  The total energy E of a star as a function of its angular momentum J and mass
M in the Newtonian theory: E = E(J, M) [in general relativity, the
gravitational mass M of a star as a function of its angular momentum J and rest
mass m, M = M(J, m)], is used to determine the remaining parameters (angular
velocity, equatorial radius, chemical potential, etc.) in the case of rigid
rotation. Expressions are derived for the energy release during accretion onto
a cool (with constant entropy), rapidly rotating neutron star (NS) in the
Newtonian theory and in general relativity. A separate analysis is performed
for the cases where the NS equatorial radius is larger and smaller than the
radius of the marginally stable orbit in the disk plane. An approximate formula
is proposed for the NS equatorial radius for an arbitrary equation of state,
which matches the exact one at J = 0.
