Moment of inertia and polar ice caps

Some questions to lead you towards the answer:

What is the moment of inertia of the Earth before the caps melt?

What is the moment of inertia of the Earth after the caps melt?

What do you expect to happen to the length of a day? Why?

What law of physics lets you write an equation here? (You only know a short list of actual physics laws so far, so run down them all if you don't know. I'm guessing you know F=ma, the third law, conservation of energy, conservation of momentum, conservation of angular momentum...) One of those applies.

You have guessed that moment of inertia is relevant. What formulas use it?

Think about those before you continue reading...

Okay, the main idea here is angular momentum is conserved. The angular momentum can be written as $Iomega$ and we have a before and after situation, so $I_1omega_1 = I_2omega_2$. How is $omega$ related to period? How long is the period of the Earth's rotation?