A fan rotating with an initial angular velocity of 1000 rev/min is switched off. In 2 seconds, the angular velocity decreases to 200 rev/min. Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time

20 revolutions

Explanation:

Using,

Ф = (ω+ω')t/2 Equation 1

Where Ф = amount of revolution the blade undergo, ω = initial angular velocity  of the blade, ω' = Final angular velocity of the blade, t = time after switch off.

Given: ω = 1000 rev/min, ω' = 200 rev/min, t = 2 seconds = (2/60) min = 1/30 min

Substitute into equation 1

Ф = (1000+200)(1/30)/2

Ф = 1200/(30×2)

Ф = 1200/60

Ф = 20 rev.

Hence the blade undergoes 20 revolutions

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