Physics midterm question: rim-axis ring

Physics 8A Midterm 3, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q9.3

[3.0 points.] A thin ring of mass M and radius R rotates about an axis perpendicular to the ring's plane, through its rim. Which one of the following choices best describes the moment of inertia about this rim axis?

(A) (1/2)*M*R^2.
(B) M*R^2.
(C) (3/2)*M*R^2.
(D) 2*M*R^2.

(Cf. Young and Freeman, University Physics, 11/e, Exercise 9.52.)

Correct answer: (D)
The parallel-axis theorem is used to relate the moment of inertia about a point on its rim (I_parallel) with the moment of inertia of the ring (I_ring) about its own center of mass:

I_parallel = I_ring + M*d^2,

where I_ring = M*R*^2, and d = R, thus I_parallel = 2*M*R^2.

Student responses:
(A) : 2 students
(B) : 8 students
(C) : 3 students
(D) : 20 students