By sheer experimentation, I have found that my cat, claire, totally enjoys the old playscape oddity of spinning one's self around, very fast, on my office chair.

She not only likes it, she loves it. She perches on the chair and then looks at me like "hey lady, would you mind giving me a little push here?"

I comply.

And around and around and around she goes. Where she'll stop I certainly don't know. The faster the better, and the more best ever is when I spin her while she's traveling across the (wooden) floor. Gets me dizzy just watching her.

Hence, Claire's "Daredevil Chair". For cats. Dogs just don't work for me in this instance. ( Sees spittle and ears and tail and such, going everywhere.)

A furry, cozy, itsy-bitsy feline rolling chair, in the same style as an office chair, with a seat belt, naturally. The fore mentioned kitty would propel itself by trying to catch the pretend bird that is placed a scant bit out of reach, overhead. The more the cat tries to catch it, the faster the chair spins. (Self-control little girly).

You say "but how does this chair spin, exactly?" What is the mechanism that the cat actually: pushs, pulls, pumps, prods, or toys with.
//Sighs// Simple, aerodynamics.

***Uhm... little helmet not included***