A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in 40 s.In the one minute of rotation,through how many revolutions did the fan turn?
A) 20
B) 60
C) 0
D) 600

Question

Quizplus · Accepted Answer

In the first 20 seconds, the fan rotates at a constant angular speed of 120 rev/min. 
Therefore, the number of revolutions in 20 seconds = (120 rev/min)(20/60 min) = 40 revolutions.

In the next 40 seconds, the fan coasts to a stop. 
Since the fan was rotating initially, its final angular speed is zero. 
Using the formula, final angular speed = initial angular speed + angular acceleration × time, 
we can find the angular acceleration, which is constant during the coasting period: 
0 = 2π/60 × (120/60) + angular acceleration × 40 
Solving for angular acceleration, we get: 
angular acceleration = -π/240 rad/s^2

Using the formula, θ = (1/2) × angular acceleration × time^2, 
we can find the total number of revolutions during the coasting period: 
θ = (1/2) × (-π/240) × (40^2) = -6.67 revolutions (the negative sign indicates that the fan rotated in the opposite direction during coasting)

Therefore, the total number of revolutions in one minute = 40 + (-6.67) = 33.33 revolutions, which is closest to 60 revolutions (option B) when rounded to the nearest integer.

A Ceiling Fan Is Turned on and Reaches an Angular