How do you split a list into teams with one wheel?
Spin once per player and give each name to the next team in turn: the first result joins team one, the second joins team two, the third goes back to team one. The rim empties as you go, so the wheel itself shows who is still unpicked, and the draw ends when there is nothing left to draw.
Three or four teams work the same way, you just count further before you come back to the top. If you would rather nobody watched the sides forming, spin the whole list first and read the session log afterwards: with two teams, positions one, three and five are one side and two, four and six are the other.
Why draw the teams instead of letting captains pick?
Because captains pick in public and in order, and the last name called learns something about themselves that has nothing to do with the game. Every PE teacher has a workaround for that moment and most of the workarounds are a draw of some kind. A wheel is the version that needs no cards, no hat and no preparation.
It also ends the argument about who arranged the sides. Nobody negotiates with a wheel that emptied itself in front of the room, and whoever organised the game stops being the person accused of stacking one team and becomes the person who pressed spin. That is worth more than the thirty seconds it costs.
How do you keep one team from getting all the strong players?
Draw in pots, the way a tournament does. Put the strongest handful on one wheel and everybody else on another, then alternate: one pick from the top wheel for each team, then work through the rest. It is two short draws instead of one, and the sides come out level.
The wheel knows nothing about ability, and weights cannot fake that knowledge either: a weight changes how often a name comes up, not which side it lands on. The judgement belongs in the pots, where it stays out in the open and somebody can disagree with it.
What else is this wheel good for?
It is the plain picker wheel with a list of names on it, so elimination, saving and sharing behave exactly as they do there. Once the sides exist and the question is who starts or which court they get, the number wheel answers it without another list to type.
Call one name and stop rather than emptying the rim, and the same list is a classroom pick. Keep spinning to the end without splitting the results, and the log is a running order.