The answer to the original question has already been pointed out - you see the wheels stop, slow down, change direction on TV/film or when strobe-lit when the shutter (or strobe) frame-rate no-longer captures the position of the wheels fast enough to accurately represent (or sample) the motion of the wheel. It's only fancy words, but this is an example of "aliasing".
The effect is vivid only when the shutter of the camera has a short "duty cycle" ie the exposure is short compared to the frame rate (sometimes for historical reasons this is called the shutter angle, where 180degrees equals 50% duty cycle). If the exposure time was equal to 1/frame rate then the wheel simply becomes a blur when it gets too fast, rather than appearing to go backwards.
Mobile-phone cameras typically have a top-to-bottom "rolling shutter" (purely electronic) and this causes weird shearing artifacts if you pan the camera horizontally, or stretch-shrink artifacts if you wiggle it vertically. Have fun!