Not only do dust particles spinning in the interstellar medium radiate electromagnetic waves, they also emit longitudinal plasma waves. In this paper the slowing-down time resulting from this plasma-wave emission is estimated analytically. For very small grains with an intrinsic electric dipole moment, it is, in most interstellar environments, orders of magnitude shorter than the usual slowing-down time due to collisional friction. For larger grains, the conclusion depends on the carried by the grain. Still, a rotating charge number of a few units is sufficient to preserve these trends in most cases, and the slow down of all dust particles up to a fraction of a micron may be determined by the plasma-wave emission. The effect of plasma-wave emission on the grain spin is also estimated. Spin-up is predicted for grain speeds V higher than the electron thermal speed. For subthermal speeds, the rotation is damped, however, and the damping time is derived analytically in the limit of small V. In this limit, the damping timescale is again shorter than the damping time due to binary collisions. This is true for the smallest grains in most interstellar environments and is conditioned by the existence of an intrinsic electric dipole moment. For larger grains, the conclusions again depend on the variation of the with the grain size. Finally, the plasma effects described in this paper are expected to be at their maximum in the cold neutral medium and in reflection nebulae, where a low temperature is combined with a still relatively high electron density. In third and fourth ranks come the warm ionized and warm neutral media, followed by photodissociation regions and molecular clouds.