Masses rotating on a strap (important for University Physics, worth understanding but not essential for General College Physics)

For a magnet on a rotating strap, some points of the magnet are closer to the axis of rotation than others.  The closest point is moving more slowly than the furthest, and the point halfway between the two is moving at a speed which is the average of the speeds of these two points.

A gram of the magnet at the closest point therefore has less KE than a gram of the magnet at the furthest point (of course the amount of magnet at a point is zero, since a point has zero volume, but let's not split those hairs just yet).  If asked to compare these values with the KE of a gram at the midpoint, the first response would typically be that since the speed at the midpoint is halfway between the other two, the KE at the midpoint would also be halfway between the other two.

However it can't be so, since KE is proportional to v^2, not to v, and v^2 is not linear with respect to v.