A fan rotating with an initial angular velocity of 1500 rev/min is switched off. In 2.5 seconds, the angular velocity decreases to 400 rev/m

Question

A fan rotating with an initial angular velocity of 1500 rev/min is switched off. In 2.5 seconds, the angular velocity decreases to 400 rev/min. Assuming the angular acceleration is constant, answer the following questions.
How many revolutions does the blade undergo during this time?
A) 10
B) 20
C) 100
D) 125
E) 1200

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Khoii Minh 4 years 2021-08-08T12:16:01+00:00 1 Answers 10 views 0

Answers ( )

  1. trungdung22
    0
    2021-08-08T12:17:35+00:00
    Reply

    Answer:

    The blade undergoes 40 revolutions, so neither of the given options is correct!

    Explanation:

    The revolutions can be found using the following equation:

    \theta_{f} = \theta_{i} + \omega_{i}*t + \frac{1}{2}\alpha*t^{2}

    Where:

    α is the angular acceleration

    t is the time = 2.5 s

    \omega_{i} is the initial angular velocity = 1500 rev/min                

    First, we need to find the angular acceleration:

    \alpha = \frac{\omega_{f} - \omega_{i}}{t} = \frac{400 rev/min*2\pi rad*1 min/60 s - 1500 rev/min *2\pi rad*1 min/60 s}{2.5 s} = -46.08 rad/s^{2}

    Now, the revolutions that the blade undergo are:

    \theta_{f} - \theta_{i} = \omega_{i}*t + \frac{1}{2}\alpha*t^{2}

    \Delta \theta = 1500 rev/min *2\pi rad*1 min/60 s*2.5 s - \frac{1}{2}*(46.08 rad/s^{2})*(2.5)^{2} = 248.7 rad = 39.9 rev        

    Therefore, the blade undergoes 40 revolutions, so neither of the given options is correct!

    I hope it helps you!                              

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