I definitely encourage you to head to the World Beyblade Organization : http://worldbeyblade.org/
Are you already registered there ? It is basically a community that gathers all the competitive bladers, and any other fans. Not a lot of them know all about physics, however I know you will definitely get a serious answer from a veteran as soon as possible. You should look at these topics :
http://worldbeyblade.org/Thread-Question-for-the-general-bey-community-about-the-technical-aspect-of-Bey
http://worldbeyblade.org/Thread-Physics
http://worldbeyblade.org/Thread-Spin-Velocity

I understand that not all of your questions will be answered with only those topics though, so you should also try using this thread for all the questions you have :
http://worldbeyblade.org/Thread-Ask-a-question-get-an-answer-New-Thread-Rules

Otherwise, those pages from Wikipedia could always help :
http://en.wikipedia.org/wiki/Gyroscope
http://en.wikipedia.org/wiki/Moment_of_inertia
http://en.wikipedia.org/wiki/Rotational_energy
http://en.wikipedia.org/wiki/Torque
http://en.wikipedia.org/wiki/Angular_momentum

There is definitely a lot to cover on the physics of any spinning top.

Hopefully this gives you a good start,

Kai-V

http://en.wikipedia.org/wiki/Beyblade_(toy)

Hope it helps!!