Question

A celling fan has two different angular speed setting: omega_1 = 440 rev/min and omega_2 = 110 rev/min. what is the ratio a_1/a_2 of the centripetal accelerations of a given point on a blade?

Answer 1

Ratio of the centripetal accelerations = 16

Step-by-step explanation:

We have ω₁ = 440 rev/min, ω₂ = 110 rev/min

We have centripetal acceleration

`a=(v^2)/(r)=((r\omega )^2)/(r)=r\omega ^2`

Ratio of centripetal acceleration

`(a_1)/(a_2)=(r\omega_1 ^2)/(r\omega_2 ^2)=\left ( (440)/(110)\right )^2=4^2=16`

Ratio of the centripetal accelerations = 16