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Center of Mass and Moment of Inertia

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Ball a, of mass m_a, is connected to ball b, of mass m_b, by a massless rod of length L. The two vertical dashed lines in the figure, one through each ball, represent two different axes of rotation, axes a and b. These axes are parallel to each other and perpendicular to the rod. The moment of inertia of the two-mass system about axis a is I_a, and the moment of inertia of the system about axis b is I_b. It is observed that the ratio of I_a to I_b is equal to 3:

{I_a}/{I_b} = 3
Assume that both balls are pointlike; that is, neither has any moment of inertia about its own center of mass.

a). Find the ratio of the masses of the two balls.

b). Find d_a, the distance from ball A to the system's center of mass.
Express your answer in terms of L, the length of the rod.

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This solution provides a detailed step-by-step solution to this physics problem involving center of mass and moments of inertia. The principles given in this example can be applied to more difficult problems. Solution is given in a pdf file.

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