Final answer:
If the polar ice sheets moved towards the equator without melting, Earth's angular velocity would decrease due to the conservation of angular momentum, which dictates that the moment of inertia would increase as mass moves farther from the rotation axis.
Step-by-step explanation:
If the polar ice sheets broke free and floated toward Earth's equator without melting, Earth's angular velocity would decrease. This is because, according to the conservation of angular momentum, if an object's mass moves closer to the rotation axis, its moment of inertia decreases and its angular velocity increases. Conversely, if mass moves away from the axis, as the ice sheets would be in moving towards the equator, the moment of inertia increases and, as a result, the angular velocity decreases. This principle is similar to a figure skater spinning faster when arms are pulled in and slowing down when they extend their arms out.
Therefore, as the ice sheets migrate towards the equator, Earth's moment of inertia increases and the angular velocity decreases to conserve angular momentum, assuming no external torques are acting on the system.