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If you spin it too fast, it becomes a centrifuge instead of a tumbler and no polishing action happens. Think of a front loading washer during it's spin cycle.
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Very good point. With a 12-inch diameter tumbler, a rotational speed of 240 rpm gives an apparent centrifugal acceleration of 9.81 meters per second squared (one "g"), which means that cases and media won't ever "fall" as the tumbler rotates - they'll just stick to the tumbler walls.