Why do you feel like the room's spinning around right after you've stopped spinning in circles?

Your inner ear has a structure inside called Eustachian tubes that provide your sense of balance. They are filled with fluid, and when you move, the fluid moves, activating tiny hairs called cilia. When you spin fast, you get the fluid moving within the tubes. Once you stop, the momentum of the fluid's movement keeps it moving for a while. As the fluid stops swirling within the tubes, you feel your balance return.

Because the fluid in your ears that your brain uses to know which way up it is, keep spinning round when you stop so your brain thinks you're spinning round still until the fluid stops again. (You can stop it quickly by spinning 1 or 2 turns in the opposite direction afterwards).

the fluid in your inner ear that helps you retain your balance is still sloshing back and forth causing the sensation of imbalance.