A person walks into a room and switches on the ceiling fan. The fan accelerates

Question

A person walks into a room and switches on the ceiling fan. The fan accelerates with constant angular acceleration for 18s until it reaches its operating angular speed of 2.0rotations/s - after that its speed remains constant as long as the switch is "on". The person stays in the room for a short time; then, 5.5 minutes after turning the fan on, she switches it off again and leaves the room. The fan now decelerates with constant angular acceleration, taking 2.4 minutes to come to rest.

What is the total number of revolutions made by the fan, from the time it was turned on until the time it stopped?

Express your answer using two significant figures.

Explanation / Answer

let alfa is the angular acceleration in the first 18 s

wo = 0

w1 = 2 rotations/s = 2*2*pi = 12.56 rad/s

alfa = (w1-wo)/t

= (12.56-0)/18

= 0.698 rad/s^2

let alfa' is the angular acceleration after the switch is off.

w1 = 12.56 rad/s

w2 = 0

alfa' = (w2-w1)/t

= (0-12.56)/(2.4*60)

= -0.0872 rad/s^2

total angular displacement = (wo*t1 + 0.5*alfa*t1^2) + w1*t2 + (w1*t3 + 0.5*alfa'*t3^2)

= (0 + 0.5*0.698*18^2) + (12.56*(5.5*60-18)) + (12.56*2.4*60 - 0.5*0.0872*(2.4*60)^2)

= 4936.34 radisna

= 4936.4/(2*pi)

= 785.65 rotations <<<<<<<<<--------Answer

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