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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.

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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.

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  • $\begingroup$ 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 ? $\endgroup$ – AV 198 Mar 16 '16 at 18:10
  • $\begingroup$ @AV 198, please read the question carefully. $\endgroup$ – Benjamin Mar 16 '16 at 19:21
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    $\begingroup$ 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. $\endgroup$ – Starior Mar 16 '16 at 20:43
  • $\begingroup$ @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 $\endgroup$ – AV 198 Mar 20 '16 at 18:27
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    $\begingroup$ @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. $\endgroup$ – sammy gerbil Jun 12 '16 at 10:27
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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.

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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.

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