So I'm building a boomerang to fly 200 feet in order to do that I was told to increase the moment of inertia to increase the resistance from change in state, and I was told that it would increase the wing tip speed,but why? According to the conservation of angular momentum when the radius increases the velocity decreases, this is why figure skaters spin faster when they pull their arms in, so shouldn't the boomerang's angular momentum decrease, because it's radius has been augmented. Note: I can't make weighted wings, because that's a little advanced for me. I have already purchased 12 mm birch plywood,so the only way I can increase the moment of inertia is to make the boomerang bigger. Try to explain to me keeping in mind I'm 16.
The analogy you're bringing up with a skater pulling her arms in is not as applicable here as you might think.
The skater has some set angular momentum that doesn't change. The two states that are looked at (arms extended and arms in) are both associated with this single value of angular momentum.
Your boomerang situation, on the other hand, deals with an object that is changing its angular momentum. The two states here (before the throw and after the throw) have different angular momenta. Thus, there is not an exact analogy here.
Okay, that being said, a larger moment of inertia will certainly require more torque and/or a longer time in order to get its angular momentum up to a particular value; but that's a different question.