Question

A ceiling fan is rotating at 1.1rev/s . When turned off, it slows uniformly to a stop in 2.4min .How many revolutions does the fan make in this time?
Using the result from part A, find the number of revolutions the fan must make for its speed to decrease from 1.1rev/s to 0.55rev/s .

Answer 1

The time given is t = 2.4min = 2.4 (60s) = 144s

using rotational kinematics

ωf - ωi = α t

given ωi = 1.1rev/s and ωf = 0 , so

α = - ωi / t

= -1.1 rev/s / 144s = - 0.00764 re/s^2

number of revolution made is

ωf^2 - ωi^2 = 2 α θ

0 - (1.1)^2 = 2 ( -0.00764) θ

θ = 79.2 rev

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number of revolution made froom 1.1rev /s to 0.55rev/s is

(0.55)^2 - (1.1)^2 = 2 ( -0.00764) θ

θ = 59.4 rev