Abstract In a previous work, Hoang and Tram discovered a new mechanism for destruction of nanoparticles due to suprathermal rotation of grains in stationary C-shocks, which is termed rotational disruption. In this paper, we extend our previous study for nonstationary shocks driven by outflows and young supernova remnants that have dynamical ages shorter than the time required to establish a stationary C-shock, which is composed of a C-shock and a J-shock tail (referred to as CJ-shock). For the C-shock component, we find that the smallest nanoparticles (size ≲1 nm) of weak materials (i.e., tensile strength S max ≲ 109 erg cm−3) can be rotationally disrupted owing to suprathermal rotation induced by supersonic neutral drift. For the J-shock component, although nanoparticles are rotating thermally, the smallest ones can still be disrupted because the gas is heated to higher temperatures by J-shocks. We then model microwave emission from rapidly spinning nanoparticles where the grain size distribution has the lower cutoff determined by rotational disruption for the different shock models. We also calculate the spectral flux of microwave emission from a shocked region at a distance of 100 pc from the observer for the different gas density, shock age, and shock velocities. We suggest that microwave emission from spinning dust can be used to trace nanoparticles and shock velocities in dense molecular outflows. Finally, we discuss a new way that can release molecules from the nanoparticle surface into the gas in the shocked regions, which we name rotational desorption.