Blog, General

### Trick: Nyquist theorem

Posted on June 9th, 2012 by

Why, when a wheel is spinning fast, does it sometimes appear to be turning slowly in the opposite direction?

This is a stroboscopic effect which happens when you are seeing repeated images of the tire. This can happen if you see the tire on film (often 24 frames a second) or on a TV or lit by an AC electric light or any process which regularly breaks up your image of the tire, such as looking through a fan at the tire.

Normally the eye will interpret the sucession of rotated images of the tire as the tire rotating because each image has rotated a little further than the previous one. If the tire is rotating quickly enough that by the time you see the next image of the tire, it has rotated so much that patterns on the tire are slightly backward from the previous image, (for example, maybe it made 99% of a turn), then what you are seeing is exactly the same as it would look if the tire really was moving backwards and so that is what you see.

## Exercise

A wheel is rotating with a frequency: $16revolutions/sec$ or $5760degrees/sec$ and a strobe light is flashing with $20flashes/sec$ or $288degrees/flash$. This means that wheel will not be able to rotate a full revolution $360 degrees$. That’s why will see the wheel going in the opposite direction, we can proof this with following (little trick).

Btw if you don’t know how we calculated those 288degrees:
$16 revolutions * 360 degrees = 5760 degrees$
$5760 degrees / 20 flashes = 288 degrees$

A little trick if $288degrees > 180 degrees$ then the wheel will rotate in the opposite direction else in the normal direction.

Then to find how many revolutions it’s rotating/sec.
$(360degrees - 288degrees) * 20falshes = 1440degrees / 360degrees = 4 revolutions/sec$

So the wheel is rotating 4 revolutions/sec in opposite direction.