Hole Puncher of Horrors

Bengt is building a machine. It is a most unusual kind of hole puncher. It consists of a holder for the papers, and a rather nasty-looking wheel with n sharp spikes pointing outwards at regular intervals. As the machine operates, the holder is pressed against the spike wheel, so that one spike makes a big hole in the paper. (One big hole is more effective than several small, says Bengt.) Occasionally, a spike will break. This is where it gets really clever, or so Bengt thinks. The broken spike falls off completely, making that side of the wheel lighter. If the centre of mass of the wheel is not in the axis, the wheel will spin to orient itself with the centre of mass downwards. That way, Bengt figures, the broken spike will automatically be replaced - at least for a while, until enough of them have been broken.Ideally, we would like to design the device so that this can happen as many times as possible before there is no longer a spike pointing at the paper.

At which angle on the wheel, relative to the downward angle, should the holder be located? Are some choices of n better than others? Obviously more would be better, but aside from that?