Why does the wheel of a car appear to be moving in opposite direction? When a car is about to stop, the speed of its wheel reduces. Why do we see or feel that the wheel of the car is moving in the opposite direction?  This can also be observed of a fan at home.  So why is it?
 A: Apparent reversal of rotation is a kind of visual interference effect where the frequency of the imaging system (film, tv but not human eyes) is close to the rotational frequency of spokes in the wheel. This is termed the Wagon wheel effect
In your home you have artificial light that flickers at a frequency determined by the electrical supply (usually 50 or 60 Hz) or by the lighting system. This is noticeable in fluorescent tubes suchas low-energy lighting and not really noticeable in incandescent bulbs (the filaments don't drop much in temperature in the 10 ms between voltage peaks)
This stroboscopic light-source flicker could interact with the movement of radial fan blades behind a largely radial fan grill to produce the wagon-wheel effect as the blades slow when power is removed. 
The Wikipedia article referred to above identifies some unproven hypotheses about subjective stroboscopy in the human visual perception system as a whole. This effect may also be a result of "hallucinogen persisting perception disorder" in people who have used drugs like LSD.
A: I think that the reason for that is related to the fixed framerate of our eye which is 24 frames per second. In each next frame you'll see the wheel turned by some angle relative to the previous frame. If this difference is from 0 to pi radians (0 to 180 degrees) you'll see it in one direction. If during each frame, the angle will be from pi to 2pi radians (180 to 360 degrees) then you'll see it rotated in opposite direction in each frame. That's why the wheels of the car go through at least 3 stages of illusion: rotating in clockwise direction, slowing down up to non-rotating state and then rotate in opposite direction, while the car accelerates or stops. But in reality of course the rotation rate of the wheels in increasing or decreasing constantly.
