Physics quiz question: ring vs. larger disk with smaller mass

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: I_ring = M·R², I_disk = (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:

I_ring = M·R² = (2·m)·(r)² = 2·m·r².

The disk will have a rotational inertia of:

I_disk = (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