6. Prove that the given force, F (r) (-ky, -k:r, -4bz3), is conservative and find the corresponding potential. 7. Write down the generalized coordinates for a dust particle at the outer edge of one of the shafts of a three-shaft system being lifted upward. 8. Find the equation of constraint for a sphere of radius a constrained to roll without slipping on the lower half of the inner surface of the hollow cylinder of inside radius R. Is that constraint holonomic? Justify your answer.