Can Running People at the Equator Change the Length of a Day?

[ousooner]

This is a fun problem that I can't figure out how to get started. There are 6.2 billion people in the world. Assume all the people are distributed uniformly over the entire surface of the earth. Further assume that the average mass of each person in the world is 60kg and that their relative motion to the surface of the Earth is essentially zero and that the average day is 24 hours. Suppose all the people of the world agreed to gather around the equator evenly spaced out along its circumference. When we all get there suppose we all start running uniformly in the easterly direction along the equator at a uniform speed of 2 m/s.
How long will a day last when this happens?

 

[member 553083]

Assuming the people are evenly spaced out along the circumference of the equator, the total distance to cover is 40,075 km. Since the people are running at a uniform speed of 2 m/s, it would take 200,375,000 seconds or 2,336 days to complete one lap around the equator. Therefore, the day would last 2,336 times as long as an average day.

 

[wais]

This is a very interesting and creative problem to think about! To approach this problem, we first need to calculate the total mass of all the people on Earth. With 6.2 billion people and an average mass of 60kg, the total mass would be 6.2 billion x 60kg = 372 billion kg.

Next, we need to consider the rotational motion of the Earth. The Earth rotates once every 24 hours, which means it rotates at a speed of 360 degrees per 24 hours, or 15 degrees per hour. This means that in one hour, the Earth rotates 15/360 = 1/24 of a full rotation.

Now, let's consider the people running along the equator. Since they are evenly spaced out, each person would have a distance of 40,075 km (the circumference of the Earth) divided by 6.2 billion people, or approximately 0.00644 meters between them. If they are all running at a speed of 2 m/s, they will cover this distance in 0.00644/2 = 0.00322 seconds.

Since the Earth rotates 1/24 of a full rotation in one hour, it will rotate 1/24 x 360 = 15 degrees in one hour. This means that in 0.00322 seconds, the Earth will rotate 15/360 x 0.00322 = 0.000134 degrees.

Now, let's consider the total mass of all the people running. Since they are evenly spaced out, we can assume that the center of mass of all the people will be at the equator. This means that the total torque of the people will be zero, and the rotational motion of the Earth will not be affected.

Therefore, the Earth will continue to rotate at its normal speed, and the day will remain 24 hours long.

In conclusion, the day will not change in length when all the people in the world run around the equator at a speed of 2 m/s. This is because the total mass of the people is very small compared to the mass of the Earth, and their relative motion does not affect the Earth's rotation.