Physics quiz question: rotational inertiae of point-mass systems

Physics 205A Quiz 5, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 8.5

Two identical point masses are attached with a massless rod, but with different rotation axes. The masses rotating about a perpendicular axis located __________ the rod has the larger rotational inertia.
(A) at the middle of.
(B) one-third of the way along.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer: (B)

The rotational inertia of a single point mass is given by I = m·r2. The total rotational inertia of the system on the left is then given by:

I = m·(L/2)2 + m·(L/2)2 = (1/2)·m·L2.

The total rotational inertia of the system on the right is similarly given by:

I = m·(2·L/3)2 + m·(L/3)2 = (4/9)·m·L2 + (1/9)·m·L2 = (5/9)·m·L2.

Thus the system on the right will have a greater rotational inertia.

Sections 70854, 70855
Exam code: quiz05L4mN
(A) : 2 students
(B) : 40 students
(C) : 10 students
(D) : 0 students

Success level: 77%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.33

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