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 an additional 60 s.The ratio of the average angular acceleration for the first 20 s to that for the last 60 s is which of the following?
A) 3
B) -3
C) 0.3
D) -0.3

Question

Quizplus · Accepted Answer

Using the formula:
ω = ω0 + αt

Where:
ω0 = initial angular velocity
ω = final angular velocity
α = angular acceleration
t = time

For the first part, we have:
ω0 = 0 (initially not moving)
ω = 120 rev/min
t = 20 s

So, α1 = (ω - ω0)/t = 6 rev/min^2

For the second part, we have:
ω0 = 120 rev/min (initially moving)
ω = 0 (coasting to a stop)
t = 60 s

So, α2 = (ω - ω0)/t = -2 rev/min^2

The ratio of average angular accelerations is:
α1/α2 = (6 rev/min^2)/(-2 rev/min^2) = -3

Therefore, the answer is B) -3.

A Ceiling Fan Is Turned on and Reaches an Angular