A stroboscope is a light that flashes on and off at a constant rate

Problem: A stroboscope is a light that flashes on and off at a constant rate. It can be used to illuminate a rotating object, and if the flashing rate is adjusted properly, the object can be made to appear stationary. (a.) What is the shortest time between flashes of light that will make a three-bladed propeller appear stationary when it is rotating with an angular speed of 16.7 rev/s?(b.) What is the next shortest time?

The frequency of the propeller = f = 16.7 rps.
The time period of the propeller (time taken for one complete rotation) = 1/f = 1/16.7 = 0.06 sec

Let the blades of the propeller be marked 1,2 and 3. Let the blade no. 1 be at a given position at time t=0. Let a light flash from stroboscope fall on it so that it can be seen by an observer.

The next blade (no.2) will be at the same position which no.1 had at t=0 after 0.06/3 = 0.02 sec. If the next light flash arrives after 0.02 sec, the observer will see blade no. 2 at the earlier position of blade no.1. As all blades are identical, to the observer it will appear as if the blade has not moved at all i.e. the propeller will appear as stationary.

a) Shortest time between flashes to make the propeller stationary = 0.02 sec

After another 0.02 sec, blade no. 3 will be at the given position. If the second flash arrives after 0.04 sec (instead of 0.02 sec), the observer will see blade no. 3 at the position and again to him the propeller will appear stationary.

b) Next shortest time = 0.04 sec