Physics quiz question: unwinding rolling yo-yo

Physics 8A Quiz 6, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q6.4

[3.0 points.] A yo-yo is initially at rest on a horizontal surface. A string is attached to the yo-yo and is pulled in the direction shown. There is sufficient friction for the yo-yo to roll without slipping.

Which one of the choices below best describes the direction of the static friction force of the floor on the yo-yo, and the resulting rolling direction of the yo-yo?

(A) The static friction force points to the left, and the yo-yo will begin to roll along the floor to the left.
(B) The static friction force points to the left, and the yo-yo will begin to roll along the floor to the right.
(C) The static friction force points to the right, and the yo-yo will begin to roll along the floor to the left.
(D) The static friction force points to the right, and the yo-yo will begin to roll along the floor to the right.

(Cf. Young and Freeman, University Physics, 11/e, Problem 10.70.)

Correct answer: (D)
The forces acting on the yo-yo are the tension force (up), normal force of the floor (down), weight (down), and the static friction force (direction unknown). In order for the yo-yo to unwind the string while rolling without slipping across the floor, it must accelerate clockwise, while translationally accelerating to the right. Thus the static friction force must point to the right, in order to translationally accelerate the yo-yo to the right. Alternatively, the yo-yo would like to slip its bottom surface to the left across the floor as it unwinds, but the static friction force will prevent that from occuring by opposing that sliding, and thus point to the right.

Student responses:
(A) : 3 students
(B) : 18 students
(C) : 1 student
(D) : 11 students