Which structures of the inner ear would be activated by a somersault? A cartwheel? By fast acceleration in a race car?

Answer 1

Semicircular canals

http://www.google.com/search?client=safari&rls=en&q=semicircular+canals&ie=UTF-8&oe=UTF-8

Answer 2

As you turn your body and head while doing an activity like a somersault, different hair cells in the vestibule and semicircular canals change direction. When this happens, electrical signals are sent through the nerve fibers which connect to your eye muscles, which causes your eyes to move in different directions depending on how your body is twisting and turning.