The force fields of uniform gravity and of gravity inside a spherical body of uniform density were previously known to possess the property that the brachistochrone and the tautochrone are identical (cycloid and hypocycloid, respectively,). It is shown that centrifugal force in a rotating reference frame possesses the same property. In a plane normal to the axis of rotation the brachistochrone tautochrone is the epicycloid. The evolutes of hypocycloid and epicycloid are found. The figures of cycloid, hypocycloid, and epicycloid each with its evolute are shown to produce tesselations of the plane. In a plane including the axis of rotation the rotating reference frame has other brachistochrones and tautochrones which are not identical.
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© 1979 American Association of Physics Teachers.
1979
American Association of Physics Teachers
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