Physics midterm question: radial acceleration

Physics 205A Midterm 1, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Question 5.2

Two children ride on a merry-go-round rotating at a constant rate. One is 1 m from the axis of rotation and the other is 2 m from it. The child __________ has a greater radial acceleration.
(A) 1 m from the axis of rotation.
(B) 2 m from the axis of rotation.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer: (B)

The magnitude of the radial acceleration of an object undergoing uniform circular motion is given by:

a_r = v²/r = rω²,

where the tangential speed v = rω. Since both children undergo the same angular speed ω, then the child farther from the rotation axis will have a greater radial acceleration.

Sections 70854, 70855
Exam code: midterm01w4Sh
(A) : 13 students
(B) : 27 students
(C) : 13 students
(D) : 0 students

Success level: 51%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.46