Physics quiz question: ice skater angular momentum conservation

Physics 5A Quiz 5, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 8.78

[3.0 points.] A figure skater is spinning at a rate of 2.00 rev/s with his arms pulled into his chest. He then extends his arms outwards, increasing his rotational inertia to 150% of its original value. What is the magnitude of his new rate of rotation?
(A) 0.67 rev/s.
(B) 0.89 rev/s.
(C) 1.3 rev/s.
(D) 1.5 rev/s.

Correct answer: (C)

Assume that there are no external torques, or that this process takes a sufficiently short time such that angular momentum is conserved. Then:

L_i = L_f,

I_i*w_i = I_f*w_f,

where 1.5*I_i = I_f. Thus w_f = (I_i/I_f)*w_i = (1/1.5)*w_i.

Student responses
Sections 0906, 0907
(A) : 3 students
(B) : 6 students
(C) : 23 students
(D) : 7 students