Does a balance occur when angular momentum is conserved?

 

I'm still stuck with that bicycle question. I'm thinking that angular momentum might indeed be one of the answers to it.

Angular momentum is conserved when there is no net torque on a system. That will be important in some systems, but not all, e.g. a three-leggd stool with wheels will balance but that doesn't rely on angular momentum. That configuration is already inherently stable.

 

But conservation of angular momentum is important in the balance (or stable orientation) of many systems, which is why people use gyroscopes for stability. It can give you balance when there is no other feedback in an otherwise unstable system.