How come wheels rotate backwards in movies?

Most of us must have observed in ads / movies how the wheels of a car rotate backwards or even stay still even though the car itself is moving at a breakneck speed. See the following video to see this illusion in action. Notice how the wheels appear to be spinning backwards, forwards and at a certain point even appear to be not rotating at all.

This illusion is called Wagon-Wheel effect (no clue why it is called so). So what causes this illusion?

Camera basics:
To understand why we see the wheels spinning backwards, we need to understand how video recording works. Videos are basically a series of photos played so fast that our naked eye perceives it as continuous motion. For example, most movie cameras shoot at 24 frames per seconds (fps) which means they take 24 photos per second. When we go to a movie, these photos are played back at 24 fps and perceived as continuous motion by our eyes (when in panic human eyes are known to operate at a much higher frame rate but in relaxed state they operate at about 20 fps).

With the understanding that videos are actually discreet shots in time, it is easy to see why wagon wheel effect occurs. Imagine a camera that operates at 1 fps and a wheel that is spinning 340° clockwise per second. The first row in the following illustration shows what each of the photos shot by the camera would look like. Now imagine these photos being played one after the other to a human eye that operates at 1 fps. It sees counter clockwise motion!

Illustration showing various stages in wagon wheel effect

The second row in the above illustration shows why the wheel would appear still in some cases. This happens when the time between individual shots by the camera exactly matches the time taken by the wheel to complete n-rotations. 

Artificial Illumination:
While camera recording is one way to observe wagon wheel effect, artificial illumination also results in similar effects. Lighting powered by alternating current actually flickers about 50 times per second (in other words, the bulb turns on and off 50 times per second). As an object is rotating, depending on the frequency of the flicker, certain positions of the wheel will not be observed by the observer thus creating the illusion.

Continuous Illumination:
It is common knowledge that wagon wheel effect can also be observed by naked human eye under continuous illuminating conditions like sun light. A simpler explanation for this is that human eye, like a camera, actually takes snapshots of the world it sees and thus is no different from a movie camera observing wagon wheel effect. While this is definitely true, many scientists agree that this only part of the answer. There is another somewhat more complicated reason as to why human eye can directly perceive this effect. Unfortunately that is a little too complicated for this article. Curious readers can visit a library.

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