Interstellar dust grains can be spun up by radiative torques, and the resulting centrifugal force may be strong enough to disrupt large dust grains. We examine the effect of this rotational disruption on the evolution of grain size distribution in galaxies. To this goal, we modify our previous model by assuming that rotational disruption is the major small-grain production mechanism. We find that rotational disruption can have a large influence on the evolution of grain size distribution in the following two aspects especially for composites and grain mantles (with tensile strength $sim 10^7$ erg cm$^{-3}$). First, because of the short time-scale of rotational disruption, the small-grain production occurs even in the early phase of galaxy evolution. Therefore, even though stars produce large grains, the abundance of small grains can be large enough to steepen the extinction curve. Secondly, rotational disruption is important in determining the maximum grain radius, which regulates the steepness of the extinction curve. For compact grains with tensile strength $gtrsim 10^9$ erg cm$^{-3}$, the size evolution is significantly affected by rotational disruption only if the radiation field is as strong as (or the dust temperature is as high as) expected for starburst galaxies. For compact grains, rotational disruption predicts that the maximum grain radius becomes less than 0.2 $mu$m for galaxies with a dust temperature $gtrsim 50$ K.
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