Spindle - what is it in Britain?

I've been following a stay-at-home father's blog, Diplo_Dad, who is living in the United Kingdom. He posted an interesting thing about something his 5-year-old son repeated from what the teacher said. Now when I saw the word, my mind went directly to this image (which by the definitions he found in a wikipedia article, this is what he is associating the word with):

So if a teacher says, “Don’t stick your fingers in the spindle, or they will be cut off,” one would not expect the image of this to be what a spindle is.

So I ask you all - what would you think a spindle is in British terms? What is the American version of said spindle? Something that could cut your fingers off if you so happened to get them caught in in it? If anyone finds out what the equivalent of a spindle is, please let me know, or pop over to Diplo_Dad's blog and let him know - E :)