Hi all.  This is Irv.  An interesting demonstration of physics is when you begin to fall on a bicycle, you need to steer in the direction of the fall to regain balance.  This is the fundimental problem with trying to learn how to ride a bicycle using training wheels (the training wheels eliminates the need for balance correction).

Several years ago now, a small company made a "Gyrobike" 12" diameter bicycle wheel with an integral flywheel, electronics, a small DC motor, and rechargable batteries.  It retailed for about $150 US.  The flywheel could be made to operate at three different speeds.  The idea was that the student cyclist would start with the highest speed and the flywheel speed was reduced as the student gained experience/confidence.  The battery lasted about 3 hours between the need for recharging.  Only the front wheel was replaced with a "Gyrobike" on a normal bicycle.  

It was an extremely good training aid and a child quickly learned how to ride a bicycle with its use (about 3 to 4 hours).  The effectiveness of the device caused the company to fold.  People would by a "Gyrobike" on a friday, train their child over the week end, and return the device to the store for a refund on a monday.  They are still available on eBay and I told the local day care center about them last year.  They were extremely excited and purchased one (I had to replace one of the batteries for about $4 and my time to solder it in).  They trained about 60 pre schoolers how to ride a bicycle with it.  An interesting note, the wheel is "handed" and they initially installed it backwards.  The student pushed to start the bike, and the wheel pushed back to stop it.  

I purchased two of the Gyrowheels for my grandson and put them on a push bicycle (they have no pedals), replacing both the front and back wheels.  The bicycle stands erect with no passenger when the wheels are powered up.  It defies your attempts at pushing it over.