An electric fan is running on HIGH. After fan has been running for 1.1 minutes, the LOW button is pushed. The fan slows down to 105 rad/sec in 1.85 seconds. The blades of the fan have a diameter of 6.2 meters and their deceleration rate is 4.4 rad/sec2. 1)What was the initial angular speed of the fan in rev/sec? ωi =

ωi = 15.4 rev/sec

Explanation:

Since the movement of the fan is rotating, we are thus dealing with Rotational motion. In rotational motion, for angular speed to take place also means angular acceleration is also occurring.

angular acceleration = α = (change in speed)/(change in time)

angular acceleration = α = Δw/Δt = (ω - ωi) /(t- t₀) (equation 1)

                                      α =  (ω -ωi) /(t- 0)

                                      α =  (ω-ωi) /t

                                      ωi  =  ω - αt (equation 2)

where ωi is the initial angular speed.

We replace the values for ω, t and α

ωi = 105 rad/sec - ( 4.4 rad/sec² )(1.85s) = 96.86 rad/s = 15.415747788 rev/sec