This demo has two parts: linear momentum and angular momentum
To begin, ask whether anyone knows what momentum is. Normally, younger kids have never heard this term, but older kids know about it. Ask: what is momentum related to? You don't want a detailed description, just that it is related to motion. If no one says anything, just explain: momentum is a quantity that is related to motion, and we are going to investigate how it works with an experiment. Then ask for two volunteers, and try to pick two people of more or less the same size. Instruct your volunteers to sit on the skateboards, facing each other, with their hands together, against each other's. Make sure they are near the edge of the boards, so they can reach each other easily. Ask the audience: what will happen if they push off each other? This is an easy question, even for young kids, but you should also ask: do you think they will both move the same distance, or will one of them move more?. There is usually some controversy here, but just accept all answers and try the experiment. Make sure you stand in between the two boards before asking your volunteers to push, so there is a reference point indicating how much they moved. When the experiment is done, confirm the predictions: they both moved approximately the same amount. This is something we expected. In physics, we say that this is because "momentum was conserved." Do you think there was any momentum before they pushed each other? If you get a yes, point out that you said momentum is related to movement, and no one was moving at the beginning. You can then ask if they think there was momentum after they pushed. Once you get a yes, you can explain: that's the tricky part! Physicists say there was no momentum at the end either, because the person moving to the right had positive momentum, but the one moving to the left had negative momentum. What happens when you add a positive number to a negative number?. Once again, some younger kids might nto have heard about negative numbers yet. If that's the case, just explain that you get zero. Then conclude: so at the end the total momentum was still zero, just like at the beginning. This is always true: momentum always stays the same.
The next experiment, still with the skateboards and your two volunteers, is to show that the fact they both moved is not related to the fact that they both pushed. Ask one of your volunteers to turn around, so that his back faces the other volunteer. Ask the audience again: what will happen now? Will they both move again, or will only one of them move? who?. Then ask the volunteers to push each other off again. Afterwards, you can explain: the law that says that momentum always stays the same doesn't care who is pushing. If one moves in one direction, the other one must move in the opposite direction. You can also ask if they've heard about Newton's laws. Younger kids won't have, but you can explain to the older ones that this also follows from Newton's third law (for every action there is an equal an opposite reaction)
For the next part of the experiment, you will need another volunteer. Make sure to pick someone small enough to fit behind one of your volunteers on the skateboard. This experiment is to explore the effects of mass on momentum. Once you have two people on one board and one on the other, ask the audience what they think will happen this time. Most people get it right, intuitively. Regardless of the answers, test it out by asking your volunteers to push off each other once again. Of course, the heavier board moves a lot less than the lighter one. You should now ask: I said momentum is always the same, but now they moved a lot less than s/he did. Why is that? After some answers from the audience, explain: momentum is not only related to speed, but to weight as well. We can have a lot of momentum by having a lot of speed, like s/he did, or by having a lot of mass, like they did. Either way, the amount of momentum that each skateboard had was the same and opposite, so they still add up to zero, like before.
The second part of this experiment is about angular momentum, and for this you will use the rotating platform. Keep in mind that angular momentum is a lot less intuitive than linear momentum, so don't expect as many right answers as before. That's OK. You should always emphasize that in science, when we don't know the answer to something, we do an experiment and see what happens.
To begin, ask for a volunteer, and ask them to stand on the rotating platform (make sure to keep ir from moving with your foot while they climb on it). Explain to the audience: so far we've only been talking about movement in a straight line, but we can also move in a circle. We want to figure out how weight matters in this case. Give your volunteer the water bottles. Explain that they should hold them out, with their arms stretched out, and that you will spin them. When you tell them to, they should bring their arms in very quickly (it's a good idea to ask them to practice before you do this, to make sure they understand what to do). Before you start spinning them, ask the audience what they think will happen when your volunteer brings their arms in. They've usually seen something like this before, so their answers will probably be right. Do the experiment and afterwards ask: why did s/he speed up when s/he brought the bottle closer to the center?. Listen to some answers (notice there is usually an answer that relates this to air resistance. Point out that resistance can slow thing down, but not speed them up) then explain: when the bottles are far from the center, they have to go around in big circles. This takes a lot of energy. When they are near the center, it takes less energy to make them go around in small circles, so the extra energy can be used to go faster. Depending on the level of your audience, you can also say: this is another example of how momentum always stays the same, but in a more complicated way. In the case of the skateboards we saw how adding more weight changed things around. In this case, weight also matters, but in a different way. Instead of adding weight, we put weight far from the center. This makes us heavy for rotations. We say it gives us a lot of moment of inertia. When the extra weight is near the center, it's as if we were light again, because we have a small moment of inertia. This explanation can be confusing for younger kids, so use it if appropriate.
For the next experiment, you need to pick a volunteer with arms long and strong enough to be able to hold the bicycle wheel. The wheel is heavy as it is, and it's hard to turn it once it's spinning, so it's a good idea to have your volunteer hold it up and make sure it's not too heavy for them before you start the experiment. Ask your volunteer to stand on the rotating platform (while holding it with your foot) and explain to them that you will give them the spinning wheel and they should tilt it to a side. You should show your volunteer what you want them to do, rather than just explain it with words, to make sure they understand what way to turn it. Then ask the audience what they think will happen. This one usually leaves them without too many ideas, so just try it out. Ask your volunteer to tilt it one way and then the other, to show how s/he spins in both directions. Afterwards, explain: we said that momentum always stays the same. So when I gave my volunteer a spinning wheel, which had some momentum of its own, s/he started spinning in the other direction, to keep the total momentum at zero, just like it was at the beginning. That's why when s/he switched the wheel around, the direction of the spinning switched, too.
For the last experiment, you don't need a volunteer, just the bicycle wheel. It has some duct tape attached to one of the handles. Point this out to the audience, and ask what happens to the wheel if you hold it by the tape (without spinning it yet). Then demonstrate: it simply falls over. Now spin it, and, once again, ask what they think will happen. Then let go of the wheel and hold it only by the tape. The wheel stays upright and begins a precession movement. You can say: the wheel doesn't fall over anymore! Do you know of anything in your life that uses this principle? The answer is, of course, a bicycle. It's much easier to stay on it when it's moving than when it's stationary, because the spinning of the wheels help us stay upright. Then explain: when we say that momentum always stays the same, we don't just mean how much momentum there is, but also in what direction. If something is spinning in one direction, it wants to stay in that direction. So if the wheel is spinning, so it has angular momentum, it wants to stay upright. With older kids (middle school or higher, usually) you might also want to explain the precession movement: there is still gravity pulling it down, so the wheel still wants to fall over. As a compromise between the two factors, it starts spinning instead