Gyroscopic Precession

Hey everyone, it's me, Derek from the channel Veritasium. I've been following this series by Destin on Smarter Every Day about helicopters, and gyroscopic precession is just one of those things that still blows my mind, as it did Destin. So, I'm here at the University of Sydney, my old stomping grounds. I'm going to borrow some of their lecture demo equipment to hopefully teach you a bit about how gyroscopic precession works.

The first thing I need to do is talk about vectors because a lot of things in physics are vectors. That means they have direction. So, an example would be momentum and force; those are two examples of some pretty common vectors. So if I have a cart moving along here, it has some momentum in that direction. And, um, if I apply a force to it, I can change its momentum.

So, for example, if I push it to the right, then its momentum will increase to the right. It all makes a lot of sense. Well, there's a similar statement we could make about rotating bodies, which is that a torque increases the angular momentum of an object in the direction of that torque. So let's try to figure out those terms. If I apply a force down on this side of the wheel, I create a torque.

Now torque is force times the distance from the rotating axis; you could call it R. So torque is the force applied times the radius away from the turning axis. Now, what's the direction of that torque? Well, we actually use a right-hand rule to define this. And so what you do is you put your fingers in the direction of the radius from the turning axis and curl them in the direction of the force, and your thumb points in the direction of the torque.

So the torque is actually out this way, at 90° to the force. The force is down that way, but the torque vector is actually pointing out this way. So the angular momentum of this wheel is being increased in that direction. So, the more I apply this torque, the more I increase the angular momentum of the wheel in the direction of the torque. So I'm making this wheel have a very large angular momentum out towards the camera, out towards you.

Now, before I go any further, let's have a look at this setup that I've got. I have a wheel here hanging from only one side by this rope, and so right now there's actually a torque on the whole system. If I let go, because the weight of this wheel is pulling down and that force is applied at this distance away from its pivoting point, there. So if I let go, well, it does exactly what you'd expect. The wheel swings down this way, but I want to see that as an example of rotational motion.

There's a torque which is pointing out this way, which is trying to increase the angular momentum of the system in that direction. Now, angular momentum in that direction requires that the whole system starts swinging anticlockwise, and so that is what happens. But what happens if I only let go after I've already spun up the bicycle wheel? Well, in that case, the bicycle wheel would already have angular momentum this way, and so a torque pushing that way actually swings this angular momentum round that way.

Okay, so let me try to get the wheel spinning and make it work. Come on! Look at that! It's rotating as we predicted! See the angular momentum vector is pointing out this way, but torque is pushing it this way. So, angular momentum, torque, and torque is pushing that angular momentum vector around. Except not for long because this appears to be quite a frictional wheel.

So, check out Destin's other videos about helicopter physics, and then come check out my channel, Veritasium, where you can find more like this, except I don't often nearly get my head cut off by a bicycle wheel!