Physics quiz question: ring vs. smaller disk of same mass

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA

A ring and a solid disk rotate about their centers. The ring and the solid disk each have the same mass of 1.2 kg. The ring has a radius of 0.25 m, and the solid disk has a smaller radius than the ring. (I_ring = M·R², I_disk = (1/2)·M·R².)

The rotational inertia of the ring is __________ the rotational inertia of the solid disk.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

The rotational inertia of the ring of mass M = 1.2 kg and radius R = 0.25 m is:

I_ring = M·R² = (1.2 kg)·(0.25 m)² = 0.075 kg·m².

The rotational inertia of the disk of mass M = 1.2 kg and a radius smaller than 0.25 m, along with the factor of (1/2) then must be smaller than the rotational inertia of the ring:

I_disk = (1/2)·M·R² = (1/2)·(1.2 kg)·(some value less than 0.25 m)²,

such that I_ring > I_disk.

Sections 70854, 70855
Exam code: quiz05nWaW
(A) : 6 students
(B) : 4 students
(C) : 39 students
(D) : 0 students

Success level: 80%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.34