This paper endeavors to show (within the realm of Newtonian mechanics [6]) that the mass of a gyroscope consisting of a thin cylindrical rotor and weightless shaft having a fixed pivot and steadily precessing (without nutation) in a horizontal plane appears to gain mass if the rotor is spinning compared to the same situation but with non-spinning rotor in that if the precession is stopped dead (not altering the rotor spin angular velocity), then the impact is considerably greater in the spinning rotor case than in the case where the gyroscope is constrained to move freely in the horizontal plane with the same angular velocity as the former precessional velocity just prior to impact. This is surprising because French [5] (in his discussion of a steadily precessing gyroscope) shows that the centrifugal force of a gyroscope in the same situation except that it is allowed to precess steadily, and is not stopped dead, exhibits no apparent change of mass within the realm of Newtonian mechanics in that the spinning rotor exhibits the same centrifugal force independent of spin, the angular velocity of the non-spinning gyroscope (for comparison’s sake) which is constrained to move freely in a horizontal plane being the same. But, experimentally [2, 3], both in the impact case and also in the steadily precessing case which were just mentioned, these Newtonian results are not, in general, observed … even to first order! Also, it is shown that Newtonian mechanics is either discontinuous or paradoxical.
