Does it really matter whether your arms are in or out when you try to spin really fast? Take a look ... then find out for yourself!
You've probably seen an ice skater spinning during a performance and suddenly she starts to spin dramatically faster. A diver or gymnast may also suddenly flip or twist much faster in the air. This speeded-up rotation results from a sudden redistribution of mass. You can make yourself suddenly spin faster while sitting in a rotating chair.
Sit in a chair with one of the masses in each hand and with arms outstretched. Have your partner start rotating you slowly, then have that person let go and move away. Quickly pull the masses inward and notice that you rotate faster.
Be careful! You never know when a chair might tip over! Also, depending on your tolerance, you may be slightly off balance when you try to walk away.
Why does this happen?
When an ice skater spins, they are using angular momentum. In a spin, their arms act as weights. When arms are extended, the skater spins slowly. When the skater changes their moment of inertia and bring their arms into their body, they spin faster.
Check out these resources for more information:
Introduction to Rotational Inertia - this playlist is a full unit on rotational inertia including formulas and calculations.