# Is the torque on a gyroscope a conventional virtual force perpendicular to rotation?

So I am having some difficulty understanding gyroscopic precession. I understand that mathematically by convention torque is perpendicular to the force and so is angular momentum but surely that force is a true force acting outwards as this is what occurs in gyroscopic precession. My question is is this torque a conventional virtual force perpendicular to rotation?

This is a good question. Gyroscopic precession is also what has baffled me the most of all classical mechanics I've encountered.

The force comes from the inertia of the spinning mass. Gravity tries to make the gyroscope (the top) tilt and fall straight down. But while falling down it also spins. The particles at the lower part of the periphery thus experience falling sideways. As they all have this tendency, they collectively turn and the gyroscope as a whole starts turning in a horizontal plane.

In the next moment this exact same thing happens. And just like with circular motion, the turning takes place as infinitesimal changes while the system simultaneously adjust, so that there is no magnitude change but only a direction change. In that same way the gyroscope doesn't fall down (no angular displacement change) but only turns.

So no, no involved torques are virtual here. All are real forces and torques. But they appear in an unintuitive manner, just like how unintuitive classical circular motion is where a centripetal force pulls inwards but still the object never comes nearer the centre.

Vsauce has a quite good explanation here (from 6:25): https://youtu.be/XHGKIzCcVa0?t=385.

• Unfortunately the theory offered in that Vsauce video (a commonly offered theory) has a fatal flaw. I will refer to that theory as the 'instead' theory. The instead theory says that a gyroscope, when subjected to a torque, will always precess instead of flopping over. But when the rotation rate is slow the gyroscope does flop over; you don't get that 'instead'. The instead theory offers no clue to explain why it fails for slow rotation rate. In 2012 I posted an answer about gyroscopic precession That answer covers all rotation rates. Commented Nov 17, 2020 at 20:08
• Thank you for adding that point, @Cleonis. I think Vsauce succeeded in explaining precession intuitively, which is quite an impressive feat - even though his intuitive visualisation doesn't cover the whole situation, I find it quite useful. Commented Nov 17, 2020 at 23:48
• Here's the thing: the flaw extends to all cases. While the flaw is blatantly obvious at slow rotation rates it isn't limited to slow rotation rates. That which feels intuitive can be wrong. Generally: a theory failing catastrofically in a subset of cases is a strong sign that there is a fundamental problem. (Example: Caloric theory gives a strong appearance of being correct, and scientists like Lavoisier and Carnot were convinced of it being correct. But Caloric theory fails for heat generated by friction. This failure for a subset of cases foretells failure for all cases.) Commented Nov 18, 2020 at 19:56
• @Cleonis Yes, I agree that a wrong but intuitively easier model can bring misunderstandings if they are applied in detail. But sometimes the wrong but intutive model is a better pedagogical tool for the newcomer, for whom accessing the topic can be overwhelmingly complex otherwise. Commented Nov 19, 2020 at 11:36

In situations like these I prefer to start with the most symmetrical case, and (if need be) generalize from there.

The setup depicted in the image (uploaded by me for a 2012 answer), shows a gimbal mounted gyroscope wheel. The three axis of the gimbal mounting intersect at the center of mass of the gyroscope wheel.

I introduce three names for axes.

• Roll axis - the gyroscope wheel spins around the roll axis.
• Pitch axis - motion of the red frame.
• Swivel axis - motion of the yellow housing.

A force exerted on any part of the gimbal mounting result in a change of orentiation of the gyroscope wheel.

That is why in the case of gyroscopic motion it is standard practice to represent a force that is exerted in terms of a torque. (A spinning top has the same degrees of freedom.)

The purpose of the image is to make the relation between force and torque transparent.

An obvious way of introducing a torque is to add a weight on one of the blue axis extensions. (The blue axis is fixed to the red frame, the blue wheel is free to rotate around that axis.)

A weight on one end of the blue axis will tend to pitch the gyroscope wheel.

If you would add a weight suddenly you would cause nutation. The faster the wheel spins, the faster the nutation. In the usual demonstrations the nutation is fast, and has a very small amplitude, so it tends to go unnoticed. Usually any induced nutation is dampened in seconds.

Usually the demonstration will add the weight gingerly, suppressing nutation altogether. When the weight has been added gingerly we see the gyroscope wheel proceed in steady precession.

It's crucial to be aware that while the torque is necesary to sustain the state of precessing motion, the torque isn't driving the precessing motion. Rather, it is analogous to the case of a centripetal force sustaining circular motion. The centripetal force is necessary for the circular motion, but the centripetal force is not driving the circular motion.

I cannot emphasize this enough: if the torque would drive the precession then the precessing motion would accelerate. But the precessing motion is steady.

The process of how precessing motion is set in motion is described in my 2012 answer about the mechanics of gyroscopic precession

• I don't quite understand how a mutation would be caused isn't a mutation a rocking motion? Commented Nov 18, 2020 at 11:07
• @Thehomeschooler About the 'nodding' (the word 'nutation' is imported from a latin. The latin word means 'nodding') To see examples of nutation, look up (youtube) videos that present gyroscopic precession of a bicycle wheel. A bicycle wheel is so large that the rotation rate is comparitively slow (hence slow nutation rate). When the demonstrator just allows the spinning bicycle wheel to plonk down the overall motion pattern is a combination of nutation and precession. A nutation without precession is that the spin axis sweeps out a cone. Releasing gingerly suppresses opportunity for nutation. Commented Nov 18, 2020 at 20:10
• @Thehomeschooler Comment continued: the combination of nutation and precessing motion gives an appearance of the gyroscope wheel bobbing up and down. The nutation is not only up and down, there is also regular acceleration and deceleration of the precessing motion, but with the overall precessing motion it isn't straightforward to see that the nutation motion is the spin axis sweeping out a cone. See also this article describing a tabletop gyroscopic precession experiment They allowed the wheel to plonk down: nutation Commented Nov 18, 2020 at 20:16

I cannot add to the excellent responses earlier by others. Here are a few comments. Gyroscopic motion is hardly intuitive to anyone. My problem with basics physics discussions is they just discuss the effect of torque on the spinning gyro but do not really provide a good intuitive explanation; also, some of these discussions fail to mention that their simple evaluation of precession assumes the gyro is initially spinning rapidly.

More advanced treatments of the motion use a Lagrangian approach, but that does not help me really visualize what is going on either.

The earlier answers provided by others are as good an intuitive explanation for the motion as I have seen; I will save these responses in my files:)

There are many variations of such motion that have surprising answers that you can find on the web, such as the practical joke played on a hotel porter by the physicist R. W. Wood.

• Yeah, an exhaustive treatment is in terms of Lagrangian mechanics. Short of exhaustive treatment: I am positive that it is possible to present a visualisation that is both intuitive and correct. I wrote my 2012 answer about gyroscopic precession to demonstrate that. Commented Nov 18, 2020 at 20:23
• Yes, that is why I saved your 2012 answer:) Commented Nov 18, 2020 at 20:41