A 250 g , 25-cm diameter plastic disk is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 1900 rpm in 4.7 s ? Express your answer in newton-meters.

Question

Jonathan Burroughs · Accepted Answer

Mass of the disc, m = 250 g = 0.25 kg  Diameter of the disc, d = 25 cm = 0.25 m  Disc rotate from 0 to 1900 rmp, in t = 4.7 sec.   Moment of inertia of the disc  I=12mγ2=12(0.25)(0.252)2  I=0.00195 kgm2  =0.002 kgm2  angular frequency, ω=2π(190060)  ω=198.96 rads  ω=α  α=ωt=198.964.7=42.33 rads2  The torque is  τ=Iα=(0.00195)(42.33)  =0.0825 N⋅m