Tim, ripping a round piece of wood on either a table saw or a band saw without the use of an appropriate sled is very dangerous. In the case of the table saw, the chance of a kickback is highly likely. I would imagine that is what happened to you. Kickback occurs when the teeth at the back of the blade catch the wood as they come up through the table. As they do this they throw the workpiece back at you, normally dragging your fingers across the blade.
With the limited depth of a table saw using a sled to cut a round blank is fairly impractical. You are better off to use a sled on a band saw to do this.
Another thing which could have caused the kickback is an uneven surface against the fence. It sounds like you were cutting a small rough log on the saw. If so, the surface running against the fence was not perfectly straight and so as you fed the piece through the uneven surface could have pushed the back of the piece into the blade causing a kickback. Generally when cutting on the table saw you need two flat surfaces, one riding on the table and the other riding against the fence.