Disco de 40kg: Calculo do Tempo para Parada com Forca de Freio P

194 The 40kg disk is rotating at ω 100 rads When the force P is applied to the brake as indicated by the graph If the coefficient of kinetic friction at B is μk 03 determine the time t needed to stay the disk from rotating Neglect the thickness of the brake SOLUTION Equilibrium Since slipping occurs at brake pad Ff μkN 03 N Referring to the FBD the brakes lever Fig a ζ MA 0 N06 03 N02 P03 0 N 05556 P Thus Ff 0305556 P 01667 P Principle of Impulse and Momentum The mass moment of inertia of the disk about its center O is IO 12 mr2 12 400152 045 kgm2 IOω1 t1t2 MOdt IOω2 It is required that ω2 0 Assuming that t 2 s 045100 0t 01667 P015 dt 0450 0025 0t P dt 45 0t P dt 1800 12 5002 500t 2 1800 t 460 s Ans Since t 2 s the assumption was correct Ans t 460 s