Question

a ceiling fan is rotating at 0.96 rev/sec. when turned off, it slows uniformly to a stop in 2.4 min. How many revolutions does the fan make in this time? Can anyone help me with this question?

Answer 1

When the decrease in velocity (the acceleration) is uniform, the average velocity is [Initial velocity - Final velocity]/2

We know tha the initial velocity is 0.96 rev / sec and the final velocity is 0,

Then, the average velocity is  [0.96 / 2 ]rev /sec = 0.48 rev/sec.

Also, by defintion,

average velocity = number of  rev / time,

From which, number of rev = average velocity *  time

So, number of rev = 0.48 rev/sec * 2.4 min * 60sec /min = 69.12 rev

Answer: 69.12 revolutions