A Ferris wheel completes 7 revolutions in 14 minutes. The radius of the Ferris wheel is 30 feet. What is the linear velocity of the Ferris wheel in inches per second?

Answer 1

Convert rev/min to radians per min:

(7 rev/14 min) * (2pi rad/1 rev) = pi radian/min

Convert rad/min to rad/sec. This is the angular velocity:

(pi rad/min)*(1min/60 sec) = pi/60 rad/sec

Linear velocity = angular velocity * radius

(pi/60 rad/sec) * 30ft = 0.5pi ft/sec

Convert ft/sec to in/sec:

(0.5pi ft/sec) * 12 in/1 ft = 6pi in/sec