Why is that at certain speeds car wheels appear to be moving backward?

Answer 1

First you need to understand that your eye can see only about 25-30 frames per second. Moving image is perceived by putting together static images, just like a movie, where individual static frames are changed quickly before your eyes and you understand them as continuous movement.

Now about the wheel. That wheel has spokes that look identical. That confuses your eye, it can't distinguish between them.
Your brain takes a picture of the wheel, than the wheel turns AND YOU CAN"T SEE THE MOVEMENT, than your brain takes another picture of the wheel in the new position 0.04 seconds later ant it tryes to put the 2 images together to create a moving image. Now how does your brain knows exactly how many spokes the wheel turned in that time? It doesn't know. Let's say the speed that wheel turned from one spoke to the next one is adentical with your viewing frame rate. You know what happens? YOU WILL SEE THE WHEEL AS NOT MOVING AT ALL, because the next spoke will be exactly in the same position where your first spoke was in the previous frame. Now if you decrease that speed just a little bit you will see the movement backwards because it's more obvious for the brain to assume the slow movement (the 2nd spoke being almost where the first one was in the previous frame). So the brain thinks the second spoke is in fact the first one and it moved a little backwards, instead of guessing the truth.

It's all a processing error of the brain, due to limitted information it receives from the eye.

Answer 2

It's what's known as the stroboscopic effect. It's to do with the frequency of the light compared with the frequency of the moving object, in this case the wheels of the car.

Did you ever see this happen in only daylight conditions?
No, why not ? Because the frequency of natural daylight and the frequency of the car wheel are different (revolution frequency).
In the evening time, when traveling along it's most likely then you will notice it. This is because the street lights have there own frequencies (often 50/60 Hz).

When the frequency of the moving wheel is the same as the frequency of the street lamp, then the wheel will appear to be static.

When the frequency of the wheel is slightly less then the frequency of the street lamp, it's appears to be moving backwards (just a slight mismatch of frequencies).

When the frequency of the wheel is slightly more then the frequency of the street lamp, it's appears to be moving forwards (just a slight mismatch of frequencies).

Of course, in order to see anything, our precetpion is a factor too.

Answer 3

I think of it as more of an aliasing effect - that is, the rate at which you are taking "samples" (frames) is slower than the frequency of the spokes on the wheel. This gives an inaccurate view of the wheel's movement.

See the links below for a full explanation. The first one has an excellent hands-on example.

Answer 4

Because of the strobing effect. Our eyes seems not to be as perfect. That's why we can watch the movie reel, too without seeing every single frame static.

http://www.answers.com/topic/stroboscope