We present new radial velocities for 87 globular clusters around the ellipt
ical galaxy NGC 4472 and combine these with our previously published data t
o create a data set of velocities for 144 globular clusters around NGC 4472
. We utilize this data set to analyze the kinematics of the NGC 4472 globul
ar cluster system. The new data confirm our previous discovery that the met
al-poor clusters have significantly higher velocity dispersion than the met
al-rich clusters in NGC 4472. We also find very little or no rotation in th
e more spatially concentrated metal-rich population, with a resulting upper
limit for this population of (nu/sigma)(proj) < 0.34 at a 99% confidence l
evel. The very small angular momentum in the metal-rich population requires
efficient angular momentum transport during the formation of this populati
on, which is spatially concentrated and chemically enriched. Such angular m
omentum transfer can be provided by galaxy mergers, but it has not been ach
ieved in other extant models of elliptical galaxy formation that include da
rk matter halos. We also calculate the velocity dispersion as a function of
radius and show that it is consistent with roughly isotropic orbits for th
e clusters and the mass distribution of NGC 4472 inferred from X-ray observ
ations of the hot gas around the galaxy.