By using a spinning chair, weird effects due conservation of angular momentum can felt. Have a go before demonstrating, but beware - it's difficult to concentrate when your head is spinning!
Try to make sure the chair is level, there is more than a metre of clear space around it in all directions, and the floor is something that won't graze anyone who lands on it (e.g. carpet).
Find somewhere convenient to keep the bits of kit so that people don't trip over them.
What can you do with it?
- By holding the masses at different distances from the body, the speed of spinning changes. For small children, it's enough to get them to just stick their arms and legs out.
- Before sitting on the spinny chair, hold the bicycle wheel between two hands and spin it. Turn your arms so that the wheel is horizontal. There is a pull in the opposite direction.
- Stopping the wheel while it's spinning. For a child standing, stop the wheel so that they feel a twist in their feet. For a child on the chair, if they are stationary, start the wheel spinning then stop it. They will start to spin.
- Turning the wheel over while sitting on the spinny chair (initially stationary) so they move in one direction then the other.
- Demonstrating the precession of a wheel while hanging from a string due to the moment caused by gravity.
Other things to talk about
Artificial satellites use gyroscopes to orient themselves without wasting reaction mass.
Stable rotation axes - important for satellites.
Gyros are used in ships for navigation, by pointing to True North (not Magnetic North) as determined by the rotation of the Earth, which is more useful for navigation. Also, magnetic compasses can be affected by the steel in ship hulls, whereas gyrocompasses are immune to this effect.
Spinning in trampolining or ice-skating: to go faster, trampolinists and ice-skaters bring their arms and/or legs in.
A very brief explanation
Change of rotation speed: Explaining angular momentum can be very difficult as it's very unintuitive (the entire reason this experiment is fun, that and the spinning) but there are some simple approximations you can make by just assuming children are point masses in a vacuum, but don't tell them that.
If you ignore the mass of the children, but not of the bags of rice, then by conservation of angular momentum you would expect the rice bags to move with constant velocity (for a point mass m at distance from axis r and angular speed w, velocity v = rw and angular momentum L= mr2w is conserved, therefore v is conserved). You can show them, by spinning around on foot with the masses in your hands, one arm outstretched the other bent, that the mass on the outside is moving further in the same amount of time, thus must be going faster. Alternatively use the streamer sticks to show that air is passing the sticks faster when held out at arm's length compared to close in.
But we know that masses should not change speed (can explain via some rudimentary newtons first law, rather than angular momentum), therefore the only way to conserve linear speed is to change angular speed, and speed up or slow down the chair.
If they understand this you can then explain that human beings, much like rice bags, do also have some mass and therefore some effect, and for the really keen ones, there are nice discussions about the limits of the speeds if they were massless, if the masses were at an infinite distance, or at a distance approaching 0.
Gyroscopic effects: Pixies
(or see below)
Tips for Demonstrating:
There is some potential for slipping off the chair and landing badly. Get people to sit well back on the chair - that way they have good contact with the seat, and they can easily adjust their centre of gyration by leaning forwards. Small children need to be lifted onto the chair.
Some of the more spindly kids can build up an impressive amount of spin as they pull their arms and legs in, heavier kids will tend to slide off the chair, while with adults there is a risk of toppling the chair. Use only moderate speeds. Alternatively, always start the kids with their arms and legs / weights close in to them. You can then start them spinning and all that can happen when they move is their angular velocity decreases.
Some kids like to experiment with how dizzy they can make themselves - best to stop this before it gets out of hand with a lecture on how the semi-circular canals in the inner ear detect rotation, and why they are getting dizzy. Slosh the water in the plastic bottle to show how the fluid in the inner ear moves around.
The wheels are heavy, and when spinning move in unexpected ways. This has lead to a couple of minor abrasions where the rim has rubbed against the bare arms of the person holding it. Test the child's ability to hold the weight of the wheel before starting it spinning - remember that they will also need to hold it up for a while, and have some spare strength to resist its gyration.
The kids will almost always notice the spinny chair, or have seen people on it earlier, but it’s often best to talk about what you’re going to do first before anyone gets too dizzy.
Basic Procedure and Explanation:
"Who wants a go on my spinny chair?"
In Depth Explanation:
Talk about pushing something to make it move, and what determines how hard you need to push.
Give them the masses and set them spinning with a gentle push on the arm. Two masses, one in each hand, arms out sideways is most effective (add legs up forwards too, if the child is heavy)
For smaller children, you don’t often need the masses: they will be able to feel themselves speeding up and slowing down. However, the masses do make it more obvious for the people watching.
