Question

If all the Earth’s human inhabitants moved to the equator, how would this affect Earth’s rotational inertia? How would it affect the length of a day?

Answer 1

Humans can be considered as point masses as their size is small relative to the earth.

Now, moment of inertia of point masses= md2, where m is mass and d is distance between the mass and the axis.

If all humans move to equator, d will become maximum and hence, moment of inertia(or rotational inertia) will increase.

Now, angular momentum=(rotational inertia)*(angular velocity)

Since there are no external torques, angular momentum will be conserved. So,since rotational inertia has increased, angular velocity must decrease and hence, length of a day will increase.