Bignate603 is right - at least partly. The appearance of backwards rotation does NOT happen in real life observation. It is the stroboscope effect. It was noticed especially in movies which are composed of a sequence of frozen images taken at 24 (originally 16) frames per second. As a wheel turns at a particular rotational rate, its spokes pass a fixed point at a rate of (rotation rate x spokes per wheel turn). If movie frames are taken at exactly the same rate as the repeat pattern of the spokes (or some sub-harmonic of that) the spokes will appear absolutely stationary. That's because each frame is taken ONLY when the spokes are in the same place as before, but just rotated exactly one spoke further. Now if, instead, the camera frame rate is just slightly faster than the spoke repeat rate, each frame gets a picture with the spoke slightly not quite there yet, and the sequence played back appears to have the wheel spinning backwards. On the other hand, if the wheel speeds up a little and gets faster than the frame rate, it will appear to turn forward very slowly.
On TV this effect is more difficult to observe for three reasons. Firstly, no TV frame gets recorded all at once - it takes a full 60th of a second to scan half of one frame, and the wheel is actually turning during this time, so some parts of the frame are converted to an image at a different time from other parts. Secondly, interlaced scanning means that a full TV frame actually is done by scanning the scene twice: all the odd-numbered scan lines are done in 1/60th of a second, then all the even-numbered scan lines in the next 1/60th of a second. So a full frame is composed of two half-images taken 1/60th of a second apart, and the resulting picture is messed up. Thirdly, TV gets away with all this in part because the resolution of the screen is not very good, and you don't notice the blurriness of the image. But you WILL see this effect when the show on TV is a movie, because the original frames actually were frozen in time, and the broadcast process can reproduce the whole frame without movement of the wheel spokes during the scanning process.
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