We have all complained that there aren\'t enough hours in a day. In an attempt t

Question

We have all complained that there aren't enough hours in a day. In an attempt to fix that, suppose all the people in the world line up at the equator and all start running east at 4.00 m/s relative to the surface of the Earth. By how much does the length of a day increase? Assume that the world population to be 7.00 *109 people with an average mass of 65 kg each and the Earth to be a solid homogeneous sphere. In addition, depending on the details of your solution, you may need to use the approximation 1/(1 - x) 1 + x for small x.

Explanation / Answer

Iinitial=Ifinal +mvR WHERE R is the radius of the earth and I the moment of inertia of earth

M(mass of earth)=5.97*1024 radius (R)=6400000m

I=(2/5)MR2=9.78*1037 kgm2

initial=(2/24*60*60)=7.26*10-5 rad/s

final= can be calculated from above expression where m is the total mass of the people and v is the velocity wrt to the earth surface

final can be used to find the modified time period of earth rotation using (2/final )

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