Question

A 210 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 2000 rpm in 4.6 s ?

Answer 1

given

mass m = 0.21 kg

diameter d = 0.25 m

radius r = d/2 = 0.125 m

initial angular speed wi = 0

final angular speed wf = 2000 rpm = 2000*2*3.14/60 = 209.3 rad/s

time t = 4.6 sec

angular acceleration (alpha) = wf-wi/t = 209.3-0/4.6 = 45.5 rad/s^2

moment of inertia I = 1/2mr^2 = 1/2*0.21*0.125^2 = 1.64*10^-3 kg m^2

torque T = I*alpha

T = 1.64*10^-3*45.5 = 0.0746 Nm