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You are focused on only one of the impacts of a lightened flywheel – and the least important one – that is in the decrease in the total mass of the vehicle. The best way to understand the other impacts is to recognize that a flywheel is a device for storing energy in the form of angular momentum. Angular momentum is equal to the polar moment of inertia of the flywheel (basically the flywheel’s mass times the square of that mass’s distance from the center of the flywheel) multiplied by the flywheel’s angular velocity (how fast it is spinning). Making the flywheel spin at a certain speed – say 3000 rpm - takes energy. Slowing the flywheel from 3000 rpm to 1000 rpm requires energy to be removed. If you reduce the mass of the flywheel or move mass closer to the center of the flywheel, it takes less energy to get the flywheel up to 3000rpm and less energy needs to be removed to get the flywheel from 3000rpm back to 1000rpm. The traditional purpose of the flywheel (in an automobile) is to store energy before the car begins to accelerate and then use the energy stored in the flywheel to help get the vehicle going. This is particularly useful in underpowered vehicles that need help getting off the line. A flywheel with greater mass further from its center is actually better for this. The tradeoff is, you have to reapply that energy to the flywheel as the engine speed continues to increase – potentially multiple times to make it to your target speed. And each time you put the clutch in and wait for the engine to slow down to shift, all of that stored energy is wasted through friction and pumping losses. With a lighter flywheel that wasted energy would have been used to accelerate your 10 lbm lighter car. Also, with a heavier flywheel, it takes longer to bleed off the energy stored in the flywheel which is why lighter flywheels give you a quicker drop in revs when you shift (my favorite part). Automotive engineers spend a fair amount of time balancing these considerations for a given application. In our relatively high powered cars, that balance is almost always altered to the lighter the better when it comes to flywheels. Incidentally, the same principals apply to all rotating components in the drive train with a somewhat different impact for those items that are downstream of the clutch which is why lighter engine components, drive shafts, wheels, and brakes have a much bigger impact than just reducing mass of the car.
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