  Dissipative and dispersive optomechanical couplings are experimentally
observed in a photonic crystal split-beam nanocavity optimized for detecting
nanoscale sources of torque. Dissipative coupling of up to approximately $500$
MHz/nm and dispersive coupling of $2$ GHz/nm enable measurements of sub-pg
torsional and cantilever-like mechanical resonances with a thermally-limited
torque detection sensitivity of 1.2$\times 10^{-20} \text{N} \,
\text{m}/\sqrt{\text{Hz}}$ in ambient conditions and 1.3$\times 10^{-21}
\text{N} \, \text{m}/\sqrt{\text{Hz}}$ in low vacuum. Interference between
optomechanical coupling mechanisms is observed to enhance detection sensitivity
and generate a mechanical-mode-dependent optomechanical wavelength response.
