1 HP = 745.69987 Watts.
We're going to need to know the electrical power budget of the bike; which is a list of anything that uses electrical power.
Computer,
Headlight(s),
Tailight (s),
Stoplight,
ignition.
alternator excitation voltage/power,
Hand warmers
Beer refrigerator,
Anti-gravitic drive,
tractive suction fans,
etc.
This will give us the watts consumed,what the alternator has to provide on a routine basis, and for a foundation on the electromotive force stolen from the crank during run time.
Using some estimate numbers, say 10 amps for bike devices and 1.5 amps for battery charging, we get 11.5A*13V=149.5 Watts consumption, which the alternator must provide to maintain the status quo.
We will have to asses a conversion efficiency of the alternator. Meaning it will have to be more than what is used, due to losses in converting from rotation force to EMF (every time you convert energy, losses occur). Rule of thumb for alternator is 60-80%. But, even if we say it's a 50% conversion efficiency, this means our 150 watt consumption would rob 300 watts from the crankshaft.
If we divide 300 watts by 745 we get 0.4 HP consumed at the crank for driving the alternator rotation.
None of this accounts for power absorbed when fighting inertial effects. It takes energy to both increase rotational speed and reduce rotational speed. But, usually the energy needed to increase the rotational speed (acceleration) is more a factor in racing than reducing the rotational speed (braking effects).
Mass/energy/time calculations ARE possible. But, just an exercise unless some numbers are available. Weight of the rotational mass, the rpm variance, and rate of change.
Cheers,