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AP Physics C: Mechanics
5.4 Rotational Inertia
AdvancedMCQMathematical14.8k
A horizontal rod lies on the x-axis. The left end is at x=0 (the origin) and the right end is at x=L. A small vertical axis of rotation is drawn through the origin. The rod is shaded with a gradient that is light at the origin and becomes increasingly dark towards the right end at x=L to represent the increasing mass density.
Non-uniform rod of length L and total mass M.
A thin, non-uniform rod of length \(L\) and total mass \(M\) is placed along the \(x\)-axis with one end at the origin. The linear mass density of the rod varies with position according to the function \(\lambda(x) = cx^2\), where \(c\) is a constant. Which of the following expressions represents the rotational inertia of the rod about an axis through the origin and perpendicular to the rod, in terms of \(M\) and \(L\)?

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