The blades of a fan running at low speed turn at 270 rpm. When the fan is switched to high speed, the rotation rate increases uniformly to 4

Question

The blades of a fan running at low speed turn at 270 rpm. When the fan is switched to high speed, the rotation rate increases uniformly to 440 rpm in 5.95 s. What is the magnitude of the angular acceleration of the blades?

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Ladonna 4 years 2021-08-14T09:29:50+00:00 1 Answers 71 views 0

Answers ( )

  1. haidang
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    2021-08-14T09:31:14+00:00
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    Answer:

    The angular acceleration of the blades is 3\ rad/s^2.                                

    Explanation:

    Given that,

    Initial angular velocity of the blade of fan, \omega_i=270\ rpm=28.27\ rad/s

    Final angular velocity of the blade of a fan, \omega_f=440\ rpm=46.07\ rad/s

    Time, t = 5.95 s

    The angular acceleration of the blades is equal to the rate of change of its angular velocity. It is given by :

    \alpha =\dfrac{\omega_f-\omega_i}{t}\\\\\alpha =\dfrac{46.07-28.27}{5.95}\\\\\alpha =2.99\ rad/s^2\\\\\alpha =3\ rad/s^2

    So, the magnitude of the angular acceleration of the blades is 3\ rad/s^2.

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