You've been asked to design a flywheel and the associated emergency friction braking system for an electric vehicle. In order to fit the available space, the flywheel must be cast in the form of a solid steel disk with a thickness of \(50 \mathrm{~mm}\) and a radius that cannot exceed \(0.20 \mathrm{~m}\). For safety purposes, the emergency braking system must slow the flywheel from 6000 revolutions per minute to 0 in 12 revolutions. You know that typical braking systems utilize a pair of "shoes" mounted on calipers to squeeze the thickness of the disc symmetrically near its edge, but you are concerned about how much force the brake shoes might have to exert on the disk.