An electric motor exerts a constant torque of 10N⋅m to the shaft of a grindstone with mass 16kg and radius 0.5m. If the system starts from rest, find (a) the rotational kinetic energy of the grindstone after 8s, (b) the work done by the motor during this time, and (c) the average power delivered by the motor.

Question

An electric motor exerts a constant torque of  10N⋅m to the shaft of a grindstone with mass   16kg and radius  0.5m.  If the system starts from rest, find (a) the rotational kinetic energy of the grindstone after 8s, (b) the work done by the motor during this time, and (c) the average power delivered by the motor.

bobpursley · Answer

1. find moment if inertia I
2. angular acceleration a= torque/I
3. final angular speed= wf=a*time
4. rotalional KE= 1/2 I wf^2
5. angular displacement : wf^2=2 a*d or d= wf^2/2a or 1/2 wf^2/a
6. work done by motor=torque*d
7. average power=work done/time= torque*d/8