A cooling fan is turned off when it is running at 920 rev/min. It turns 1100 revolutions before it comes to a stop. What was the fan's angular acceleration? How long did it take the fan to come to a complete stop?
To find the fan's angular acceleration, we can use the formula:
Angular acceleration (α) = (Final angular velocity (ωf) - Initial angular velocity (ωi)) / Time (t)
Given that the fan's initial angular velocity (ωi) is 920 rev/min and the final angular velocity (ωf) is 0 rev/min (since it comes to a stop), we can plug these values into the formula:
α = (0 rev/min - 920 rev/min) / t
Simplifying further, we get:
α = -920 rev/min / t
To find the time it took for the fan to come to a complete stop, we can use the formula:
ωf = ωi + α * t
Since ωf is 0 rev/min and ωi is 920 rev/min, we rearrange the formula:
t = (ωf - ωi) / α
Substituting the values, we get:
t = (0 rev/min - 920 rev/min) / -920 rev/min / t
Simplifying further:
t = 1 min
Therefore, the fan's angular acceleration is -920 rev/min divided by t, and it took 1 minute for the fan to come to a complete stop.