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University Physics with Modern Physics
A cylinder with radius $R$ and mass $M$ has density that increases linearly with distance $r$ from the cylinder axis, $\rho=\alpha r$ where $\alpha$ is a positive constant. (a) Calculate the moment of inertia
of the cylinder about a longitudinal axis through its center in terms of $M$ and $R .$ (b) Is your answer
greater or smaller than the moment of inertia of a cylinder of the same mass and radius but of uniform density? Explain why this result makes qualitative sense.