Solution: A non-uniform rod rotates about an axis through one end of the rod, perpendicular to its length. If the mass distribution of the rod is λm = βx3, what is the moment of inertia of the rod about the axis? What would the moment of inertia of the rod be about an aixs at the center of the rod, perpendicular to its length?

A non-uniform rod rotates about an axis through one end of the rod, perpendicular to its length. If the mass distribution of the rod is λ_{m} = βx^{3}, what is the moment of inertia of the rod about the axis? What would the moment of inertia of the rod be about an aixs at the center of the rod, perpendicular to its length?