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... Students should be taught to use free object diagrams in both
equilibrium and non-equilibrium conditions. Far from being gratuitous,
the centripetal force (that is shown in the diagram ONLY when the object
is experiencing an acceleration perpendicular to its velocity) is
necessary to justify and explain the non-uniform motion. The student
should be taught that the force MUST be there because of the motion; the
task for the student, then, is to discover the source of this force.