  It is pointed out that the current form of extrinsic equation of motion for a
particle constrained to remain on a hypersurface is in fact a half-finished
version for it is established without regard to the fact that the particle can
never depart from the geodesics on the surface. Once the fact be taken into
consideration, the equation takes that same form as that for centripetal force
law, provided that the symbols are re-interpreted so that the law is applicable
for higher dimensions. The controversial issue of constructing operator forms
of these equations is addressed, and our studies show the quantization of
constrained system based on the extrinsic equation of motion is favorable.