Get them to experiment with bringing the masses in to their bodies and away again (concentrating and distributing their mass). Miming the actions as you say them helps communication here.
Stop them spinning then ask first what happens when the masses are in different places, then ask why it happens.
Get them to observe the paths the masses are moving along (repeat experiment if necessary). The idea is: it is a
shorter distance around a small circle than a large one, while the masses want to keep the same speed, so get
around the smaller circle quicker.
Hold one weight close in to your body and one far away whilst you are sat on the chair. Ask which is going fastest. Kids are often quite bad at this so get them to work out which goes furthest, , then propose a race around a circle, where one person is close to the centre and the other is further away. Who has to go fastest if you get around in the same time? Now think about the weights, as they come in they are going 'too fast' for the distance out that they are so they get ahead of your spin. This drags you forwards until you're going a bit faster. As you allow them to go further out they're going too slowly for how far out they are, so they drag behind and slow you down.
Momentum can be difficult to explain, especially with younger children, although it can sometimes be done. Often talking about loaded shopping trolleys is a good way to start: once you get them moving, they will carry on going until they are stopped. Amount of spin, or spinniness helps in the explanation of the spinny chair, then angular momentum can be introduced as “what scientists call it”.
To give them a feeling for how moment of inertia varies with mass distribution you can get on the chair yourself
with the two large masses, and get them to spin you slowly, first with concentrated mass, then distributed.
What happens to all the extra effort they put in to spin you in distributed configuration when you make yourself
concentrated? (True - the extra angular momentum they supplied is conserved, and you did start with more energy,
but you do work too when you pull the masses in) (Warning: it can be hard to demonstrate when your head is
Using the wheel on the chair:
Spin the wheel slowly on one side, ask which way it is spinning, turn it over. Which way is it spinning now? We can change the way the wheel is spinning just by turning it over. It is often worth giving the wheel to a couple of the kids before putting anyone on the chair, even if it’s just so they can see how funny it feels- ask them how their feet feel. Make sure you have explained what you’re doing and be careful they don’t scrape the spinning wheel against themselves.
Get them on the chair, spin up the wheel and get them to hold it up-right, one hand on each side. Stand back and let them experiment with turning the wheel (slowly!) onto one side and then the other. Sometimes they don’t know which way to turn the wheel, so maybe show them what you mean before-hand. Observe directions of rotation, and if you think they will follow, talk through the conservation of angular momentum about the vertical axis (transfer to the earth!).
You can also do the same thing just by starting the wheel spinning and getting them to stop it, and then feeling the force acting on them.
Using the string
Suspend the wheel from the string, hold it with the axis level and ask what will happen if you leave go. They should say that it falls down, but they'll expect you to be asking because it doesn't, so you may surprise them when it does. Now get it spinning and do the same thing again, the wheel stays up (as long as it's spinning fast enough). Ask why and see where they get. With more confident kids, talking about what made it fall over before and what that force is doing now is often a good way to start: it keeps the idea of something pushing it around.
Remind them that earlier the wheel when turned could start them spinning, and ask what it can start spinning now. If there's nowhere to put your spin you can't lose it.
Additional Background (If you read the above then you're good to go on demonstration, read the below if you have more time. Don't expect to get anywhere near precession with normal kids though, and don't go further than you know confidently, kids can smell fear):
Angular momentum is an odd concept. The conservation of angular momentum can be derived from the symmetry of the
laws of physics with respect to rotations of the reference frame (c.f. classical mechanics). Or you can ignore
it and stick to point masses with negligible structure (or things that are built up by summing or integrating
over such masses). That way the symmetry will seep into your calculations through the geometry, and you will
still automatically conserve angular momentum.
It is only when you begin to leave out large chunks of a problem's geometry (treat an extended body as a 'thing'
rather than the sum of its parts) that you need to make angular momentum explicit in a calculation. Looking at
it more positively, angular momentum is the only aspect of the dynamics of the extended body that you need to
retain - so you can discard a lot of irrelevant detail at the start of a calculation rather than waiting for it
to cancel out at the end.)
It is the tendency of people's intuition to leave out geometry (to apply their experience of large non-rotating
objects to the wheel), but not replace it with a-m that makes this seem so weird.
