Corotation of a planetary magnetosphere with the rotation frequency of the planet is maintained by the viscous torque exerted by ion-neutral collisions in the planetary atmosphere, this torque being transmitted to the magnetosphere by Birkeland currents. In a steady state this torque balances the inertial drag associated with the production and/or outward transport of magnetospheric plasma. The viscous torque in the atmosphere requires some departure from rigid corotation, i.e., some difference between the average rotation velocities of the ionospheric plasma and of the un-ionized atmosphere. In this paper we calculate the inertial corotation lag as a function of radial distance in the magnetosphere, the solution being parameterized in terms of the Pedersen conductivity of the atmosphere and the rate at which plasma mass is produced and transported outward in the magnetosphere. Although insignificant in the case of earth's magnetosphere, the calculated inertial corotation lag is significant in the case of Jupiter's magnetosphere, where the rotation frequency may decrease by a factor of the order of 2 between the planetary surface and the magnetopause. One interesting consequence is that the active sector of Jupiter's magnetosphere (which is associated with a longitudinally restricted sector of enhanced ionospheric conductivity) should rotate faster, at a given distance, than adjacent longitude sectors and should therefore sweep up plasma from adjacent longitudes, thus amplifying the preexisting enhancement of plasma concentration in the active longitude sector.