# Why does a precessing wheel remain horizontal, instead of flipping?

Suppose I have a wheel with an axle, such that one side of the axle is tied to a rope. I'm initially holding wheel in such a way, that the radius vectors of the wheel are perpendicular to a board. I release the other side of the axle. It is obvious that gravity produces a torque that goes into the board and turns the wheel in such a way that the face is now facing downwards.

Now comes the non-intuitive second part. I've given the wheel some spin in the beginning. This means the wheel has some initial angular momentum. Now I release it. Gravity would apply a torque into the board, which would induce a small change in angular momentum. This resultant angular momentum would be somewhere between the direction of the torque and the initial angular momentum, which is sideways. As gravity keeps on trying to produce the torque, the direction of the torque changes as the wheel turns ever so slightly. This causes the angular momentum to change again. Hence the angular momentum keeps on changing, causing the wheel to rotate horizontally - something we call precession.

Now I clearly seem to understand why angular momentum chases the torque, causing the wheel to turn. What I don't understand is, how does the wheel manage to remain horizontal. Let us consider the scenario again. Gravity induces an angular momentum into the board. However there is also some angular momentum sideways due to the spin. Shouldn't the wheel go down while spinning at the same time ?

Does the wheel go down only when the total angular momentum and torque is in the same direction, as in the case of non-spinning wheel ? Moreover, in the spinning case, the angular momentum chases the torque but never catches up. Is that why it remains horizontal ? Can anyone provide me with an intuitive explanation as to why precession prevents the wheel from flipping due to torque due to gravity ?

• If you spin around a weight on a string it can stay fairly horizontal even though it is being acted upon by gravity. In the case of the wheel, the rate of precession might be fairly slow, but the wheel itself is spinning very fast and can't easily just fall down. Commented Nov 6, 2021 at 17:48

## 2 Answers

This answer expands on the answer by contributor Farcher.

For an intuitive explanation see my 2012 discussion of gyroscopic precession.

That discussion is not in the abstract. (Abstract is to invoke angular momentum vector properties, and operations such as the vector cross product.) Instead it capitalizes on symmetry to connect the phenomenon of gyroscopic precession back to linear mechanics intuition.

See also the following article by Svilen Kostov and Daniel Hammer:
It has to go down a little, in order to go around

Svilen Kostov and Daniel Hammer report on a tabletop experiment that they performed.

They obtained quantitive results, and they report that the amount of drop that they measure is in accordance with the laws of motion.

When a gyroscope wheel is released the center of mass drops a little. The center of mass must drop. Not dropping (a little) is ruled out by the laws of motion.

The center of mass dropping a little always occurs, but almost always there are factors that mask that drop.

When the gyro wheel is released suddenly the resulting motion is a superposition of nutation and gyroscopic precession. Visually the superposition of nutation and gyroscopic precession presents itself as the gyro wheel precessing and bobbing up and down. The midpoint of that bobbing-up-and-down motion is actully lower than the starting height, but the bobbing motion makes it hard to see that.

Usually in classroom demonstrations the gyro wheel is released gingerly. In effect the demonstrator is selectively preventing the nutation while allowing the gyroscopic precession. Releasing gingerly will hide the drop.

It is common in classroom demonstrations to make the gyro wheel spin very fast. When the wheel spins very fast the nutation is very fast and has small amplitude (and damps out quickly), so the nutation tends to go unnoticed. The faster the spin rate the slower the corresponding gyroscopic precession, which corresponds to only a small drop; again the drop tends to go unnoticed.

There is a wide-spread belief system among physicists that in the case of gyroscopic precession the precession happens instead of dropping. That is, according to that belief system there is no drop.

(In the answer by contributor Farcher that mistake is not made. It is pointed out, correctly, that the wheel does drop)

Derek Muller (the author/presenter of the Veritasium channel) shares the erroneous belief system, by the looks of it.

The Veritasium explanation for the phenomenon of gyroscopic precession boils down to stating: 'Gyroscopic precession occurs because the vector cross product says so.'

• I was unable to understand this paradox, that the wheel must dip in order to precess. Here is my reasoning, can you verify it for me ? When the wheel precesses, there is a small angular momentum due to this precession, this points upwards. Moreover, due to spin, there is spin angular momentum sideways. In order to keep the total angular momentum conserved, the final angular momentum should be sideways. This is only possible if the initial angular momentum was slightly dipping down, only then the resultant would be perfectly horizontal. Commented Nov 7, 2021 at 8:26
• Is this why, the wheel must dip slightly in order to process ? Commented Nov 7, 2021 at 8:27
• I think what the paper linked by you, is trying to say is that, as the wheel precesses, there is an extra angular momentum, that develops as the wheel is rotating in this new direction. So, we have a mysterious vertical angular momentum that comes out of no-where. The only way this is possible is that this new vertical angular momentum is borrowed from the initial spin angular momentum by dipping the wheel slightly. Commented Nov 7, 2021 at 8:41
• @NakshatraGangopadhay The thing is: you are wrongfooting yourself. Spin angular momentum is a highly abstract concept. With a highly abstract concept the likelyhood of leading yourself astray is high. The experimental result obtained by Kostov and Hammer is rock solid. In general: if your thinking process ends up with you being at odds with the experimental result then your thinking process is wrong. If your thinking is at odds with the experimental result you have to backtrack and find where you are leading yourself astray. Commented Nov 7, 2021 at 8:44

Shouldn't the wheel go down while spinning at the same time ?
It does.

The axle tilts so that the wheel (and Earth's) gravitational potential energy decreases (centre of mass of wheel moves down towards the Earth) to provide the extra kinetic energy of the wheel due to the precession.

Watch the video Veritasium - Gyroscopic Precession from $$3:05$$ at a speed of $$0.25\times$$ and you will see that the axle of the wheel which is horizontal just before release becomes inclined after release.