  We have developed a mechanical absolute-rotation sensor capable of resolving
ground rotation angle of less than 1 nrad$/\sqrt{\text{Hz}}$ above $30$ mHz and
0.2 nrad$/\sqrt{\text{Hz}}$ above $100$ mHz about a single horizontal axis. The
device consists of a meter-scale beam balance, suspended by a pair of flexures,
with a resonance frequency of 10.8 mHz. The center of mass is located 3 $\mu$m
above the pivot, giving an excellent horizontal displacement rejection of
better than $3\times10^{-5}$ rad/m. The angle of the beam is read out optically
using a high-sensitivity autocollimator. We have also built a tiltmeter with
better than 1 nrad$/\sqrt{\text{Hz}}$ sensitivity above 30 mHz. Co-located
measurements using the two instruments allowed us to distinguish between
background rotation signal at low frequencies and intrinsic instrument noise.
The rotation sensor is useful for rotational seismology and for rejecting
background rotation signal from seismometers in experiments demanding high
levels of seismic isolation, such as Advanced LIGO.
