The angular momentum of a flywheel having a rotational inertia of 0.140 kg ·m2 about its central axis decreases from 3.00 to 0.800 kg ·m2/s in 1.50 s.

(a) what is the magnitude of the average torque acting on the flywheel about its central axis during this period?
(b) assuming a constant angular acceleration, through what angle does the flywheel turn?
(c) how much work is done on the wheel?
(d) what is the average power of the flywheel?

(a). The magnitude of the average torque acting on the flywheel about its central axis during this period is 1.47 N-m.

(b). The angle that the flywheel does turn is 20.3 rad.

(c). The work done is -29.84 J.

(d). The average power of the flywheel is 19.89 W.

Explanation:

Given that,

Rotational inertia = 0.140 kg m²

Initial angular momentum of flywheel = 3.00 kg m²/s

Final angular momentum of flywheel = 0.800 kg m²/s

Time = 1.50 sec

(a). We need to calculate the magnitude of the average torque acting on the flywheel about its central axis during this period

Using formula of torque

Put the value into the formula

(b). Assuming a constant angular acceleration, through what angle does the flywheel turn

We need to calculate the angle that the flywheel does turn

Using equation for angle

Here,

Put the value of angular acceleration and angular velocity

Put the value into the formula

(c). We need to calculate the work done on the wheel

Using formula of work done

Put the value into the formula

(d). We need to calculate the average power of the flywheel

Using formula of average power

Put the value into the formula

Hence, (a). The magnitude of the average torque acting on the flywheel about its central axis during this period is 1.47 N-m.

(b). The angle that the flywheel does turn is 20.3 rad.

(c). The work done is -29.84 J.

(d). The average power of the flywheel is 19.89 W.

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