My normal approach to the spinny chair is to begin by working in terms of point masses, showing how this gives
rise to angular momentum (although I shy away from the technical term, and just call it spin) - trying to get people
to add these ideas to their intuition. Then if they stick it out all the way through to the precessing gyroscope,
I try and pick that apart in terms of point masses and centripetal forces.
For the 'ice-skater' experiment, to bring the weights onto a smaller circle in the lab frame, you have to give them some radial velocity
in addition to the tangential velocity they already have. You don't get to take this velocity away again
when the weights reach the desired radius. To see this, consider applying the delta v as a single inward radial
impulse, then turn off the centripetal force until the desired radius is reached. The minimum impulse that
can be applied to achieve a given radius will make the mass's velocity tangent to a circle of that radius, so
that when the minimum radius is reached there is no radial velocity to reclaim.
In the original rotating frame, the particle begins by moving radially inward, but gets increasingly ahead of the
rotating frame (in the lab frame it is taking a short-cut across a chord of the circle), so its path curves in the
direction of rotation. This is the fictitious Coriolis force.
To move to a larger radius, first turn off the centripetal force, then apply the impulse once the new radius is
reached. This time the angle between the radial impulse and the particle's velocity is obtuse, so we can extract
energy from the particle. This is not straightforward to explain to children. You might be able to say something
about how, when the masses are spiralling inward, the inward pull is no longer purely sideways to their paths.
Also, they might accept the conservation of energy argument as they will have really been able to feel the work
they do to pull the masses in. This could be confusing though as in the person's instantaneous rest frame, radius
acts like height for potential energy.
The Angular Momentum Version:
A-M is not constant, but its magnitude remains the same because the plane of the couple is always at right-angles to the current plane of rotation (because the . Say the wheel is spinning in the x-z plane, while the couple is in the y-z plane - the wheel precesses so that it is spinning in the y-z plane (you can only spin around one axis at a time). But the couple is still 90 degrees ahead... (or use axial vectors if you prefer.)
My Gyroscope Explanation
Standing on the ground, let them hold the wheel with one hand on each handle.
(Be consistent in which way you spin the wheel for this part of the experiment - it is harder to get lost
in your explanation if you always do it the same way). Twist opposite handles of the wheel up and down,
feeling the pushes and pulls on the handles (in and out in alternate arms). Hold the handles level, and
rotate whole body from side to side (i.e. twisting the wheel sideways without bashing it against arms), again
feeling the forces (up and down in opposite hands).
Get their observations and help them summarise them while you thread the string through the end of one of
the handles. With the wheel not spinning, hold the string in one hand and keep the handles level with the other,
get them to predict, then release so that you are only holding the string. Describe this motion as a twist. Try for
predictions of what will happen when we try the same thing with a spinning wheel, then demonstrate it. Once released,
push the handle without string around in the direction of precession a little so that the wheel sits up and looks
The key to picking apart what is happening here is to realise that things can only spin round in one lot of circles
at a time, if you try make it something spin two ways at once its component particles are doing something much more
Talk about how things move in straight lines unless they are being pulled sideways. Go back to shopping trollies,
conkers on strings, (drop blue-tac onto the rim and show how it flies off?).
Discuss how when wheel is rotating only one way, forces are all towards the middle, and all balance out,
so are not felt in the handles. Twirling a conker, forces don't balance. With the handles level, and the wheel
spinning top towards you while precessing around anti-clockwise (when looked down on), think about the motion of
its consitiuent particles, and the forces required to generate that motion (and thus supplied by the hands). The
bit of the wheel that is at the top would just come towards you, but as you are forcing the wheel to precess round,
you are making it curve sideways to your right. Likewise the bottom of the wheel needs a sideways force in the other
direction to make it curve to your left. These forces are opposite, but don't line up, so they are a twist. You can
feel your hands supplying this push as you force the wheel to precess, or you can hold the handles only at one end
and balance out the twist this generates with the precession force.
(This seems to add up correctly to a linear dependance of the force on the angular velocity of the wheel: as it goes
faster, the curves become straighter, but the mass flows around them faster, /and/ at a greater rate.) If drawing a
diagram of this, follow the path of the top of the wheel for a few more revolutions - projected on the horizontal
plane this will be a complicated epicyclic curve (see glowstick photo) - it is all the sideways curving that is generating the odd forces.
The more I think about nutation, the less sure I am that I understand it. This link shows you how complicated you can make it. At some point I intend to try and translate some of that into english... (Anyone with brain-cells to burn is welcome to try and beat me to it.)