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.

Answer 1

Heretime taken to attain the angular speed of ?_f is t= 18 sec

?_f =  2.0

?_i = initila angular speed = 0

We know that total number of revolutions for 18 sec is N1 =[(?_i+ ?_f)/2]*t

                                                                                         =[(2 rot/s+ 0)/2]*18 sec

                                                                                        = 18 rotations

Now fan isz rotating with constant angular speed?_f for 5.5 min

Then time t ' = 5.5 min = 330 sec

Then total rotations during interval t ' is N2 =?_f*t ' = 2 rot/sec*330 sec = 660 rotations

Now after this it decelerates and comes to rest in 2.4min

Then t " = 2.4 min = 2.4*60 sec = 144 sec

Then number of rotations during this time interval is N3 =[(?f + 0 )/2]* t" = (2 rot/sec/2)*144 sec

                                                                                  = 144 rotations

Then total rotations is N = N1 + N2 + N3 = 18 + 660 + 144 =822 ROTATIONS