An electric fan blade is rotating at a rate of 230 rev/min when it is subsequently switched off.

Question

An electric fan blade is rotating at a rate of 230 rev/min when it is subsequently switched off. The blade then takes 37 seconds to come to rest.

A. What is the initial angular speed of the fan blade?

𝜔₀ =  rad/s

B. What is the angular acceleration of the fan blade?

𝛼 =  rad/s²

C. How many revolutions does the fan blade go through after the fan is switched off?

 revolutions

I don't know how to do this, the only problems we went over in class had a radius and rotating speed :(

Answer 1

Given

Frequency =230 rev/min= 230/60 rev /s

angular velocity = 2∏ Frequency = 2∏ * 23/6 rad /s

Final angular velocity = 0

Using w = w0 + ∝t

∝ = angular acceleration

w = 0 as as fan stops after 37 sec

0 = 2∏ * 23/6 + ∝ *37

∝ = - (2∏ * 23)/(37*6) rad/s2

Angle travelled before it stops is θ

Use w² = w0² + 2 ∝ θ

θ= w0² /2 ∝

Plug in w0 and ∝ to get θ

No of revolutions = θ/2∏