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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?

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Answer:

Ratio of the centripetal accelerations = 16

Explanation:

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

We have centripetal acceleration

         [tex]a=\frac{v^2}{r}=\frac{(r\omega )^2}{r}=r\omega ^2[/tex]

Ratio of centripetal acceleration

         [tex]\frac{a_1}{a_2}=\frac{r\omega_1 ^2}{r\omega_2 ^2}=\left ( \frac{440}{110}\right )^2=4^2=16[/tex]

Ratio of the centripetal accelerations = 16

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