Work Step by Step
There is no external torque on the Earth, so its angular momentum is conserved, i.e., remains constant. The magnitude of the angular momentum L is the moment of inertia multiplied by the angular speed, $L = I \omega$. If people were to migrate toward the equator, this would move mass away from the Earth’s axis of rotation. This increases the Earth’s moment of inertia, $I$. For angular momentum L to remain constant, i.e., be conserved, the angular speed $\omega$ decreases to compensate. The length of the day would increase.