Anisotropic outgassing from comets exerts a torque sufficient to rapidly change the angular momentum of the nucleus, potentially leading to rotational instability. Here, we use empirical measures of spin changes in a sample of comets to characterize the torques and to compare them with expectations from a simple model. Both the data and the model show that the characteristic spin-up timescale, $tau_s$, is a strong function of nucleus radius, $r_n$. Empirically, we find that the timescale for comets (most with perihelion 1 to 2 AU and eccentricity $sim$0.5) varies as $tau_s sim 100 r_n^{2}$, where $r_n$ is expressed in kilometers and $tau_s$ is in years. The fraction of the nucleus surface that is active varies as $f_A sim 0.1 r_n^{-2}$. We find that the median value of the dimensionless moment arm of the torque is $k_T$ = 0.007 (i.e. $sim$0.7% of the escaping momentum torques the nucleus), with weak ($<$3$sigma$) evidence for a size dependence $k_T sim 10^{-3} r_n^2$. Sub-kilometer nuclei have spin-up timescales comparable to their orbital periods, confirming that outgassing torques are quickly capable of driving small nuclei towards rotational disruption. Torque-induced rotational instability likely accounts for the paucity of sub-kilometer short-period cometary nuclei, and for the pre-perihelion destruction of sungrazing comets. Torques from sustained outgassing on small active asteroids can rival YORP torques, even for very small ($lesssim$1 g s$^{-1}$) mass loss rates. Finally, we highlight the important role played by observational biases in the measured distributions of $tau_s$, $f_A$ and $k_T$.
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