These wheels are available from lab suppliers or can be made in various ways. Sticking to thin segments of primary colours (red, green and blue) pretty much guarantees a near white colour when spun quickly though you could experiment with other colours and lighter or darker pigments.
Just like colour mixing lights which some lab suppliers now stock, using a disk of just red and blue, magenta can be made. Red and green disks will make yellow and green and blue disks will make cyan.
Some schools opt for attaching a wheel to an electric drill but a hand turned wheel or low voltage motor works just as well and is probably a lot safer. Simply attaching a wheel to a board with a nail through the centre will provide sufficient turning when spun by hand.
The theory behind the colour wheel shows that white light is made up of many colours, seeing a red object just means that it reflects only the red part of the spectrum the remaining colours are absorbed. By spinning the wheel, you are in essence combining these colours to recreate white light.