3550.21 – Clock with Revolutionary Bug


The largest four-faced clock in the USA is the Allen Bradley Corporation clock in Milwaukee, Wisconsin. The diameter of its face is 40 feet 3.5 inches, and its minute hand is 20 feet in length. If you are an 11-spotted ladybug riding on the very tip of the outer end of the minute hand, how fast are you traveling?


Solution

The number 11 is a distraction, and so is the diameter of the clock's face.

If we assume that the ladybug at the tip of the minute hand rotates around a circle of radius r=20 ftr = 20 \text{ ft} at a constant rate of 1 full rotation every hour, then the circumference of the circle is 2πr125.662\pi r \approx 125.66 and the speed of the ladybug is 125.66 fthr\dfrac{125.66\text{ ft}}{\text{hr}}.

Larger ladybugs are about a centimeter in size, so to put that in perspective, 125 feet per hour is a little more than 1 centimeter per second.