|MadSci Network: Physics|
one can answer this question by a strict mathematical approach and that would be the exact one, but I will try to explain it more intuitively, and I think it should be possible to explain it that way.
If water (or any other liquid) freezes, you deprive the molecules of energy - of translational (i.e. used for moving) energy, of rotational and vibrational energy. In a liquid on one hand you have attractive forces between molecules, on the other hand you have energy from those categories.
So imagine two molecules of water approaching each other - they feel interaction forces, quite strong ones, in water you have strong interactions because you have a partial negative charge on oxygen and a partial positive charge on hydrogen, maybe you know that there exist "hydrogen bonds". But on the other hand each of the molecules has a certain amount of energy, here mainly of translational energy - so they don't hold to each other, they fly away.
If you cool a liquid down, you deprive it of energy in all categories, so at a certain stage the attractive intermolecular forces are stronger than the translational energy and you have a solid, here "ice".
If you stir it while you are cooling it down, you transfer translational energy to the system - so the transition liquid/solid occurs later.
How you can quantify it? You have a equivalence between heat energy and mechanical energy, so if you just measure the mechanical energy you put into the system you know how much more energy you have to withdraw (thermally) to bring it to the solid state. In reality it's not so easy, because you have friction and efficiency factors etc., but that's the way it "works in theory".
I hope that's what you wanted to know,
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