Using a Stroboscope to Make a Propeller Appear Stationary

[rcmango]

Homework Statement

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 14.4 rev/s?
s

(b) What is the next shortest time?

Homework Equations

The Attempt at a Solution

not sure where to start.

 

[Shooting Star]

When the propellor rotates by 120 deg, it looks the same. The light should flash again by the time the propellor has done this.

 

[ogb p]

I would approach this problem by first understanding the basic principles of a stroboscope and how it works. A stroboscope uses the concept of persistence of vision, where the human eye retains an image for a brief moment after it is no longer present. By flashing a light at a consistent rate, the stroboscope can create an illusion of a stationary object.

To answer part (a), we can use the formula for rotational frequency, f = ω/2π, where f is the frequency in Hz and ω is the angular speed in radians per second. Rearranging the formula, we get ω = 2πf. Substituting the given values, we get ω = 2π(14.4 rev/s) = 28.8π rad/s.

Since we want the propeller to appear stationary, we need the flashing rate of the stroboscope to match the angular speed of the propeller. This means the time between flashes should be equal to the time it takes for the propeller to complete one full rotation (2π/ω). Therefore, the shortest time between flashes in this case would be 2π/28.8π = 1/14.4 s = 0.0694 s.

For part (b), we can find the next shortest time by dividing the time between flashes by a whole number, as this will still match the angular speed of the propeller. So, the next shortest time would be 1/28.8 s = 0.0347 s.

In conclusion, by understanding the principles of a stroboscope and using the formula for rotational frequency, we can determine the shortest and next shortest times between flashes of light to make a three-bladed propeller appear stationary when rotating at an angular speed of 14.4 rev/s.