++=+. Thus, the final angular velocity of the Earth is
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