In distinguishing between `category of quantities' and `dimension' the author intends to reach a new understanding of the quantity plane angle. One basis is tensor algebra. Accordingly, the common angle φ (or θ) can be separated into the quantity `arc-radius ratio x' on the one hand and the quantity `angle γ' on the other, each belonging to different categories of quantities.Another basis is the mathematical concept of `embedding'. It allows the mapping of specific `categories of quantities' into a selected `dimension'. Therefore, the category of angles can be embedded either into the `dimension(-less) ratio' or into a specific `dimension angle'.The examples in this paper show that there is no need for a change in teaching mathematics if the angle is explicitly used in defining rotary-motion quantities.The author emphasizes transparency and perspicuity. He argues for an explicit use of the angle γ in rotational mechanics. Furthermore, he suggests that there should be an internationally applicable unit name (e.g. Ri, Re or Ro) for the reference magnitude `full angle Γ'.
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