A volunteer stands on the spinning table with hand weights. She spins around with her arms out and then brings them in. What happens?
As she brings in her arms she speeds up. This demonstrates the conservation of angular momentum which says that bigger things (a girl with her arms out) rotate slower than smaller things (a girl with her arms in).
The spinning table is also used to illustrate the principle of inertia. When a person stands on the spinning table, they will not be able to turn themselves around. The law of inertia tells us that an object at rest stays at rest. The person wants to stay at rest, not spin around. When the person pushes off of the ground or another person that has more inertia, then they can move. Recall that if something has a lot of inertia, it is hard to move. If something has not much inertia, it is easy to move. The person on the spinning table moves a lot easier than the person on the ground, so the spinning person has less inertia.
When we give the volunteer some weights in her hands and spin her around, she can make herself go faster by bringing his arms in. This is the same move that ice skaters use to spin fast when they do fancy jumps. When the arms are in, it is easier for her to move, so this means she has less inertia. When arms are out, she moves slower and has more inertia. The effect is more pronounced with heavier weights, but you can see (and feel) it even without any weights at all.