Question
A ceiling fan has two different angular speed settings: 1 = 475 rev/min and 2 = 170 rev/min. What is the ratio a1/a2 of the centripetal accelerations of a given point on a fan blade?
Centripetal acceleration at a distance R and angular speed w is a = R w^2. The ratio of the centripetal accelerations, for a fixed value of R, is the square of the angular speed ratio,
a1/a2 = (w1/w2)^2 =(475/210)^2 = 5.12
Centripetal acceleration at a distance R and angular speed w is a = R w^2. The ratio of the centripetal accelerations, for a fixed value of R, is the square of the angular speed ratio,
a1/a2 = (w1/w2)^2 =(475/210)^2 = 5.12