‏A 50 – N x m torque acts on a wheel with a moment of inertia 150 kg x m² . If the wheel starts from rest , how long will it take the wheel

Question

‏A 50 – N x m torque acts on a wheel with a moment of inertia 150 kg x m² . If the wheel starts from rest , how long will it take the wheel to make one revolution ?

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Phúc Điền 5 months 2021-08-26T05:46:47+00:00 1 Answers 25 views 0

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  1. Amity
    0
    2021-08-26T05:48:11+00:00
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    Answer:

    t = 6.17 s

    Explanation:

    For a 1 revolution movement, \triangle \theta = 2\pi

    Torque, \tau = 50 Nm

    Moment of Inertia, I = 150 kg m^2

    If the wheel starts from rest, w_{0} = 0 rad/s

    The angular displacement of the wheel can be given by the formula:

    \triangle \theta = \omega_0 t + 0.5 \alpha t^2…………….(1)

    Where \alpha is the angular acceleration

    \tau = I \alpha\\\alpha = \frac{\tau}{I} \\\alpha = 50/150\\\alpha = 0.33 rad/s^2

    To get t, put all necessary parameters into equation (1)

    2\pi = 0(t) + 0.5(0.33)t^2\\2\pi =0.5(0.33)t^2\\t^2 = \frac{4 \pi}{0.33} \\t^2 = 38.08\\t = 6.17 s

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