We have investigated the NMR line shapes of superfluid He-3-B in a rotating
cylinder. In the vortex-free state at sufficiently large angular velocity
of rotation, Ohm greater than or similar to 1 rad/s, the main feature of th
e absorption spectrum is a large frequency-shifted peak above the Larmor fr
equency. The shape of this counter-flow peak is both measures and calculate
d as a function of external magnetic field strength, angular velocity, temp
erature,and number of vortex lines. The NMR spectrum is derived from the ca
lculated order-parameter texture. Reasonable agreement with the measured li
ne shape is obtained by including line-broadening effects due to the extern
al field inhomogeneity and Leggett-Takagi relaxation.