A thin rod of length 2.0 m lies along the x-axis with its center at the origin.

Question

A thin rod of length 2.0 m lies along the x-axis with its center at the origin. The non-inform linear mass density of the rod is given by PL(x) = A + Bx^2, where A = 1.2 and B = 0.25(SI units). At either end of the rod is attached a small ball of mass m = 120 g, as shown in the figure below. What must be the SI units of the constants A and B? Without working out all of the mathematics, give an argument to prove that the center-of-mass of the rod + balls system is at the origin. What is the value of the moment of inertia of the rod + balls system about the y-axis? (What is the moment of inertia of a point mass m that is a distance r from the axis of rotation? Saying that the balls are "small" implies that we may treat them as point masses

Explanation / Answer

A thin rod of length 2.0 m lies along the x-axis with its center at the origin.

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