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I'm a class 12th student and this thought just struck me from nowhere.

Assume a situation where every human on this planet turns towards west. All of them start walking simultaneously in west direction (exactly west i.e. antiparallel to Earth's rotation and none of their paths cross each other).

As Earth spins from west to east would this activity cause the earth's rotation speed to increase?

(There is frictional force acting on the earth due to motion by nearly a billion people which should produce enough torque to increase angular velocity of the earth.)

p.s. If the magnitude of friction force not enough to rotate the earth then assume each person to weigh more than 100 kg.

Also if it does happen would earth remain in the same orbit around the sun with just increased angular velocity about axis? (or would path around the sun also change due to this? )

I would really appreciate an easy solution cause I am still in class 12th.

infiNity9819
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    Not measurably (see also) – rob Mar 16 '16 at 17:54
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    Better to think about it in terms of conservation of angular momentum. – Andrea Mar 16 '16 at 19:57
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    Similar Mankind vs Earth questions: http://physics.stackexchange.com/q/70732/2451, http://physics.stackexchange.com/q/56245/2451, http://physics.stackexchange.com/q/137724/2451 and links therein. – Qmechanic Mar 16 '16 at 20:19
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    Problem is, if everyone keeps walking west, most of us will eventually walk into the ocean and then what? Keep swimming west? In theory, if we build a large train that circles the earth, and run it all the time, that could, very very slowly, affect the Earth's rotation but it would be a very slow change. – userLTK Mar 16 '16 at 22:20
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    We can't change our path around the sun at all. At least not without some mass leaving our earth. Convervation of momentum means that whatever we do on earth the center of mass of humans + earth keeps moving along the same path. – AccidentalTaylorExpansion Oct 30 '20 at 11:19

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The friction due to a single person would be on the order of ~100N. There are currently 7.2 billion persons on Earth. I don't think this will affect revolution around Sun but surely it will affect the rotation of Earth about its own axis.

I did calculated this effect on the back of envelope. Assuming a very not-so-realistic assumption that all people will march along the equator simultaneously, we can calculate an upper limit on the total external torque opposing the rotation of the earth. The angular acceleration due to such a march will be so small that it will take something on the order of 100,000,000 years for all the people to march with no stop to finally being able to bring the rotation to a halt. And, obviously no one can do this for such a long time. So, we are safe.

Benjamin
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  • But then think about this. Every day 7.2 billion people walk on earth in no pirticular direction. But as humans Have capacity to think and move we cant assume their net frictional torque on earth to be zero (Like as we assume average velocity in ideal gasses to be O which move in all direction) . There should be a net resultant torque every day and hence every day the rotaion of earth should be different (everyday) . IS there some external force to keep earth rotating in proper speed ? – infiNity9819 Mar 16 '16 at 18:10
  • @AV 198, please read the question carefully. – Benjamin Mar 16 '16 at 19:21
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    Due to the astronomical scale of Earth's mass($5.97\times10^{24} kg$) and moment of inertia($8\times10^{37} kg\cdot m^2$), that mere $7.2\times10^{11} N$ wouldn't noticably affect its rotation. Thus, this would not be such a risky "predicament" afterall. – Starior Mar 16 '16 at 20:43
  • @Benjamin I am the one who asked the question. But then you answered my second question too which I asked in my comment. I was talking about normal life on earth where people dont just keep on walking west but in all direction. But this would cause even little effect to rotation according to your calculations. Thanks for answering my Questions : D – infiNity9819 Mar 20 '16 at 18:27
  • @AV198 : The resultant frictional torque due to 7.2 billion people walking in random directions will be much less than if they walked in the same direction. It will be less by a factor of roughly $\sqrt{7.2 billion} = 85000$ approx. – sammy gerbil Jun 12 '16 at 00:27
  • @Benjamin : You seem to think the Earth would continue speeding up if the people continue walking. Not true, I think. It would only speed up while they accelerated from standing still to reaching normal walking speed, say 4 kph. While they continue walking with constant speed there will be no effect until they stop walking, when the rotation speed would return to initial value. To continue supplying a constant force of 100N they would need to continue accelerating themselves. But they would soon reach the maximum speed their muscles and bones could withstand. – sammy gerbil Jun 12 '16 at 00:35
  • @sammy gerbil, let's simplify the thought experiment by thinking only about a person walking on Earth with a constant speed. Let's even not worry about the Earth itself in the large scale. To begin with, after all, what causes the person being able to walk? The static friction between Earth and the person. Without this static friction (which is pointing forward by Newton's Third Law as a result of the person's push against the Earth,) we can no longer walk in its literal meaning. Now, if you accept this fact (that there is friction even if the walk has a constant velocity,) you see the point. – Benjamin Jun 12 '16 at 07:57
  • So, such a constant frictional force being there for the whole time during the walk (even if it is uniform speed) will cause the constant torque that's been applied on Earth and any constant torque would translate into a constant angular acceleration according to Newton's Second Law. So, for the whole time of the marsh there will be a constant acceleration applied onto Earth. This opposing acceleration will be eliminated only if all walking people decide to stop walking simultaneously. So, yes! the non-zero acceleration will be there ALL the time so long as there is the practice of walking. – Benjamin Jun 12 '16 at 08:06
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    @Benjamin : The torque is not there all the time. If the forward friction force were there all the time, people would also accelerate relative to the surface of the Earth (F=ma). The relative speed would increase continuously. This cannot be sustained : human top speed is about 35 kph. Instead, there is also a backward friction force when the foot comes down. When the person walks with constant speed the forward and backward friction forces cancel over 1 complete step. The torque is only present when the walkers accelerate from rest to walking speed. When they 'cruise' it disappears. – sammy gerbil Jun 12 '16 at 10:27
  • As long as people are not ALL marshing synchronously, there is always a friction force. But whether there will be cancellation or not in one cycle on average from one person is debatable but simultaneous net force won't be zero at any moment of time. I believe the disagreement is in the picture we have about. It seems we have two different definitions for walking. Since there are billions of people walking together, but not synchronously, on average I do believe the net static friction force is backward and non-zero. But I do understand your points. Let's see what other people think about it – Benjamin Jun 14 '16 at 06:43
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In short, my answer is yes.

As people start walking from rest in western direction, they will increase the speed of rotation of earth about its axis due to conservation of angular momentum, although this increase will be very small(about $10^{-14}m/s$) as the mass of earth is much much bigger than that of all people combined together, and this boost will end when people stop or when their motion becomes random.

However, this walking can't affect earth's revolution around the sun if people were distributed uniformly over the earth.

Tofi
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Yes, it would affect the rotation and orbit of the Earth, but not by any detectable amount.

A very similar question was examined by Randall Munroe of xkcd. He refers to this ScienceBlog article which calculates the net effect of everyone on Earth jumping at the same time.

Any action upon the Earth causes an equal and opposite reaction, however the mass of the Earth is so large compared to the mass of all the people on it that the reaction would be negligible. The article estimates the recoil speed of the Earth to be $10^{-13} m/s$. That's about 10,0000 times slower than the speed that fingernails grow.

user235504
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