During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 33.3 rad/s. Find the angular displacement of t

Question

During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 33.3 rad/s. Find the angular displacement of the tub during a spin of 77.5 s, expressed both in radians and in revolutions.

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Bình An 6 months 2021-08-30T13:57:38+00:00 1 Answers 3 views 0

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    2021-08-30T13:59:03+00:00

    Answer:

    The angular displacement of the tub will be 2580.75 rad or 411 revolutions.

    Explanation:

    We know the relation between angular velocity (\omega), the angular displacement (\theta) and time (t) is given by

    \omega = \dfrac{\theta}{t}

    Given \omega = rad~s^{-1} and the time (t) required to complete a spin is 77.5 s.

    Therefore, the required angular displacment (\theta) is

    && \theta = \omega \times t\\&or,& \theta = 33.3~rad~s^{-1} \times 77.5~s = 2580.75~rad

    Also we know that,

    && 2 \pi~rad = 1~revolution\\&or,& 580.75~rad  = \dfrac{2580.75}{2~\pi} \approx 411~revolutions

    So, the angular displacement of the tub will be 2580.75 rad or 411 revolutions.

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