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It all boils down to custom in common speech (sorry, again). In writing
science there is no value to using two different words for the same
concept. Introduction of "centripetal" force has not in any way eased
the students' assimilation of the concept of radial force component,
and many students think that it is a kind of force which needs to be
considered explicitly when drawing a free body diagram. Thus they will
put in both a tension force and a centripetal force when describing a
conical pendulum. That would never happen if they routinely spoke of
the radial component of the tension force.