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Let's think about this a bit. First, if you want your flywheel to be at all efficient, it's going to be in a vacuum, using magnetic bearings, and the coupling is going to be an electric motor/generator. (You can look up recent research on flywheel energy storage for more details.)
So if you have the flywheel rotating in a horizontal plane, you're not going to have any flywheel torque from driving on level ground, only if you pitch up or down, or from side to side. So you mount it in gimbals (like a kid's gyroscope toy), with room to tilt, and some hydraulic dampers at the end of travel. Do this right, and it maybe even becomes a safety feature, the anti-rollover device :-)
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