# Why do rotating fidget spinners sometimes create a perception of opposite spinning?

Most of us have noticed that Fidget Spinners or celling fans or any kind of round shaped rotating objects (including, perhaps, bicycle rims) create a perception of them moving in an opposite direction to that of the applied force. When the speed becomes faster than what it was in the beginning, it looks as if it becomes static or that it is moving very slowly.

What is the reason behind this?

If we were dealing with a video camera, then this would likely be due to the stroboscopic effect. It is also called "the wagon wheel effect", and it's related to the Nyquist-Shannon sampling theorem.

The stroboscopic effect is a visual phenomenon caused by aliasing that occurs when continuous motion is represented by a series of short or instantaneous samples.

In the context of signal processing, "aliasing" refers to a situation where two inputs result in similar or identical outputs. Many fidget spinners have threefold rotational symmetry, which means that if you take it and rotate it one third away around (that is, 120 degrees), it looks the same: each three arms look the same, so once you rotate the spinner from one arm to the next, it looks the same as when you started. So if the camera frame rate is equal to the time it takes to rotate that much, the fidget spinner will look the same in each frame. This is called "aliasing" because a rotating fidget spinner is producing the same output as a stationary one.

So there will be some frequency that we can call the "fundamental frequency" that is indistinguishable from no rotation. Not only will this effect be produced at this rotational speed, but it will also be produced at any integer multiple: if the spinner is spinning at twice this speed, then two arms will go by, and you'll still end up with the spinner looking the same. Not only that, but any two frequencies that differ by an integer multiple of the fundamental frequency will appear the same. For instance, suppose you're spinning one spinner at 10% of the fundamental frequency, and another at 110% of it. Each frame, the first will get one tenth of the way to the next arm. The second spinner will get 10%% past the next arm. Since the arms look the same, this looks the same as getting 10% past the first arm.

This also means that going at 10% of the fundamental frequency in one direction looks the same as going 90% of the fundamental frequency in the other direction. If you spin it at 90% in the clockwise direction, then in the second frame it will be 10% away from the next arm, which looks the same as if it rotated 10% in the counterclockwise direction.

All of this applies to recording a fidget spinner, but what if you're directly looking at it? One way you could get a similar effect is if there's a flickering light source, and so your eyes are mostly seeing the fidget spinner at the peak of each flicker. The sun doesn't flicker, and the flickering of flames is generally not at a regular frequency, so you shouldn't see this effect with those light sources. However, AC power varies during its cycle (the standard in the US is 60 Hz), so with electricity-based light sources, there is regular flickering. This is especially pronounced with LEDs, less so with fluorescent, and even less with incandescent. If you can get all three light sources, you might want to see how strong the effect is which each. Laptop screens have a very regular refresh rate, so you should see a very strong strobe effect if you hold a fidget spinner up to a laptop screen.

There is, in fact, physics in this. It's a easier to understand in terms of a camera (the same phenomena happens to video) because we can talk about a frame rate. The human eye has sort of an effective frame rate, but this is far less fixed and hence makes the analysis a little more complicated.

For a video camera, a picture is taken every so many seconds. For example, a camera capturing 30 frames per second will essentially take a picture every 1/30th of a second (about 0.03 seconds).

In this 0.03s of time between frames (pictures), the spinner will continue moving. So long as the spinner doesn't move very much in that time (so spinning slow), the spinning will appear smooth because the motion we missed between the sequential frames was very small.

But what if the spinner is spinning fast? Just to be definite, let's suppose we have a fidget spinner with three prongs. So what would it look like if the spinner is going so fast that one of the prongs makes it to exactly the position the next prong had in the previous frame? Well in this case, the two frames look identical because both have prongs in the same places (assuming the prongs are identical to each other). Since every photo shows prongs in the same places (but not the same prong in each place), the video will look like the spinner is just sitting there not moving at all.

If the spinner is going ever so slightly slower, then the prong will almost, but not quite, make it to the position the next prong had in the previous frame. So each photo will show a prong that didn't quite make it to the location in the previous frame, making it look like the spinning is going backwards.

this is called the "stroboscopic effect" but it does not occur in your eye, it occurs because the light (LED or fluorescent) shining on the fan blades or fidget spinner actually blinks on and off at the mains AC frequency. Under sunlight or incandescent light, the stroboscopic effect will not occur, and the rotating element will appear to your eye as a continuous blur.