Ball a, of mass m_a, is connected to ball b, of mass m_b, by a massless rod of l

Question

Ball a, of mass m_a, is connected to ball b, of mass m_b, by a massless rod of length L. (Figure 1) 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. Assume that both balls are pointlike; that is, neither has any moment of inertia about its own center of mass. Part A Find the ratio of the masses of the two balls. Express your answer numerically. Part 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.

Explanation / Answer

a)

ma/mb = Ib/Ia = 1/3 = 0.333

b)

ma da = mb db

==> db = (ma/mb) da = 1/3 da

db + da = L

==> 1/3 da + da = L

==> da = 3L/4 = 0.75 L

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