Maximum force and revolutions

Question

An ant is at the end of a fan blade when it is turned on. It is a high speed fan with blades measuring 0.20 m long. If the ant has a mass of 0.20 g and can hold on to the fan blade with a maximum force of 0.0124 N. What is the maximum number of revolutions per minute the can can run at before the ant will be flung off?

Answer 1

The maximum force for the ant to hold on to the fan has to be greater than the centripetal force

F > mω²r, where ω = 2πN/60

So

N < 60/(2π) * sqrt(F/mr) = 60/(2π) sqrt(0.0124/(0.0002*0.2)) = 168 Revolution/min