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 certainly gross exaggeration, 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
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.