I use cryogens in chemistry demos, and quick safe easy examples with zero clean-up are always welcome. I'd found about this one - the spinning ping-pong ball - through YouTube. The video has had over 2 million views, but I was underwhelmed - a slowly rotating and gently steaming ping-pong ball is hardly the kind of thing to impress an audience of schoolchildren. I finally tried it, reasoning that one pinhole ought to be better than two, and it vastly exceeded my expectations - it leapt off the table, hissing and steaming and spinning, and motored through 100 kids, clearing a path through them like the parting of the Red Sea. The video below is, sadly, not of that event, but a close-up repeat performance at home afterwards (note: the bare feet are NOT recommended! Wear appropriate clothing, including closed footwear).
Tell the audience only that you're immersing a ping-pong ball in liquid nitrogen. Ask them to predict what will happen (a good guess would be that it will collapse in on itself). The unexpected result will give them a good opportunity to apply some bits of knowledge they possess (depending on their age: that liquid nitrogen is very cold, and at its boiling point; that a gas has a much greater volume than a liquid; how a jet works/conservation of momentum; that water droplets are visible but water vapor is not) and to analyze the problem (they should be able to figure out that the ball has a hole in it, and that the hole has particular characteristics). You can guide them to the solution by being as vague or explicit as you need to be based on how much time you have, but I recommend allowing them to closely inspect the ball only once they have deduced the existence of the hole. Temporize by repeating the demonstration.
Disclaimer: I have no idea what rate the ball is spinning at, and 10,000 rpm is a guess, but we are definitely talking some serious rotational velocity. It speeds up as the liquid nitrogen inside is consumed.
Step 1: Equipment
ping-pong ball ~ pin ~ marker pen ~ tongs ~ liquid nitrogen
Liquid nitrogen is at its boiling point of -196ºC. It's dangerous, but only on prolonged contact with skin (causes frostbite) or if confined (it will explode its way out of the vessel). Handle it with respect and in the right containers (stainless steel dewars), and wear appropriate clothing. Getting splashed with liquid nitrogen is not a problem because you are protected by the Leidenfrost effect. Getting more than splashed can cause serious burns. Companies like Praxair and Airgas sell it (you'll need an appropriate vessel), and universities always have a lot on hand in science departments.
Step 2: Preparation and Execution
Poke a hole into the ball with the pin at as shallow an angle as possible, and add random markings with the pen (so the rotation is visible). Pick up the ping-pong ball with tongs, and immerse in the liquid nitrogen for about 10 seconds. Remove and release. Throwing it on the floor works well - it will hiss and spin and move horizontally in a random direction. In the video, I confined it using an extension cord so it stayed in close camera range, but it's better if you don't - much more fun to have it go whizzing off somewhere.
When the ball is immersed in liquid nitrogen, the air inside is chilled and the pressure drops (according to PV = nRT, and further yet because the oxygen will condense). The low internal pressure sucks liquid nitrogen in through the hole. On removing the ball, the nitrogen inside begins to boil as it heats up, and because gaseous N2 takes up about 700 times the space of liquid N2, the gas has to go somewhere, and it rushes out of the hole and turns the ball into a jet. Because the hole is at an angle, the resulting force causes the ball to rotate (spin) rather than translate (move). The steam is water condensing out of the air due to the cold gas, and so this experiment is more impressive in humid conditions.
Update 2016: The Backyard Scientist saw a gif of the video on Reddit and reproduced the experiment (he used liquid propane rather than liquid nitrogen) and estimated the rotation rate at 30,000 rpm.