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We walk or ride on our vehicles to our destinations daily. Does our movement have any effect on the rotation of the earth according to Newton's law? What will be the effect if we move all the peoples along with their vehicles at their maximum velocity in one line in one direction along the equator? How much effect will it make?

Qmechanic
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Deiknymi
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3 Answers3

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In principle, yes, but the effects are almost completely negligible. As objects on the surface of the earth move around, the Earth's moment of inertia changes by minute amounts, and this affects its rotation. However, performing an order of magnitude estimate on the ratio of the contribution to the moment of inertia of a person-sized object on the equator to the Earth's moment of inertia gives $$ \frac{I_p}{I_E} \sim \frac{M_pR_E^2}{M_ER_E^2} \sim \frac{10^2\,\mathrm{kg}}{10^{24} \,\mathrm{kg}}\sim 10^{-20}, $$ and even if we were to take into account the entire population of the Earth plus their vehicles (by conservatively multiplying the numerator by $10^{11}$ or so), we would still get a number on the order of $10^{-10}$. We can thus see that such small objects on the surface will have an entirely negligible effect on the Earth's rotation (at least in the sense that our motions have a negligible affect on changing the Earth's moment of inertia.)

joshphysics
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It does, but changes are so miniscule that they don't really count.

Even if everyone in the world started running in the same direction (East, for example), their total angular momentum would be on the order of $ 10^{18} \ \text{N m s} $, in comparison to the earth, which is on the order of $ 10^{33} \ \text{N m s} $. We would change the earth's rotation by less than a trillionth of a percent.

Some crude calculations:

$\text{Population of the earth} = \text{about 7 billion}$

$\text{Average human mass} = 62 \ \text{kg}$

$\text{Average running speed} = 5 \ \text{m/s} $ (ish)

$\text{Mass of everyone in the earth} = 4.3 * 10^{11}\ \text{kg} $

$\text{Radius of the earth} = 6.37 * 10^6\ \text{m}$

$\text{Mass of the earth} = 6 *10^{24}\ \text{kg}$

$\text{Angular velocity of the earth (its spin)} = 7.29 * 10^{-5}\ \text{s}^{-1}$

$\text{Angular velocity of the human "race"}= 7.8 * 10^{-7}\ \text{s}^{-1}$

$\text{Their moment of inertia, assuming spherical distribution}= 1.2 * 10^{25}\ \text{kg m}^2$

$\text{Their angular momentum:}\ 9.2 * 10^{18}\ \text{kg m}^2\ \text s^{-1}$

$\text{Moment of inertia of the earth} = 9.7 * 10^{37}\ \text{kg m}^2$

$\text{The earth's angular momentum:}\ 7.1 * 10^{33}\ \text{kg m}^2\ \text s^{-1}$

krs013
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The major external effect slowing the earth's rotation is interaction with the moon's orbital motion through tidal friction. It is possible that damming of water in major areas of tidal friction could change the rate of slowing.

DJohnM
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