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I would assume a full rotation means to return to its starting point.
"Given an object moving in a counter-clockwise direction around a simple closed
curve, a vector tangent to the curve and associated with the object must make a
“full” rotation of 2π radians or 360◦
. In other words, if we were to think of this
tangent vector (of if you wish, a copy of it) as having its tail ﬁxed at the origin,
then as the object moves around the curve, the tangent vector will sweep through
all possible directions"
sounds good... until you consider this figure (also found in the book this came out of)
consider the path of the tangent vector around this curve, how can it possibly be said to make 360 degrees of rotation??