Rolling and pivoting

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Disessa discusses two identical coins with arrows as markers. Both arrows are pointed up on the coins. The two coins are touching each other and one is directly on top of the other one. If the bottom coin is held fixed while the other one is allowed to rotate around to the bottom of the one underneath without slipping, which direction will the arrow on the top coin face? Most respondents including myself would think the arrow would point to the bottom. This is incorrect, however. The arrow would point to the top. The reason for this is as follows: if a one to one correspondence argument is conducted joining points of the coins where they touch. The only way to satisfy this constraint is if the top of the top coin is touching the bottom of the coin underneath. Basically, the distance rolled is twice the amount of the circumference which has come in contact with the other coin. The turning of a coin is equal to the distance traveled by its center divided by its radius.