A slender rod with length L has a mass per unit length that varies with distance from the left end, where x = 0, according to dm/dx = 'YX, where 'Y has units of kg/m2.
(a) Calculate the total mass of the rod in terms of Y and L.
(b) Use Eq. (9.20) to calculate the moment of inertia of the rod for an axis at the left end, perpendicular to the rod. Use the expression you derived in part
(a) to express I in terms of M and L How does your result compare to that for a uniform rod? Explain this comparison.
(c) Repeat part (b) for an axis at the right end of the rod. How do the results for parts (b) and (c) compare? Explain this result.