Question

A wheel has a rotational inertia of 16 kgm2. Over an interval of 2.0 s its angular velocity increases from 7.0 rad/s to 9.0 rad/s. What is the average power done by the torque

Answer 1

128.61 Watts

Step-by-step explanation:

Average power done by the torque is expressed as the ratio of the workdone by the toque to time.

Power = Workdone by torque/time

Workdone by the torque =
`\tau \theta` =
`I\alpha * \theta`

I is the rotational inertia = 16kgm²

`\theta = angular\ displacement`

`\theta = 2 rev = 12.56 rad`

`\alpha \ is \ the\ angular\ acceleration`

To get the angular acceleration, we will use the formula;

`\alpha = (\omega_f^2- \omega_i^2)/(2\theta)`

`\alpha = (9.0^2- 7.0^2)/(2(12.54))\\\alpha = 1.28\ rad/s^(2)`

Workdone by the torque = 16 * 1.28 * 12.56

Workdone by the torque = 257.23 Joules

Average power done by the torque = Workdone by torque/time

= 257.23/2.0

= 128.61 Watts