Ice Age vs. Now.
Does the Earth rotate at the same rate when encased in ice during the height of an Ice Age as it does when the bulk of it's water is liquid and always in motion?
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Yes, the growth of continental glaciers can change the earth's rotation.
The length of a day can vary by a measurable amounts (microseconds) over periods of days or weeks. The motion of ordinary weather systems in the atmosphere can change the length of a day. Because the growth of glaciers during an ice age would load the continents with ice and change sea level, they would effect even greater changes to the earth's angular inertia, and even larger changes to the length of day.