A ceiling fan is rotating at 0.96 rev/s. When turned off, itslows uniformly to a

Question

A ceiling fan is rotating at 0.96 rev/s. When turned off, itslows uniformly to a stop in 2.4 min. (a) How manyrevolutions does the fan make in this time? (b) Using theresult from part (a), find the number of revolutions the fan mustmake for its speed to decrease from 0.96 rev/s to 0.48 rev/s.

Explanation / Answer

We know that w = wo + @ t ==> 0 = 0.96 rev/s + @ * 2.4 * 60 s ==> @ = - 0.00666 rev/s^2 So that we have theta = wo t + 0.5 @ t^2 = 0.96 * 2.4 * 60 - 0.5 * 0.00666 * (2.4 * 60)^2 = 69.12 rev We know that w^2 = wo^2 + 2 @ theta ==> theta = w^2 - wo^2 / 2 @ = 0.48^2 - 0.96^2 / 2 * -0.00666 = 51.89 rev

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