I never fully understood gyroscopic precession - toppling gyroscopes

[AronYstad]

TL;DR

Why does a gyroscope topple over at different rates depending on how fast it's spinning? I read that it's friction, but I don't understand that.

I tried to understand why gyroscopes fall over more slowly the faster they spin, but I couldn't wrap my head around it. So I tried looking for threads about it, but I only found people saying friction is the reason why the gyroscope topples over. And I guess that might be the main reason if it's spinning really quickly, but it doesn't really make sense to me that that would be the only reason.

Imagine the classic bicycle wheel setup, where you have a spinning bicycle wheel that is free to pivot around a point on its handle. Now imagine that without friction. If the bicycle wheel isn't spinning at all, it's obviously gonna just fall over due to gravity. There's nothing holding it up. Now imagine you spin it ever so slightly, say 1 revolution per year or something ridiculously tiny like that. I wouldn't expect it to start spinning around in circles forever just because the setup is frictionless. I'd still expect gravity to make it fall. And now, make it spin faster. It's gonna start precessing, but I'd expect it would still eventually fall over, just more slowly, as seen in a setup with friction.

What is the reason behind this behaviour? Is it friction, and in that case, how does that work?

 

[PeroK]

The main factor in the dymanics of a gyroscope is angular momentum. The precession can be deduced from Newton's laws of motion. The result goes counter to our intuition because the force holding the gyroscope up is not directly below its centre of mass. Instead of the gyroscope falling, it must precess in order to satisfy the laws of motion.

 

[AronYstad]

The main factor in the dymanics of a gyroscope is angular momentum. The precession can be deduced from Newton's laws of motion. The result goes counter to our intuition because the force holding the gyroscope up is not directly below its centre of mass. Instead of the gyroscope falling, it must precess in order to satisfy the laws of motion.

Yeah, I know that that is the case. I know that it does precess. My question was about why it still eventually topples over and doesn't keep precessing in circles forever, and how this relates to the speed of the rotation.

I would also gladly accept an explanation of this behaviour using torque and angular momentum. My lecturer just said something along the lines of "the angular momentum 'chases' the torque", and also showed the rotational version of Newton's second law. But he didn't go into depth about how this relates to the "slowing" of the fall of the wheel.

 

[A.T.]

My question was about why it still eventually topples over and doesn't keep precessing in circles forever,

Because friction dissipates it's kinetic energy, so it slows down until it doesn't work as a gyroscope anymore.

and how this relates to the speed of the rotation.

The more energy it initially has, the longer it takes to dissipate it.

My lecturer just said something along the lines of "the angular momentum 'chases' the torque"

Torque is the rate of change of angular momentum. Both are vectors, so when torque is almost perpendicular to angular momentum, then it mainly changes the direction of angular momentum, not it's magnitude. So the spin axis rotates slowly, as explained here:

http://hyperphysics.phy-astr.gsu.edu/hbase/rotv2.html

If you don't find the angular dynamics vectors intuitive, here is a good gyro explanation based on linear dynamics:

 

[PeroK]

In Newton's original principia he made the point that there are always dissipative forces. In this case, some friction at the base and air resistance on the spinning gyroscope. These are external forces that gradually reduce the angular momentum and eventually the angular momentum is not sufficient for gyroscopic precession to continue.

 

[AronYstad]

Because friction dissipates it's kinetic energy, so it slows down until it doesn't work as a gyroscope anymore.

I still don't understand. Take the example in my original post where the wheel spins extremely slowly, say 1 revolution per year, without friction. That's very similar to if it was not spinning at all, in which case it would just topple over. Wouldn't it still just topple over even without friction? It's hardly spinning at all?

 

[PeroK]

I still don't understand. Take the example in my original post where the wheel spins extremely slowly, say 1 revolution per year, without friction. That's very similar to if it was not spinning at all, in which case it would just topple over. Wouldn't it still just topple over even without friction? It's hardly spinning at all?

It doesn't have enough angular momentum. It's all about angular momentum. It's not about friction.

 

[AronYstad]

It doesn't have enough angular momentum. It's all about angular momentum. It's not about friction.

So if we disregard friction, the more angular momentum it has, the slower it topples over?

 

[PeroK]

So if we disregard friction, the more angular momentum it has, the slower it topples over?

If it has enough angular momentum it doesn't topple over. Like a wheel rolling along a road.

You are focusing on the case where it doesn't have enough angular momentum.

 

[A.T.]

I still don't understand. Take the example in my original post where the wheel spins extremely slowly, say 1 revolution per year, without friction. That's very similar to if it was not spinning at all, in which case it would just topple over. Wouldn't it still just topple over even without friction? It's hardly spinning at all?

If you would apply to a slow spinning gyro, a pure torque of constant magnitude which is always exactly perpendicular to its current angular momentum, then no matter how small the initial angular momentum is, it would never increase in magnitude, just change direction continuously. However, the angular momentum vector doesn't have to stay parallel to the gyro axis, so you would see some small wobble.

Compare this to applying to a slow moving particle, a force of constant magnitude which is always exactly perpendicular to the particles current velocity. No matter how slow the particle is moving initially, it would not speed up, just start moving in very tiny circles.

 

[PeroK]

A simpler example is a spinning top. The top would spin indefinitely, except that dissipative forces gradually slow its rotation. Eventually, it slows below some critical angular momentum. The process of collapse, however, is rather chaotic and somewhat unpredictable. If it has too little angular momentum to begin with, then it collapses immediately.