[FredZarguna]

Conservation of rotational kinetic energy -- which I agree doesn't change -- requires the angular velocity of the Earth to decrease when the jumpers jump.

The moment of inertia of the system composed of the Earth and jumping people will change. In order to conserve angular momentum -- which must be conserved because there is no external torque -- the angular velocity, ω, must decrease. [In your alternative formulation, there are no external sources of energy, therefore the angular velocity must decrease when I increases in order for the kinetic energy to remain constant: I_iω_i² = I_fω_f²]

The differential dI would (at most, assuming the people ball themselves up into spheres when they jump) would be 2m * r * dr, where r is the radius of the earth, dr is the number of meters they jump, and m is the mass of six billion people. The number is insignificant compared to the moment of inertia of the Earth, which is roughly 2/5 M r², where M is the mass of the Earth. And it is clearly this which dominates.

[loungitude]

Conservation of rotational kinetic energy -- which I agree doesn't change -- requires the angular velocity of the Earth to decrease when the jumpers jump. The moment of inertia of the system composed of the Earth and jumping people will change. In order to conserve angular momentum -- which must be conserved because there is no external torque -- the angular velocity, ω, must decrease. [In your alternative formulation, there are no external sources of energy, therefore the angular velocity must decrease when I increases in order for the kinetic energy to remain constant: Iiωi2 = Ifωf2] The differential dI would (at most, assuming the people ball themselves up into spheres when they jump) would be 2m * r * dr, where r is the radius of the earth, dr is the number of meters they jump, and m is the mass of six billion people. The number is insignificant compared to the moment of inertia of the Earth, which is roughly 2/5 M r2, where M is the mass of the Earth. And it is clearly this which dominates. =================================================================================================== Fred this sounds good, however I struggle with the fact that the jumpers become detached from the earth part of the system, momentarily creating two systems, each possessing a fraction of the initial energy of the earth/people system. I suggest that the incremental change of MOI of the people part of the system would cause their omega to change. This would result in their landing in a different spot than they jumped up from. And the angular velocity of the earth stays the same.