Quote from Cue-Ball :

No, it wouldn't. Think of a figure skater doing a spin. When she pulls her arms in close to her body the spin accelerates, but her mass has not changed.

Are you suggesting to make a variable inertia flywheel? One with actuators to move the mass of the flywheel towards the center and outwards according to the situation?

I was thinking on the lines of:

1. Take flywheel with inertia X

2. Machine 1kg worth of material of the outer rim.

The inertia is now Y

3. Add the the material close to the center of the flywheel

The inertia is now Z

Now compare the inertias and you'll get: X > Z > Y

So taking the material off will reduce the inertia. But adding it back will increase it again.

Quote from March Hare :

One with actuators to move the mass of the flywheel towards the center and outwards according to the situation?

Like a torque converter?