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

Answer:

Ratio of the centripetal accelerations = 16

Explanation:

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

We have centripetal acceleration

         $a=\frac{v^2}{r}=\frac{(r\omega )^2}{r}=r\omega ^2$

Ratio of centripetal acceleration

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

Ratio of the centripetal accelerations = 16