Draw a big circle on the paper. Then draw a spiral inside--it should go about one and a half times around the circle. Then cut the spiral shape.
Tie or staple the thread in the center of the spiral. For this experiment, it's important to use light-weight thread like you'd use for sewing, not kitchen twine or ribbon. This is because the thread allows the spiral to spin freely. If you're tying the thread, it works well to poke a tiny hole in the paper with a pencil or an earring, and then anchor it with a big knot. Tie the other end of the thread to the pencil, and pick up the spiral; it should uncoil like a paper snake.