A person walks into aroom and switches on the ceiling fan. The fan accelerates w

Question

A person walks into aroom and switches on the ceiling fan. The fan accelerates withconstant angular acceleration for 12 s until it reaches itsoperating angular speed of 1.7 rotations/s - after that its speedremains constant as long as the switch is "on". The person stays inthe room for a short time; then, 5.0 minutes after turning the fanon, she switches it off again and leaves the room. The fan nowdecelerates with constant angular acceleration, taking 2.4 minutesto come to rest.

What is the total number of revolutions madeby the fan, from the time it was turned on until the time itstopped?

= ? rev

A person walks into aroom and switches on the ceiling fan. The fan accelerates withconstant angular acceleration for 12 s until it reaches itsoperating angular speed of 1.7 rotations/s - after that its speedremains constant as long as the switch is "on". The person stays inthe room for a short time; then, 5.0 minutes after turning the fanon, she switches it off again and leaves the room. The fan nowdecelerates with constant angular acceleration, taking 2.4 minutesto come to rest.

What is the total number of revolutions madeby the fan, from the time it was turned on until the time itstopped?

= ? rev

What is the total number of revolutions madeby the fan, from the time it was turned on until the time itstopped?

= ? rev

Explanation / Answer

During acceleration and deceleration, the fan has an averagespeed of   1.7 / 2 = 0.85 rotations persecond. . So the motion of the fan is: .    accelerate for 12 seconds .    constant speed for 5 minutes - 12 seconds =    288 seconds .     decelerate for   2.4minutes = 144 seconds. . Total revolutions? just take   average speed * timefor each part and add: .      0.85 * 12   +    1.7 * 288    + 0.85 *144 =    622.2 revolutions

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