Magic Roundabout
You're standing on the edge of a turntable, holding a heavy flywheel in your hands. Beginning with both axes parallel, spin that baby up.. ..then rotate its axis 90° into the perpendicular plane. This exerts a precessional torque, which is earthed through the turntable's rigid axis, having no effect upon its current balance of momentum.. ..now brake away that counter-momentum in your hands, earthing the lot.. ..you're now stood on the edge of a rotating turntable, holding a stationary flywheel.. ..flip it back to parallel and repeat the cycle.. Simplifying, assume equal MoI's for both axes (ie. 1 kg-m²-rad/s each). Both the per-cycle input torque * angle and the resulting momentum yield appear to be RPM-invariant; that is, the input energy cost of momentum appears to be constant / invariant to system speed, whereas its rotational KE is obviously squaring up.. For example, 10 purchases of 1 kg-m²-rad/s at 1 J each costs a total of 10 J (this includes dissipating half the input energy per cycle). Yet 10 kg-m²-rad/s divided by two 1 kg-m² MoI's gives them 5 rad/s each, and so 12.5 J each, 25 J total. Using two equal MoI's, we find a 75% net loss after the first cycle, 50% following the second cycle, 25% at the third.. we hit unity at the fourth cycle, and 125% of unity at the fifth.. and efficiency keep rising by that same 25% per cycle as we accumulate ever-more 'unilateral' momentum, at fixed cost, its KE value squaring with rising velocity.. Only thought this up 24 hrs ago but barely slept since.. where am i going wrong? It's too simple!
