Final answer:
The length of the nonuniform rod must be measured or given. The mass distribution can be described by a function, such as p(x) = Po + (P1 - Po)(x/L)^2, if the density varies quadratically. The moment of inertia and center of mass require integration of functions that depend on the mass distribution along the rod.
Step-by-step explanation:
To address the student's question within the context provided, each part of the question will be considered with its corresponding physical concept in relation to a nonuniform rod.
The student must measure or be given the distance between the two ends of the rod positioned along the x-axis, as this is not something that can be determined without physical specifics or further mathematical context.
The mass distribution along the rod can be derived if the density function is known. For instance, if the density varies quadratically as per the reference information given, the mass distribution could be described by p(x) = Po + (P1 - Po)(x/L)^2 where ‘p’ is the mass per unit length at a point ‘x’ along the rod.
The moment of inertia about the y-axis (which is equivalent to the z-axis in the provided reference when the y-axis is taken as the rotation axis and is perpendicular to the length of the rod) can be calculated by integrating the mass distribution function times the square of the distance from the axis. This calculation would be specific to the mass distribution function and the geometry.
To find the center of mass of the rod, one must integrate the product of the mass distribution function and the distance x, and then divide by the total mass of the rod. This also requires information on the mass distribution function p(x).