two spheres rotating out of sync with reversed delay

Hi sorry for the ambiguous title.

Basically I need some help with rigging this. The idea is that two spheres are sharing the same space, one smaller than the other. The outer sphere is supposed to be gell-like and semi transparent. The inner smaller sphere is more solid.

The effect I’m after is so that when the inner sphere rotates, the outter sphere copies it. Which I can do no problem. But how here’s where I’m stuck, you see I want the outter sphere to carry on rotating a little while longer after the inner sphere has stopped.

I know I can animate it seperatly, but in my animation there is going to be a lot of this so was wondering if there were any practical rig ideas for this effect.

Many thanks for any help.