If all of humanity (and perhaps the animal kingdom too for good measure) were to run East at the same time for a prolonged period of time, would the equal and opposite force of their feet pushing the ground west behind them slow down the Earth's rotation?

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  • $\begingroup$ I doubt the earth will notice. $\endgroup$ – Lelouch Dec 2 '16 at 3:35
  • $\begingroup$ This is a duplicate of several prior questions. $\endgroup$ – freecharly Dec 2 '16 at 4:43
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    $\begingroup$ VTC as duplicate of physics.stackexchange.com/q/243827 $\endgroup$ – user108787 Dec 2 '16 at 5:20

As it's 4.20 am where I am, and I am pretty dreadful at simple arithmetic, I welcome anybody to refine this calculation, a wiki, if you will.

Any frills to the topic, such how long they would need to walk to make a significant difference, are welcome. But any pedestrian material or remarks will be ruthlessly eliminated. Except that previous line.

Ok, The angular momentum of the spinning earth is:

$I = [2/5]mr^2$ and $ω$ = $2π/T =[ 2π/86400]$ rad/s 

$mass = 5.978×10^{24}kg$,

$radius = 6.378×10^6m$ 

$L = [2/5]×5.978×10^{24}×6.378×10^6×6.378×10^6×[ 2π/86400]$ 

$L = 7.074 ×10^{33} kg.m^2s^{-1}$. 

My (simple, naive) idea is to calculate the force exerted by these walking people, and I make the following sweeping assumptions.

The number of people on Earth is 7.5 billion ( give or take the odd million) and I assume they average 40 kg each. This produces a total mass of $3 × 10 ^{11}$ kg

I then assume that every second, they take one step forward, on a synchronised system, so resulting in a push backwards against the Earth and treating this as an acceleration, this produces a force of $3 ×10^{11} kg.m/s^2$

So you have a force of $3×10^{11} kg.m/s^2$ trying to reduce an angular momentum of $ 7.074 ×10^{33} kg.m^2s^{-1}$.

It may take a while to notice any change.

Since answering this question, I have VTC as there is a duplicate here: Can humans slow down the Earth?

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    $\begingroup$ As per this calculation, the time required to reduce the earths angular momentum by a factor of 10, is about 6.5 *10^16 hrs or 7.4*(10^13)yrs. The sun's remaining lifespan is about another 5.5*(10^9) yrs. I doubt there will be a earth to walk on by then. The weight of the total no.of fur coats everyone wears by then will exceed the current weight of the total population. $\endgroup$ – Lelouch Dec 2 '16 at 4:58
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    $\begingroup$ @Lelouch there is a story by Arthur C Clarke, about a spy who evaded capture on Phobos by well, whoever it was that was after him. They could not manoeuvre their large spacecraft as fast as he could walk and hide on the other side of the moon. $\endgroup$ – user108787 Dec 2 '16 at 5:10
  • $\begingroup$ Perhaps all the people running would create a large enough drag force on the atmosphere which should be taken into account. This would cause a bit of wind moving west to east which would cause a drag force on the earth speeding it up (so it would take even longer to notice anything). $\endgroup$ – user273872 Dec 2 '16 at 5:13
  • $\begingroup$ The approach used in the answer is wrong; you should consider the angular momentum of the east-moving mass of the people, and not the force. $\endgroup$ – Harsha Dec 2 '16 at 7:34

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