Question

Constants| Periodic Table Part A What torque must the motor supply to take the disk from 0 to 1600 rpm in 4.2 s? Express your answer in newton-meters A 250 g, 23-cm-diameter plastic disk is spun on an axle through its center by an electric motor. TE N-m Submit Request Answer Provide Feedback Next>

Answer 1

here,

mass , m = 250 g = 0.25 kg

diameter , d = 23 cm

radius , r = d/2 = 11.5 cm = 0.115 m

the moment of inertia about the center , I = 0.5 * m *r^2

I = 0.5 * 0.25 * 0.115^2 = 1.653 * 10^-3 kg.m^2

final angular speed , w = 1600 rpm = 167.4667 rad/s

time taken , t = 4.2 s

the angular accelration , alpha = (w - w0)/t

alpha = ( 167.4667 - 0)/4.2 = 39.87 rad/s^2

the torque supplied ot the motor , T = I * alpha

T = 1.653 * 10^-3 * 39.87 N.m

T = 6.59 * 10^-2 N.m