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Rotation of a Wheel

Date: Mon May 6 18:41:53 1996
Posted by: Terry Weddleton
Grade level: 7-9
School/Organization: Traip Academy
City: Kittery State/Province: ME
Country: usa
Area of science: NeuroScience


Why does a wheel seem to move backwards as it speeds up?

I have seen this illusion too, usually on TV or in the movies. This happens because when you film something, you are really taking a series of still images and then replaying them so fast that the eye is fooled into thinking it is a continuous stream of images. I have read that the eye can see about 12-14 frames per second. Because of a physical law called the Nyquist Sampling Theorem you need to display frames twice as fast as the eye can see to fool it into seeing it as a continuous movie (Nyquist showed mathematically why that is true). So most TV shows and films use a frame rate of I believe 32 frames per second [Note (2/11/1999): Craig Berry informs me that movies use 24 frames per second and TV uses 30 fps],just to make sure they are safe (I have heard of at least one man who complains of flickering when he watches movies; perhaps his eye samples as fast as 20 fps!).

So, imagine you have a wheel that is spinning exactly once every second. If you took a picture at the same rate, it would look like it is standing still! That's because it rotates exactly once every time you take a picture. Now take a picture just a little bit faster than 1 per second. Now every time you take a picture, the wheel has not quite made it all the way around; maybe it will have gone 350 degrees around, so it's 10 degrees behind the first frame. The next frame it will have gone another 350 degrees, making it now 20 degrees behind the first frame, and so on.

When you play the film back, it will look like the wheel is moving backwards, even though you know it was going forwards! The opposite effect happens when you take pictures a bit slower than the rotation rate. It gets more complicated when the wheel does not rotate at a constant rate, like when a car accelerates. The next time you watch TV or go to the movies, watch the wheels as a car speeds up. You might see the wheel appear to go backwards, them stop, then go forwards, all while the car is moving forwards!

There is one more complication. Imagine the wheel has four spokes, each at 90 degrees from each other. If you rotate the wheel exactly 90 degrees, it looks just like it did before you rotated it! That is called "symmetry". That means you can take a picture every quarter rotation and still make it look like the wheel is standing still. If there are 8 spokes, each at 45 degrees, then you can take frames 8 times as fast, and so on. That is why, even though the wheel may be rotating very quickly, it still looks like it is going slowly when you film it.

So the next time you are watching TV, you can tell your parents it's part of a science experiment!

©2008 Phil Plait. All Rights Reserved.

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