1. A fly wheel with a mass of 50 kg is accelerated by an electric motor from rest to an angular velocity of 120rads/s in 14 seconds, if the value of k is 0.3m and there is a frictional torque of 0.07Nm calculate the torque applied, total work and the power from the motor.

Question

Assume the acceleration is constant

Answer 1

Angular acceleration of flywheel:
alpha = (120 rad/s - 0 rad/s)/14 s
alpha ~ 8.571 rad/s^2

Moment of inertia of flywheel:
I = mk^2
I = (50kg)(0.3 m)^2
I = 4.5 kg*m^2

Torque applied by motor:
Ta - Tf = I*alpha
Ta - 0.07 N*m = (4.5 kg*m^2)(8.571 rad/s^2)
Ta = 38.64 N*m

Total work done by motor on flywheel:
Work = applied torque*angle
angle = 120 rad/s * 14 s = 168 rad
Work = (38.64 N*m) (168 rad)
Work = ______ J

Power output of motor:
P = work/time
P= ______ J / 14 s
P = _______ W