Question

The angular momentum of a flywheel having a rotational inertia of 0.240 kg m2 about its axis decreases from 5.70 to 0.60 kg m2/s in 1.80 s. What is the average torque acting on the flywheel about its central axis during this period?

2) Assuming a uniform angular acceleration, through what angle will the flywheel have turned?(rad)

3) How much work was done on the wheel?

4) What is the average power of the flywheel?

Answer 1

here,

torque is rate of change of angular momentum = (0.6 - 5.7) /1.8 = - 5.1/ 1.8

T = -2.83 Nm

minus sign indicates that the torque is opposite in direction to the momentum.

b)

initial angular speed , w0 = 23.75 rad/s

final angular speed , w = 0.6/I = 2.5 rad/s

angular accelration , alpha = T/I = 11.79 rad/s^2

the angle travelled , theta = w0 * t + 0.5 * alpha * t^2

theta = 23.75 * 1.8 - 0.5 * 11.79 * 1.8^2

theta = 23.65 rad

3)

Work done , W = T * theta = - 2.83 * 23.65 = - 66.93 J

4)

Power = work / time = - 66.93 /1.8 = - 37.18 W is consumed.