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(B) Let the initial angular momentum of the system (Earth + people) be $L_i = (I_E + I_P)\omega_0$. When people run at speed $v_{rel}$ relative to the

Vedclass · Accepted Answer

If people run due east,the change in angular velocity of the Earth will be $\omega_0 - \frac{I_P v_{rel}}{(I_P + I_E)R}$.

Vedclass · Answer

(B) Let the initial angular momentum of the system (Earth + people) be $L_i = (I_E + I_P)\omega_0$. When people run at speed $v_{rel}$ relative to the surface,their velocity relative to the center of the Earth is $v = v_{rel} + \omega R$ (if running east) or $v = \omega R - v_{rel}$ (if running west). By conservation of angular momentum: $L_i = L_f$. $I_E \omega_0 + I_P \omega_0 = I_E \omega + I_P (\omega + \frac{v_{rel}}{R})$. Solving for $\omega$: $(I_E + I_P)\omega_0 = (I_E + I_P)\omega + \frac{I_P v_{rel}}{R}$. $\omega = \omega_0 - \frac{I_P v_{rel}}{(I_E + I_P)R}$. This represents the new angular velocity when running east. If running west,the sign of $v_{rel}$ changes,resulting in an increase in angular velocity.

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