Physics quiz question: comparing rotational inertiae of ring and disk

Physics 205A Quiz 5, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 8.2

A ring and a solid disk rotate about their centers. The disk has twice the radius, but half the mass of the ring. The __________ has the larger rotational inertia.
(A) ring.
(B) disk.
(C) (There is a tie.)
(D) (Not enough information is given.)

(Given: Iring = M·R2, Idisk = (1/2)·M·R2.)

Correct answer (highlight to unhide): (C)

Let the radius of the ring and the radius of the disk be r and 2·r respectively; and the masses of the ring and disk be 2·m and m respectively.

The ring will have a rotational inertia of:

Iring = M·R2 = (2·m)·(r)2 = 2·m·r2.

The disk will have a rotational inertia of:

Idisk = (1/2)·M·R2 = (1/2)·(m)·(2·r)2 = 2·m·r2.

Thus this ring and disk will have the same rotational inertia.

Sections 70854, 70855
Exam code: quiz05t0rQ
(A) : 8 students
(B) : 13 students
(C) : 29 students
(D) : 1 student

Success level: 57%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.53

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