Think of it this way... your flywheel spinning is directly related to your drive shaft spinning. So if your flywheel is lighter then the amount of work that needs to overcome its current amount of motion (either 0 - resting or spinning at X) for faster motion (called inertia of motion) is less than it would be for a heavier one. So basically you will be able to do less work and have the flywheel spin up quicker. However ... this works the other way too... let off the gas and you will notice that you are slowing down due to engine braking a lot more with a lighter one.
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