  We present new radial velocities for 87 globular clusters around the
elliptical galaxy NGC 4472, and combine these with our previously published
data to 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
globular cluster system. The new data confirms our previous discovery that the
metal-poor clusters have significantly higher velocity dispersion than the
metal-rich clusters in NGC 4472. We also find very little or no rotation in the
more spatially concentrated metal-rich population, with a resulting upper limit
for this population of (v/sigma)_{proj} < 0.34 at a 99% confidence level. The
very small angular momentum in the metal-rich population requires efficient
angular momentum transport during the formation of this population which is
spatially concentrated and chemically enriched. Such angular momentum transfer
can be provided by galaxy mergers, but has not been achieved in other extant
models of elliptical galaxy formation that include dark matter halos. We also
calculate the velocity dispersion as a function of radius, and show that it is
consistent with roughly isotropic orbits for the clusters and the mass
distribution of NGC 4472 inferred from X-ray observations of the hot gas around
the galaxy.
