This is the solution, then, or the key to it. Although you are careful not to let the half-dollar slip on the tabletop, the “point” tracing the line segment at the foot of the dime is both rotating and slipping all the time. It is slipping with respect to the tabletop. Since the dime does not touch the table top, you do not notice the slipping. If you can roll the half-dollar along the table and at the same time roll the dime (or better yet the axle) along a block of wood, you can actually observe the slipping. If you have ever parked too close to the curb, you have noticed the screech made by your hubcap as it slips (and rolls) on the curb while your tire merely rolls on the pavement. The smaller the small circle relative to the large circle, the more the small one slips. Of course the center of the two circles does not rotate at all, so it slides the whole way.