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 t

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

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Mộc Miên 6 months 2021-08-15T13:48:35+00:00 1 Answers 4 views 0

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    0
    2021-08-15T13:50:18+00:00

    Answer:

    128.61 Watts

    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 = \frac{\omega_f^2- \omega_i^2}{2\theta}

    \alpha = \frac{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

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