8/13/2019 Can We Explain Precession Without Vectors

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Can we explain precession without vectors? Qualitatively, the answer is yes. At right, below the movie, are two

stills taken from it: look at the top one. The cord on the right hand side (looking at the photo) is pulling the shaftup, the weight of the shaft is pulling it down. If it were not spinning, we know that the whole apparatus would

tip anticlockwise: the top of the wheel would move left and the bottom right. So how does the spinning make it

precess instead of falling?

Let's consider a small part of the rim of the wheel at the top call it the top piece, and let's colour it red. At the

instant of the top photograph, the top piece is travelling (for a very short time) horizontally, outwards from the

photo, at high speed. But the combined effect of weight and the tension in the cord, as we mentioned above,makes it tend to move to the left. In fact, it does go to the left a little bit, but it also comes very rapidly out

towards us. Just for this explanation, let's say that, after it has moved a quarter turn around the shaft, it will have

come out towards us and be now the closest part of the wheel to us (and going downwards), but it will bedisplaced a tiny bit left with respect to left side of the rim in the (top) photo.

Similarly, let's consider a small part of the rim of the wheel at the bottom, and let's colour it green. At the instantof the photo, the bottom piece is travelling horizontally, into the photo. This time, the combined effect of weight

and the tension in the cord makes it tend to move to the right. So again, let's say that, after it has moved a

quarter turn around the shaft, it will have gone inwards, away from us and be now the furthest part of the wheel

from us (and going upwards), but it will be displaced a tiny bit right with respect to the rim in the upper still

photo.

So, after a quarter of a turn, the closest bit of the wheel will have moved slightly to the left, and the far side of

the wheel will have moved a bit to the right. So we look at the bottom still and then run the movie and we

see that that is exactly what happens. The two coloured bits of the wheel are moving as expected from theirweight and the tension in the cord (i.e. the external torque), but they don't have time to move very far because of

their rapid rotation. The combination of these motions, and those of all the other parts, gives us the precession

we see. Note, too, that the faster the wheel turns, the less time there is for the pieces to move sideways, so the

slower the precession, as given by the equation above.

This explanation is rather longer than the vector explanation given above, and it's only qualitative. So a

physicist or engineer needs the vector analysis, and can use it quickly and accurately. However, s/he willsometimes use a qualitative explanation like this one as well.