A ceiling fan is rotating at 0.50 rev/s. When turned off, it slows uniformly to a stop in 11 s.

(a) How many revolutions does it make in this time?

(b) Using the result from part (a), find the number of revolutions the fan must make for its speed to decrease from 0.50 rev/s to 0.25 rev/s.

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  1. Wo = 0.5rev/s
    Wf = 0.25rev/s
    t = 11s
    Revolution = ?

    a) Acceleration = 0.5rev/s / 11s
    Acceleration = -0.045rad/s²

    Θ = Wot + 1/2(-a)t
    Θ = 0.5rev/s(11s) - 1/2(0.045rad/s²)(11²)
    Θ = 2.75rev <-- Answer

    b) Average speed = (0.5rev/s + 0.25rev/s) / 2
    Average speed = 0.375rev/s

    Θ = Vav * t / 2
    Θ = 0.375rev/s * 11s / 2
    Θ = 2.06rev <-- Answer

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