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J. Perelman
"Entertaining physics". Book 2.
Chapter 9. Reflection and refraction of light. Vision


Have you ever been through the cracks of the fence or, even better, on the movie screen to monitor the spokes of the wheels of a fast moving wagon or car? You've probably noticed this strange phenomenon; car hurtling at breakneck speed, the wheels also barely turning, or not turning. Moreover, they rotate sometimes even in the opposite direction!

This illusion is so extraordinary that leads to the bewilderment of everyone who sees it for the first time.

Explains it in the following way. Watching the wheel spin through the gap in the fence (moving the eyes along the fence), we see the wheel spokes are not continuously but at regular intervals of time as the Board fence every moment hide them from us. Similarly, cinematic tape captures the image of the wheels with breaks, in some moments (24 frames per second).

There are three cases that we will discuss one by one.

Firstly, it may happen that during the break, the wheel will have time to make an integer number of revolutions-no matter how much, 2 or 20, only the number that was whole. Then the wheel spins on the new picture will occupy the same position in the same. In the following period of the wheel will make again an integer number of revolutions (the size of the gap and the vehicle speed is not changed), and the position of the spokes remains the same. Seeing all time one of the spokes, we conclude that the wheel does not return (the middle column of the figure).

The cause of the mysterious movement of the wheels on the movie screen.

The second case; the wheel of time in each period to make an integer number of revolutions and another part of the turnover is very small. Watching the changing of these images, we on the whole, the number of revolutions will not guess, and see only a slow rotation of the wheel (each time for a small share of turnover). With the result, we find that, despite the rapid movement of the car, the wheels turn slowly.

Third case: during the period between filming wheel makes a partial turn, differs from the complete small proportion (for example, rotated 315°, as in the third column of the figure). Then any specified pin will appear to be rotating in the opposite direction... This is a misleading impression will be up until the wheel will not change speed.

It remains to make small additions to our explanation. In the first case, we, for the sake of simplicity, talked about the number of full revolutions of the wheel; but as the wheel spins like one another, it is sufficient that the wheel is turned to an integer number of intervals between the spokes.

The same applies to other cases.

Possible and more curiosities. If the wheel rim is a label that needles are all similar to each other, it happens that rim is moving in one direction, the spokes also run in reverse! If there is a label on the spokes, the spokes can move in the opposite direction than the label - it will be like to jump from the needles on the needle.

When the movies ordinary scene, the illusion of this little harm to the natural experience. But if you want the screen to explain the effect of any mechanism, this illusion can cause serious misunderstandings and even to pervert the idea of the work machine.

The attentive viewer seeing on the screen pseudo-stationary wheel racing car, can easily, counting his spokes, to judge, to some extent, how many revolutions does it in a second. The usual speed of feed of the tape is 24 frames per second. If the number of spokes of the wheel 12, the number of revolutions per second is 24: 12, i.e. 2, or one whole turnover in 0.5 seconds. This is the lowest number of revolutions; it can be more to an integer number of times (i.e., twice, three times and so on).

Considering the magnitude of the diameter of the wheel, it is possible to make conclusions about the vehicle speed. For example, when the wheel diameter 80 cm are considered in case the rate of about 18 km/h (or 36 km/h or 54 km/h and so on).

Considered now the illusion is used technique for counting the number of revolutions of the rapidly rotating shaft. Explain on what basis this way. Power light lamp, fed by alternating current, not constant: for every hundredth of a second light fades, although under normal conditions we no flickering but notice. But imagine that this light illuminated the rotating disk shown in the following figure. If the disk rotates so that makes 0.25 turnover down to a hundredth of a second, then something unexpected happens: instead of the usual smooth gray circle eye will see black and white sectors, like the disk remained motionless.

The drive to determine the speed of rotation of the engine.

The cause of the problem, I hope, understandable to the reader, guring in the illusion with the car wheels. It's easy to guess also, how is it possible to use this phenomenon for counting the revolutions of a rotating shaft.

Entertaining physics J. Perelman


System Orphus


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