With the can suspended, move a magnet near the can and observe what happens. You should be able to make the can spin without touching it.
Now, hold the magnet near the can and observe how it stops the motion. This is one form of a magnetic brake. This is how some roller coasters are stopped. When they are wet, friction brakes tend to fail. When a train of people is moving at high speed, and things are a little wet, this is a serious safety issue. However, when the aluminum sheet on the bottom of a roller coaster moves at high speed between 2 magnets (or electromagnets), the car slows down. The faster the car is moving, the greater the stopping force.
This same type of magnetic brake is used on laboratory scales to stop oscillations.
You should also move the magnet toward the can. The quicker you move the magnet, the greater the effect (the greater the force). There is also an effect when you quickly move the magnet away from the can.
Cutting the can
It is possible to cut up an aluminum can with a pair of scissors. Careful, if you use your wife's scissors, you might not survive long enough to perform the experiments. Fortunately, I have my own scissors.
It is relatively dangerous to cut the can. I have been cut several times. It is difficult to start the first hole. Cutting is fairly easy (the metal is so thin) but the edges are extremely sharp. When removing the bottom, there are usually a number of extremely sharp points. As a result, I suggest wearing heavy leather work gloves.
Once the pieces are cut, be sure to smooth the edges and remove any sharp point that could draw blood. I normally use files and emery cloth for this.
Please be careful.
Pieces of the can
There are 3 basic tricks.
Sometimes I use a clear sheet of plastic, or a sheet of glass, so that everyone can see the magnet.
I had been cutting up cans to try and make tubes. (This never worked.) When playing with some curved metal, I decided to see what might happen if I used a flat piece. I was able to drag these around with a magnet .. and to pick them up. Then I tried coins .. which also worked. Well, when I showed this to my juggling club, they were impressed.
The next week, Dave brought in the bottom of a can and a sheet of glass. He showed me how to spin it by placing it upside down and moving the magnet under the glass. Then I tried to pick it up using just the magnet. (It worked.) Then I used the magnet to stop the spinning disk.
I went home and started playing with whole cans suspended from a string. I tried several ways to attach the string, but my technique was worthless and the can wobbled quite a bit. Eventually, (about a month later) I realized that if I simply adjusted the tab, I could get rid of the wobble.
I think that the whole can and a copper tube make "better" demos, but they don't fit in my pocket. Instead, I sometimes carry a magnet, the bottom of a can, flat pieces of aluminum can, and a few aluminum rings.