  Core rotation rates have been measured for red giant stars using
asteroseismology. This data, along with helioseismic measurements and open
cluster spin down studies, provide powerful clues about the nature and
timescale for internal angular momentum transport in stars. We focus on two
cases: the metal poor red giant KIC 7341231 ("Otto") and intermediate mass core
helium burning stars. For both we examine limiting case studies for angular
momentum coupling between cores and envelopes under the assumption of rigid
rotation on the main sequence. We discuss the expected pattern of core rotation
as a function of mass and radius. In the case of Otto, strong
post-main-sequence coupling is ruled out and the measured core rotation rate is
in the range of 23 to 33 times the surface value expected from standard spin
down models. The minimum coupling time scale (.17 to .45 Gyr) is significantly
longer than that inferred for young open cluster stars. This implies
ineffective internal angular momentum transport in early first ascent giants.
By contrast, the core rotation rates of evolved secondary clump stars are found
to be consistent with strong coupling given their rapid main sequence rotation.
An extrapolation to the white dwarf regime predicts rotation periods between
330 and .0052 days depending on mass and decoupling time. We identify two key
ingredients that explain these features: the presence of a convective core and
inefficient angular momentum transport in the presence of larger mean molecular
weight gradients. Observational tests that can disentangle these effects are
discussed.
