An electric motor exerts a constant torque of 10 Nm on a grindstone mounted on its shaft. The moment of inertia of the grindstone is I = 2.0 kgm2. The system starts from rest. A. Determine the angular acceleration of the shaft when this torque is applied. B. Determine the kinetic energy of the shaft after 8 seconds of operation. C. Determine the work done by the motor in this time. D. Determine the average power delivered by the motor over this time interval

Angular acceleration = 5 rad / s ^2

Kinetic energy = 0.391 J

Work done = 0.391 J

P = 6.25 W

Explanation:

The torque is given as moment of inertia * angular acceleration

angular acceleration = torque / moment of inertia

= 10/2 = 5 rad / s^2

The kinetic energy is = 1/2 Iw^2

w = angular acceleration/time

=5/8 = 0.625 rad / s

1/2 * 2 * 0.625^2

=0.391 J

The work done is equal to the kinetic energy of the motor at this time

W = 0.391 J

The average power is = torque * angular speed

= 10 * 0.625

P = 6.25 W