By first spinning with the Arms extended, and then bringing the arms close to your body, you will spin faster.
This is due to the conservation of angular momentum and energy.
The equation for the amount of angular energy is (1/2)(I)(W^2)
I is inertia
W is angular velocity (pretend the W is lower case omega)
When you have your arms and legs out, You have an increased Inertia. According to the conservation of angular energy, your have to have just as much energy starting out as you do in the end. So, when you bring your arms and legs in, you increase your ending omega by decreasing you ending inertia.
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Because we have special little scales in our ears that keep us balanced, when you spin around the liquid inside those scales goes sloshing all around inside them disrupting your balance by anallowing your body to read them.
At first, when skater are just beginning the often get dizzy all the time and fall over. But as you spin more and more you build you a tolerance for it. Being a skater for over ten years, I no longer get dizzy at all on any spins with only a few exceptions. Unlike many dancers, figure skaters don't usually spot, which helps them get use to the concept.