Boomerangs and Gyroscopes

Is a gyroscope an anti-gravity device?

A question that is often asked is whether a gyroscope is an anti-gravity device. The answer is that of course it isn't. What holds the bike wheel up is the piece of string. If the wheel isn't spinning, the piece of string holds the wheel up. If the wheel is spinning, again the string holds the wheel up. If I let go of the string, the wheel falls to the floor, so the string is still holding the wheel up - gravity is still acting. If we look closely at what's happening, then we see that on a 3-body diagram (as such diagrams are called) like the one on the right, that mg is the weight of the wheel (its mass multiplied by g, the acceleration due to gravity), and also the tension in the string. We have vertical equilibrium - the wheel is not moving up or down - so the forces must be equal. We also have horizontal equilibrium because there are no horizontal forces applied at all. But we do not have moment equilibrium, and this means that the wheel accelerates in the direction of the applied moment.

Gyroscopes all around us

There are gyroscopic things all around us, and I want to show you a few. In the home, we have a coffee grinder. If I turn it on and move it around in the air, I can feel the gyroscopic effect - it feels really strange! Try it for yourself. You can always tell when an object is going to give you a good gyroscopic effect because it takes a while to speed up and a while to slow down - it has a high moment of inertia. High moments of inertia give you good gyroscopic effects. I have here also an angle grinder. Don't play with these - they are dangerous! Ask someone who knows how to use one to show you. When you switch it on, it makes a lot of noise, and has an amazing gyroscopic effect - and it also takes a very long time to slow down. Some people say you can feel a gyroscopic effect with a hair dryer. I'm not really convinced - it slows down very quickly. If you know someone with an industrial grade hair dryer, who works in a hair dressing salon, you might get a good gyroscopic effect.

One of the exercises is all about experiencing gyroscopic effects, and looking at the bicycle wheel, and verifying that these effects do as we've discussed above.

In our Dynamics and Machine laboratory here in the Engineering Department at Cambridge University we have various experiments set up. You can see how gyroscopes can be used in space for navigation. If I'm in space then I've got nothing to push against. When I'm on the rotating stool, if I want to turn around I can't do it. So imagine I'm the Hubble space telescope and I'm looking at some star up in the sky. If I want to turn around to look at some star in a different part of the sky, I could use a gyroscope to do this. If I hold a rotating gyroscope it will turn me around on my stool, so if I were the Hubble telescope I would be looking at a different star. I can move in whichever direction I like using the gyroscopic effect of the gyroscope. This use of gyroscopes in space is very important.

How do gyroscopes work?

This is the way it works. Angular momentum is conserved, as we have talked about before. If the rotor is spinning about a horizontal axis, and then I tip it up so that it's spinning about a vertical axis, this changes the angular momentum. Conservation of angular momentum then requires that I go round in the opposite direction to the rotor to make sure that there is no net change in angular momentum. Since my moment of inertia is quite small, I can go round quite fast using a gyroscope to push me around. The same principle is what allows gyroscopes to change the orientation of the Hubble telescope.

Big gyroscopes are not readily available, but you can buy small ones in toyshops. They are often driven by a piece of string, wound around the gyroscope. Once it is spinning you can rest it on a stand and see the gyroscopic effect - this is exactly the same as for the bicycle wheel or a big battery-operated gyroscope. A tooth belt is a more effective way of operating a small gyroscope than a piece of string. You can experiment with these small gyroscopes, and see what they will do. You can even balance one gyroscope on top of another!

What's the connection between gyroscopes and boomerangs?

To finish off, I'm going to explain the connection between gyroscopes and boomerangs. The boomerang I'm going to talk about is a cross-shaped one, which is very easy to make out of balsa wood, and instructions are available on my website at http://www2.eng.cam.ac.uk/~hemh/boomerangs.htm. This is effectively two ordinary boomerangs joined together in the middle.

When you throw the boomerang, it moves along in a vertical plane and also spins in the direction given by the right hand thumb rule. The fact that it's moving forwards and spinning at the same time means that the top of the boomerang is moving faster than the bottom. This means that there is less lift at the bottom of the boomerang than at the top, and that provides a couple or twisting effect, which is perpendicular to the spin, just like the bicycle wheel and the gyroscope and leads to gyroscopic precession.

We can then derive equations to see how simple cross-shaped boomerangs behave. The radius of flight of the boomerang is given by

If you make a boomerang according to the instructions on my webpage, you can adjust J with small pieces of blu-tak on the wing. If the blu-tak is close to the centre of the boomerang, the moment of inertia is low, and vice versa. If I increase J too much the flight radius will be too great, and the boomerang will hit the walls. A low value of J gives a small R, but R does not depend on how hard I throw it - this just affects how quickly it returns to me. Throwing it gently may mean it doesn't get all the way round because of air resistance, but R is still the same.

But surely spin must matter! There is a second formula which explains this.

It doesn't matter if you make a right- or left-handed boomerang. The only difference is the direction of the aerofoils on the boomerang. Right- or left-handed just tells you which way round the room they will fly, not whether you throw them right- or left-handed.

Real boomerangs require some space, and you also need to make sure there's no one around you might accidentally hit, particularly small children. Keep people gathered together when you're throwing the boomerangs, not scattered around.

I hope you will now feel enthusiastic about spinning objects, toys, and so on, and that you will collect them for yourselves.

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