A flywheel of moment of inertia 0.32 kgm^2 is rotated steadily at 120rad/s by a 50 W electric motor. (i)find the kinetic energy and angular momentum of the flywheel. (ii) calculate the value of frictional couple opposing the rotation. (iii)find the time taken for the wheel to come to rest after the motor has been switched off.

Answer 1

(i) First compute the moment of inertia, I, with the formula for a disc or cyliner. The kinetic energy is (1/2)I w^2 and the angular momentum is I w.

(ii) The electric power driving the motion is T*w, where T is the torque. Set that equal to the 50W electrical power input and solve for T. The electrical motor torque in steady state operation equals the frictional torque. The words torque and couple are interchangeable.

(iii) During the slowdown time, t:

T*t = initial angular momentum = I w.

You know T from (ii) and I w from (i). . Solve for the time, t.