# Impact of Gearbox on Motor Inertia

If you consider a motor attached to a spur gearbox with a reduction ratio of say $$r=50:1$$ which is then back-driven so that the motor acts as a generator, what would be the effective moment of inertia of the system? If the motor has a rotor inertia of say $$1*10^{-5} kgm^2$$ and the gearbox has a mass inertia of $$1*10^{-6} kgm^2$$ would I be correct in calculating the overall inertia through

$$I_{total}=r^2I_{rotor}+I_{gearbox}=0.025 kgm^2$$