Question

The Montauk Point Lighthouse on Long Island has dual beams (two light sources opposite each other). Ships at sea observe a blinking light every five seconds. What rotation speed is required to do this?

Short answer

The required rotation speed is$\frac{2\mathrm{\pi }}{5}\mathrm{rad}/\sec$.

Step-by-step solution

Step 1. Given information.

Since the ships are observing the blinking light in every $5$seconds, this means, that the light source is completing its one revolution in $5$seconds.

We know that in one revolution the light source will rotate by $360°$or $2\mathrm{\pi }$radians.

So the angular speed is,

$$\begin{gathered} \omega =\frac{2\mathrm{\pi }}{T} \\ \omega =\frac{2\mathrm{\pi }}{5}\mathrm{rad}/\sec \end{gathered}$$