# Parallel axis theorem proof?

First, I thought theorems do not have proofs. Anyway, for parallel axis theorem, I was given that the addition of translational kinetic energy and rotational kinetic energy proves the parallel axis theorem. I am confused how that happens, although I can see it mathematically. But I cannot understand, what does translational kinetic energy has to do with trying to find the equivalent of inertia of an object that rotates in a different that its centre of mass axis. I don't see where the translational kinetic energy occurs in that example! I would expect in that case the object would have a rotational kinetic energy with an Igg different than the regular Igg which is calculated in respect to the centre of mass axis. But how can we add the translational kinetic energy and then assume that the sum of it with the rotational kinetic energy will help us calculate the Izz? Can you clarify this to me please?

• "First, I thought theorems do not have proofs." /quote From the Wikipedia article on "theorem": "In mathematics, a theorem is a statement that has been proven on the basis of previously established statements". Commented Feb 28, 2016 at 22:45
• If theorems don't have proofs, you should tell that to the millions of mathematicians who have been proving theorems over the years... Commented Feb 28, 2016 at 22:47
• Regarding your first sentence, see Difference between axioms, theorems, postulates, corollaries, and hypotheses Commented Feb 29, 2016 at 1:14