how does conservation of linear momentum apply?
edit: this question was asked when the parent comment claimed that this machine could "generate linear momentum" from the wheels.
Conservation of momentum applies when there are "no external forces", which wouldn't be the case here when you apply the brake.
EDIT: Yeah, my apologies. I didn't mean to write "momentum".
Come to think of it - in air you're constantly bumping into things - air molecules. I think it could technically be possible to steer in zero-g within an atmosphere by pure rotation (e.g. consider that a fast-spinning object is kind of a (crappy) fan).
It uses an array of 12 small rotating fans placed around its surface to push jets of air and move itself from place to place.
My point was that in principle, you could abuse reaction wheels to give you translation capability if you're moving through air.
In the person + bike system, the brake action would result in internal forces. I don't see how this system could translate.
Thinking about it, the bicycle would only rotate about the center unless it had something to react against, as was pointed out by others.