How fast does a fidget spinner spin? It's a simple question with a simple answer, but a complex path to that answer. The issue lies in analyzing an extremely fast-moving object with simple tools, like a smartphone.
In the video below, mathematician Matt Parker turns to a spectrogram sound-analyzing app to solve this problem. Spectrograms are visual representations of sound, allowing the viewer to pick out certain frequencies within an audio clip and measure their intensity. By figuring out the sound the fidget spinner makes, Parker can sort out how many Hertz (cycles per second) the spinner is rotating at.
The first task is making the spinner itself stable, so it's easy to spin and becomes a reliable target for audio recording. Parker attaches the device to a drinking glass, and mounts the smartphone above it, with the microphone pointed at the edge of the spinner. Then by blowing the fidget spinner with compressed air, the mathemagic happens.
Parker calculates the absolute speed of the tips of the fidget spinner, as well as the speed of the spinner in revolutions per minute—the latter is roughly 3750 rpm! (For comparison, a typical car engine runs around 2000-3000 rpm when cruising.) The video is full of further analysis and methodology.
Tune in for some delightful applied mathematics...and be sure to wear your safety gear!