338_Physics ProblemsTechnical Physics

338_Physics ProblemsTechnical Physics - 340 Angular...

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340 Angular Momentum Additional Problems *P11.43 First, we define the following symbols: I P = moment of inertia due to mass of people on the equator I E = moment of inertia of the Earth alone (without people) ω = angular velocity of the Earth (due to rotation on its axis) T == 2 π rotational period of the Earth (length of the day) R = radius of the Earth The initial angular momentum of the system (before people start running) is LI I I I iP iE i PE i =+= + ωω bg When the Earth has angular speed , the tangential speed of a point on the equator is vR t = . Thus, when the people run eastward along the equator at speed v relative to the surface of the Earth, their tangential speed is vv v R v pt =+= + and their angular speed is P p v R v R + . The angular momentum of the system after the people begin to run is I I v R II I Iv R fP pE P E P =+ F H G I K J += + + ωωω . Since no external torques have acted on the system, angular momentum is conserved LL fi = di , giving R P i ++ = + . Thus, the final angular velocity of the Earth is
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